# Faculty Activities[ Edit ]

*Announcement:*

A research workshop on C^0 aspects of symplectic geometry and Hamiltonian dynamics, Technion (Amado 232), May 12-16, 2019. For the program of the workshop and other information see the workshop webpage: http://www.math.tau.ac.il/~levbuh/Conference/C0SGHD/C0SGHD.html

*Announcement:*

ALL TALKS WILL BE HELD AT AMADO 232

**Speakers and schedule:**

09:30 -10:00 Coffee and refreshments at the 8th floor lounge

10:00-11:00 Ron Peled (Tel Aviv University)

11:00-11:30 Coffee break

11:30-12:30 Nir Lev (Bar Ilan University)

12:30-14:00 Lunch break

14:00-15:00 Amitay Kamber (Hebrew University)

15:00-15:30 Coffee/Tea

15:30-16:30 Anatoly Vershik (Steklov Institute, St. Petersburg).

**TITLES AND ABSTRACTS:**

**1. Ron Peled:**

**Title**: Rigidity of proper colorings of Z^d (and other graph homomorphisms)

**Abstract**: A proper q-coloring of Z^d is an assignment of one of q values to each vertex of Z^d such that adjacent vertices are assigned different values. Such colorings arise naturally in combinatorics, ergodic theory (as a subshift of finite type) and statistical physics (as the ground states of the antiferromagnetic q-state Potts model). How does a "uniformly picked" proper q-coloring of Z^d look like? To make sense of this question, one may sample uniformly a proper q-coloring of a large finite domain in Z^d and seek possible patterns in the resulting coloring. Alternatively one may seek to classify the translation-invariant probability measures on proper q-colorings having maximal entropy. Work of Dobrushin (1968) implies that when q is large compared with d, q-colorings support a unique measure of maximal entropy. We focus on the opposite regime, when d is large compared with q, and prove that long-range order emerges in typical colorings, leading to multiplicity of measures of maximal entropy. Concretely, the extremal measures of maximal entropy are in correspondence with partitions (A,B) of the q colors into two equal-sized sets (near-equal if q is odd), and in the measure corresponding to (A,B) most of the vertices of the even (odd) sublattice of Z^d are assigned values from A (from B). The results address questions going back to Berker-Kadanoff (1980), Kotecký (1985) and Salas-Sokal (1997). The methods extend to the study of other graph homomorphism models on Z^d satisfying a certain symmetry condition and to their "low temperature" versions. Joint work with Yinon Spinka.

**2. Nir Lev:**

**Title**: On tiling the real line by translates of a function

**Abstract**: If f is a function on the real line, then a system of translates of f is said to be a << tiling >> if it constitutes a partition of unity. Which functions can tile the line by translations, and what can be said about the structure of the tiling? I will give some background on the problem and present our results obtained in joint work with Mihail Kolountzakis.

**3. Amitay Kamber:**

**Title**: Optimal Lifting in SL3

**Abstract**: Sarnak proved in one of his letters that as q goes to infinity, for every $\epsilon>0$ almost every matrix in $SL_2(F_q)$ can be lifted to a matrix in $SL_2(Z)$, where every coordinate is bounded by q^(3/2+\epsilon). The exponent 3/2 is optimal, since the number of matrices in $SL_2(Z)$ with coordinates bounded by $T$ is asymptotic to $T^2$. We prove a similar theorem, with optimal exponent, in the context of the action of $SL_3(Z)$ on the projective 2-dimensional space over $F_q$. Our work is based on lattice point counting arguments as in the work of Sarnak and Xue, and on property T for SL3. We will also explain the relation of this theorem to the work of Ghosh, Gorodnik and Nevo, and to some general conjectures of Sarnak whose aim is to "approximate" the Generalized Ramanujan Conjecture to deduce Diophantine results. Based on joint works with Konstantin Golubev and Hagai Lavner.

**4. Anatoly Vershik:**

**Title** : Graded graphs and central measures

**Abstract** : Graded graphs (Bratteli diagrams) as dynamical language : Markov compact of paths, central measures, connections to asymptotic representation theory of locally finite groups, characters as central measures, limit-shape type theorems and generalized law of large numbers.

*Announcement:*

International Workshop

** How modern is modern math? **

The area near M. Zhitomirskii's office Amado 306

**10:00 - 10:30 B. Doubrov (Minsk):**

*Invariants and Symmetries: Lie, Cartan, Tanaka *

**11:00 - 11:30 M. Zhitomirskii (Technion):**

*Invariants and symmetries: Lie, Cartan, Poincare *

**12:00 - 12:30 G. Bor (Guanajuato):**

* Kepler orbits: new symmetries? *

**13:00 - 13:30 M. Lyubich (Stony Brook):**

* Why z ^{2} + C requires several books?*

For more information, please contact M. Zhitomirskii:

Phone: 04-8294026 or email: mzhi@technion.ac.il

*Abstract:*

**Abstract** : We will discuss important examples of brackets and superalgebras that they lead to.

*Abstract:*

Link to the registration form and further information about the program and the event : https://applied-math.net.technion.ac.il

*Abstract:*

**Advisor: ** Prof. Barak Fishbain

**Abstract: **Air pollution is one of the most prominent environmental health risks and pathogen generator. Many air pollution studies are based on data collected from air quality monitoring stations (AQMS). AQMS are the “gold standard” for the air pollution data measurements. Yet, due to their high costs they are scattered sparingly. As the number of measuring sites is limited, the AQMS data is generalized through mathematical methods. Here we introduce two methods to improve the spatiotemporal coverage.

The first method deals with the spatial coverage expansion. The method consists of two stages. At the first stage, the method finds sources’ locations and emission rates in the model’s parameters space ("source term"). At the second stage, the method uses the source term as an input and generates dense pollution maps using the dispersion model. The suggested algorithm is model invariant to the gas dispersion model, hence it is applicable for a wide range of applications in which different gas dispersion model are used. Simulation for an industrial-area shows that the suggested scheme generates more accurate maps than the state-of-the-art technique. The resulted air pollution dens map may serve as a valuable tool for mitigation acts and regulatory agencies.

Extending the temporal coverage of the measuring array is achieved through long‐term forecasting.While short-termforecasting, a few days into the future, is a well-established research domain, there is no method for long-term forecasting (e.g., the pollution level distribution in the upcoming months or years). Here we introduce and define *long-term* air pollution forecasting, where *long-term* refers to estimating pollution levels in the next few months or years. A Discrete-Time-Markov-based model for forecasting ambient nitrogen oxides patterns is presented. The modelaccurately forecasts overall pollution level distributions, and the expectancy for tomorrow’s pollution level given today’s level, based on longitudinal historical data. It thus characterizes the temporal behavior of pollution. The model was applied to five distinctive regions in Israel and Australia and was compared against several forecasting methods and was shown to provide better results with a relatively lower total error rate.

*Abstract:*

**Abstract: **The notion of roots is absolutely central to Lie theory and, in its classical version, very much tied to groups generated by reflections. My goal in this talk it to explore how this notion may be broadened to incorporate what is currently happening on the frontiers of Lie theory. One interesting new phenomenon, which I am hoping to discuss, is the possibility that roots and dual roots live in lattices of different rank. This makes the Langlands-like duality that exchanges them a particularly dramatic operation.

*Light refreshments on the 8^{th} floor (faculty lounge) at 16:30*

*Abstract:*

**מנחה: **אלי אלחדף

**תקציר: **נאפיין אלגבראות חילוק מדורגות מעל הממשיים המדורגות על ידי חבורה סופית. נראה את הקשר בין אלגבראות חילוק מדורגות לבין חבורות קוהומולוגיה. נמיין עד כדי איזומורפיזם את כל אלגבראות החילוק המדורגות על ידי חבורה אבלית סופית ונספור אותן.

*Abstract:*

**Advisor:** Naama Brenner

**Abstract: **Cellular networks exhibit pre-designed responses to many challenges, but also endow the cell with the ability to adapt and display novel phenotypes in the face of unforeseen challenges. In this seminar we will present a computational framework which attempts to describe such plasticity in random networks. We show that the convergence of this exploration in the high-dimensional space of network connections depends crucially on network topology. For large networks, convergence is most efficient for networks with scale-free out going degree distributions which are typical of cellular networks.

In order to investigate the dynamics and convergence properties of such networks we develop an approximation for scale-free networks, the *STAR network,* which is based on the crucial role hubs play in network dynamics.

We show that *STAR networks* retain many of the properties of scale-free networks and enable analytical understanding of the convergence properties exhibited in our model.

*Abstract:*

**Advisor: **Chen Meiri

**Abstract: **The structure of a random permutation has been extensively studied, and Dixon has shown in 1969 that two such independent permutations almost surely generate Sn or An. But what if the permutations are not entirely random, or ARE dependent? for example, does x and yxy generate An for random x and y? We show that the group generated from such permutations is (almost surely) transitive, and in special cases, that it's Sn or An.

*Abstract:*

**Advisor**: Prof. Gershon Wolansky

**Abstract**: In the last years, efficient computation of the optimal transport distance, also known as the earth mover's distance (EMD), has become an area of active study. In this talk I shall focus on semi-discrete approaches. We propose to discretize the cost function itself, rather than one of the measures. The resulting problem has a dual formulation which converts the optimization to a convex optimization on a smaller dimension space. This approach accelerates the computation and can also be used for related problems such as unbalanced transport, vector valued optimal transport and barycenters. We also consider the entropic regularized version of the optimal transport distance, also known as the Sinkhorn distance. We propose to accelerate the calculation of this distance using a low-rank decomposition, based on the semi-discrete cost approximation. This part was done in collaboration with R. Kimmel.

*Abstract:*

**Advisors**: Leshansky Alexander, Morozov Konstantin

**Abstract**: Controlled steering of chiral magnetic micro-/nano propellers by rotating

magnetic field is a promising technology for targeted delivery in various biomedical applications. In most of these applications magnetized chiral (helical) propellers are actuated by rotating magnetic field as they propel unidirectionally through a fluidic environment similar to a rotating corkscrew. It was shown recently that achiral magnetized objects, such as planar V-shaped motors, can propel as well. However, unidirectionality of the propulsion is not guaranteed due to the high symmetry of the problem. We study dynamics of planar V-shaped propellers actuated by a precessing magnetic fi eld provided by superimposing the dc magnetic fi eld onto the uniform rotating fi eld along the the field rotation axis. We demonstrate that the dc fi eld reduces the above symmetry and can, in fact, lead to unidirectional propulsion of planar and in-plane magnetized objects, that otherwise exhibit no net propulsion in a plane rotating field.

*Abstract:*

**Advisors: **Dan Garber and Sabach Shoham** **

**Abstract**: Composite convex optimization problems that include a low-rank promoting term have important applications in data and imaging sciences. However, such problems are highly challenging to solve in large-scale: the low-rank promoting term prohibits efficient implementations of proximal based methods and even simple subgradient methods are very limited. On the other hand, methods which are tailored for low-rank optimization, such as conditional gradient-type methods, are usually slow. Motivated by these drawbacks, we present new algorithms and complexity results for some optimization problems in this class. At the heart of our results is the idea of using a low-rank SVD computations in every iteration. This talk is based on joint works with Dan Garber and Shoham Sabach.

*Abstract:*

**Advisor: **Emanuel Milman

**Abstract: **We establish new sharp inequalities of Poincare or log-Sobolev type, on weighted Riemannian manifolds whose (generalized) Ricci curvature is bounded from below. To this end we establish a general method which complements the 'localization' theorem which has recently been established by B. Klartag. Klartag's theorem is based on optimal transport techniques, leading to a disintegration of the manifold measure into marginal measures supported on geodesics of the manifold. This leads to a reduction of the problem of proving a n-dimensional inequality into an optimization problem over a class of measures with 1-dimensional supports. Our method is based on functional analytic techniques, and leads to a further reduction of the optimization problem into a simpler problem over a sub-class of model-space measures. By employing ad-hoc analytical techniques we solve the optimization problems associated with the Poincare and the log-Sobolev inequalities. Quiet unexpectedly the solution to the problem of characterizing the sharp Poincare constant reveals anomalous behavior within a certain domain of the generalized-dimension parameter, hinting on a new phenomena.

*Abstract:*

It is in general a very difficult (algebraic) problem to ascertain whether a group $H$ is a subgroup of a group $G$. The geometric version of this question (for finitely generated groups) is to ask whether there exists a coarse embedding of a Cayley graph of $H$ into a Cayley graph of $G$. We can control the growth and asymptotic dimension of $H$ in terms of $G$, but these are not sufficient to dismiss a (relatively naive) statement like For every $k$ there exists some $l$ such that any hyperbolic group of asymptotic dimension $k$ coarsely embeds into real hyperbolic space of dimension $l$. In this talk I will introduce a new class of geometric invariants and use them to disprove the statement above, and also prove that the only Baumslag-Solitar group which can be coarsely embedded into a hyperbolic group is $\mathbb Z^2=BS(1,1)$.

*Abstract:*

**Advisor: **Prof**. **Amos Nevo

**Abstract: **Counting lattice points has a long history in number theory, that can be traced back to Gauss. I will introduce this subject, and its relation to questions regarding asymptotic properties of integral points in the plane. The main focus will be an arithmetic result regarding equidistribution of parameters that characterize primitive integral points. I will also present a similar result for rings of integers in C (e.g., Gaussian integers).

Both these results are achieved via counting lattice points w.r.t. the Iwasawa decomposition in certain simple rank-one Lie groups, a topic which I will discuss more generally, if time permits.

*Abstract:*

**Advisor:** Savir Yonatan

**Abstract: ** One of the main determinants of the the fitness of biological systems is their ability to accurately sense their environment and respond accordingly. In particular, cells have to sense the nutrients in their environment and coordinate their metabolic gene program appropriately. One of the well-studied examples of such regulation is catabolite repression - a phenomenon where a preferred carbon source represses the transcription of genes which encode enzymes required for the utilization of alternative carbon sources. The decision of when to switch from a preferred to a less-preferred carbon source is akin to a general optimal switching problem which has long been of interest in management science and operations research. Using dynamical models we determine the optimal switching strategy - the optimal time in which cells will induce genes required for metabolizing the less-preferred carbon source. We derive the conditions in which the optimal switching strategy includes preparation for impending depletion of the preferred nutrient by inducing early, and the conditions for when the switching mechanism depends on either threshold-sensing or ratio-sensing of the external nutrient concentrations. We formalize the problem in terms of evolutionary game theory and show that an optimal switching strategy which involves preparation is not always evolutionarily stable and determine the particular environment in which preparing is evolutionarily stable.

*Abstract:*

**Advisor: **Uri Shapira

**Abstract: **

The highlight of my presentation is the wedding of p-arithmetic extension and the thickening trick. The result is a beautiful offspring: an equidistribution result regarding periodic geodesics along certain paths in the p-Hecke graph. This result calls on an ingenious use of the decay of matrix coefficients in tandem with the astonishing notion of tubes around compact orbits, which is the diva of this talk so we handle it with care.

*Abstract:*

**Advisor: **Orr Shalit

**Abstract: **In this talk I will give a brief survey on my Ph.D. thesis which mainly focus on certain types of operator-algebras. The talk, correspondingly to my thesis, is divided into two parts.

The first part is about subalgebras (and also other subsets) of graph C*-algebras. I will present some results from a joint work with Adam Dor-On, in which we studied maximal representations of graph tensor algebra. I will first provide a complete description of these maximal representations and then show some dilation theoretical applications, as well as a characterization of a certain rigidity phenomenon, called hyperrigidity, that may or may not occur for a subset of a C*-algebra. I will then present an independent follow-up work in which I studied, in addition to hyperrigidity, other types of rigidity of other types of subsets of graph C*-algebras and obtained some more delicate results.

The second part is devoted to operator-algebras arising from noncommutative (nc) varieties and is based on a joint work with Orr Shalit and Eli Shamovich. The algebra of bounded nc functions over a nc subvariety of the nc ball can be identified as the multiplier algebra of a certain reproducing kernel Hilbert space consisting of nc functions on the subvariety. I will try to answer the following question: in terms of the underlying varieties, when are two such algebras isomorphic? Along the way, if time allows, I will show that while in some aspects the nc and the classical commutative settings share a similar behavior, the first enjoys – and also suffers from – some unique noncommutative phenomena.

*Abstract:*

* Abstract: *Given n uniform points on the surface of a two-dimensional sphere, how can we partition the sphere fairly among them?

It turns out that if the given points apply a two-dimensional gravity force to the rest of the sphere, then the basins of attraction for the resulting flow yield such a partition—with exactly equal areas, no matter how the points are distributed. (See http://www.ams.org/publications/journals/notices/201705/rnoti-cvr1.pdf) Our main result is that this partition minimizes, up to a bounded factor, the average distance between points in the same cell. This has an application to almost optimal matching of n uniform blue points to n uniform red points on the sphere. I will also describe open problems regarding greedy and electrostatic matching (Joint work with Nina Holden and Alex Zhai) Another topic where local and global optimization sharply differ appears starts from the classical overhang problem: Given n blocks supported on a table, how far can they be arranged to extend beyond the edge of the table without falling off? With Paterson, Thorup, Winkler and Zwick we showed ten years ago that an overhang of order cube root of n is the best possible; a crucial element in the proof involves an optimal control problem for diffusion on a line segment and I will describe generalizations of this problem to higher dimensions (with Florescu and Racz).

*Abstract:*

**Advisor**: Reichart Roi

**Abstract**: Natural Language Processing (NLP) problems are usually structured, as a natural language is. Most models for such problems are designed to predict the "highest quality" structure of the input example (sentence, document etc.), but in many cases a diverse list of structures is of fundamental importance. We propose a new method for learning high quality and diverse lists using structured prediction models. Our method is based on perturbations: learning a noise function that is particularly suitable for generating such lists. We further develop a novel method (max over marginals) that can distill a new high quality tree from the perturbation-based list. In experiments with cross-lingual dependency parsing across 16 languages, we show that our method can lead to substantial gains in parsing accuracy over existing methods

*Abstract:*

**Advisor: **Roy Meshulam

**Abstract**: Attached

*Abstract:*

ALL TALKS WILL BE HELD AT AMADO 232

Speakers and schedule :

09:30-10:00 Coffee and refreshments at the 8-th floor lounge

10:00-10:50 : Tali Pinsky (Technion Mathematics Department)

10:50-11:10 : Coffee break

11:10:-12:00 : Anish Ghosh (Tata Institute of Fundamental Research)

12:00-14:00 : Lunch

14:00-14:50 : Konstantin Golubev (Bar Ilan and Weizmann Institute)

14:50-15:10 : Coffee break

15:10-16:00 : Sanghoon Kwon (Korea Institute for Advanced Study)

TITLES AND ABSTRACTS

1) Tali Pinsky :

Title: An upper bound for volumes of geodesics

Abstract: Consider a closed geodesic gamma on a hyperbolic surface S, embedded in the unit tangent bundle of S. If gamma is filling its complement is a hyperbolic three manifold, and thus has a well defined volume. I will discuss how to use Ghys' template for the geodesic flow on the modular surface to obtain an upper bound for this volume in terms of the length of gamma. This is joint work with Maxime Bergeron and Lior Silberman.

2) Anish Ghosh :

Title: The metric theory of dense lattice orbits

Abstract: The classical theory of metric Diophantine approximation is very well developed and has, in recent years, seen significant advances, partly due to connections with homogeneous dynamics. Several problems in this subject can be viewed as particular examples of a very general setup, that of lattice actions on homogeneous varieties of semisimple groups. The latter setup presents significant challenges, including but not limited to, the non-abelian nature of the objects under study. In joint work with Alexander Gorodnik and Amos Nevo, we develop the first systematic metric theory for dense lattice orbits, including analogues of Khintchine's theorems.

3) Konstantin Golubev :

Title: Density theorems and almost diameter of quotient spaces

Abstract: We examine the typical distance between points in various quotient spaces. This question has an interesting approach inspired by the work of Lubetzky and Peres. They showed that the random walk on a graph expresses under the assumption of the graph being Ramanujan. We show that this condition can be relaxed to some density condition on the eigenvalues, and apply it to various settings. Joint work with Amitay Kamber.

4) Sanghoon Kwon :

Title: A combinatorial approach to the Littlewood conjecture in positive characteristic

Abstract: The Littlewood conjecture is an open problem in simultaneous Diophantine approximation of two real numbers. Similar problem in a field K of formal series over finite fields is also still open. This positive characteristic version of problem is equivalent to whether there is a certain bounded orbit of diagonal semigroup action on Bruhat-Tits building of PGL(3,K). We describe geometric properties of buildings associated to PGL(3,K), explore the combinatorics of the diagonal action on it and discuss how it helps to investigate the conjecture.

*Abstract:*

**Advisor**: Shai Haran

**Abstract**: We discuss the notion of a non-reduced arithmetic plane of the integers Z tensored with itself over F_1, the field with one element. It is a coproduct object in the category FR_c, which is a strictly larger category than the category of commutative rings (but there is an fully- faithfull embedding). We study its combinatorics, algebraic properties and show a connection with commutative rings.

*Abstract:*

**Advisor:** Prof. Simeon Reich

**Abstract: **We develop new iterative methods for solving convex feasibility and common fixed point problems, based on the notion of coherence. We also present new concepts and results in Nonlinear Analysis related to the theory of coherence and Opial's demi-closedness principle. We investigate, in particular, the properties of relaxations, convex combinations and compositions of certain kinds of operators defined on a real Hilbert space, under static and dynamic controls, as well as other properties regarding the algorithmic structure of some operators. Our iterative techniques are applied, for example, to the study of various metric and subgradient projection methods. Furthermore, all the methods are presented in both weak and strong convergence versions.

*Abstract:*

**Advisor**: Prof. Udi Yariv

**Abstract**: Surrounded by a spherically symmetric solute cloud, chemically active homogeneous spheres do not undergo conventional autophoresis when suspended in an unbounded liquid domain. When exposed to external flows, solute advection deforms that cloud, resulting in a generally asymmetric distribution of diffusio-osmotic slip which, in turn, modifies particle motion. We illustrate this phoretic phenomenon using two prototypic configurations, one where the particle sediments under a uniform force field and one where it is subject to a simple shear flow. In addition to the Peclet number associated with the imposed flow, the governing nonlinear problem also depends upon the intrinsic Peclet number associated with the chemical activity of the particle. As in the forced-convection problems, the small-Peclet-number limit is nonuniform, breaking down at large distances away from the particle. Calculation of the leading-order autophoretic effects thus requires use of matched asymptotic expansions. We considered two problems: sedimentation and shear problems. In the sedimentation problem we find an effective drag reduction; in the shear problem we find that the magnitude of the stresslet is decreased. For a dilute particle suspension the latter result is manifested by a reduction of the effective viscosity.

*Abstract:*

Real interpolation for the coinvariant subspaces of the shift operator on the circle will be discussed in the first part of the talk.

In the second part it will be shown that, given two closed ideals in a uniform algebra such that the complex conjugate of their intersection

is not included in some of them, the sum of these ideals is not closed.

The problem about nonclosed sums of ideals stems from a detail that emerged during the study of interpolation.

This is a joint work with I. Zlotnikov.

*Abstract:*

**Advisor**:Uri Peskin

**Abstract:** Hole transport is an important transport mechanism in solid state based electronic devices. In recent years charge transport through biomolecules (such as DNA) is also attributed to hole dynamics and/or kinetics. In this work we study fundamental aspects of quantum hole dynamics in nano-scale system. Using reduced models we follow the many body dynamics of interacting electrons in the presence of a few (one or two) holes, and study the validity of the interpretation of the dynamics in terms of holes dynamics. In this seminar I will describe the models and a new computational algorithm developed in order to solve the many body Schroedinger equation for these models. I will present results which demonstrate intriguing aspects of hole dynamics in small systems, such as transition from hole repulsion to hole attraction induced by changes in the system dimensions, or in the electron-electron interaction parameter. Conclusions with respect to the common interpretation of holes in terms of effective positive charges will be given.

*Abstract:*

**advisor: **Nir Gavish

**Abstract: **Concentrated electrolytes are an integral part of many electrochemical and biological systems, including ion channels, dye sensitized solar cells, fuel cells, batteries and super-capacitors. Spatiotemporal theoretical formulation for electrolytes goes back to 1890's where Poisson-Nernst-Planck (PNP) framework was originated. Extensive research efforts during the last century attempted to extend the PNP approach to concentrated electrolyte solutions. Nevertheless, recent experimental observations show qualitative features that are beyond the scope of all existing generalized PNP models. These phenomena include bulk self-assembly, multiple-time relaxation, and underscreening, which all impact the interfacial dynamics, and the transport in these systems.

In this talk, we shall present a thermodynamically consistent, unified framework for ternary media with an evolution mechanism based on a gradient flow approach . In contrast with generalized PNP models, the starting point of this work stems from models for ionic liquids with an explicit account of the solvent density. We show that the model captures the aforementioned phenomena together, and by using tools from bifurcation theory reveal their underlying mathematical origin.

*Abstract:*

**Advisor**: Danny Neftin

**Abstract:** Function fields of genus 0 are of interest in the study of many questions regarding polynomials and rational functions. We use group and field theoretic results to determine the subfields of genus 0 in extensions of large degree with symmetric or alternating Galois group. As time permits we shall describe the applications towards a question of Ritt concerning decompositions of rational functions, and questions concerning reducibility of bivariate polynomials.

*Abstract:*

**Advisor: **Prof. Roy Meshulam

**Abstract: **Let X be a simplicial complex on n vertices without missing faces of dimension larger than d. Let L_k denote the k-Laplacian acting on real k-cochains of X and let μ_k(X) denote its minimal eigenvalue. We study the connection between the spectral gaps μ_k(X) for k ≥ d and μ_{d-1}(X). As an application we prove a fractional extension of a Hall type theorem of Holmsen, Martinez-Sandoval and Montejano for general position sets in matroids.

*Abstract:*

**Advisor: **Eli Aljadeff

**Abstract:**

For a Galois extension $K/k$ we consider the question of classifying

the $K/k$-forms of a finite dimensional path algebra $A=k\Gamma$, i.e., find

up to $k$-isomorphism all the $k$-algebras $B$ such

that $A\otimes_{k}K\cong B\otimes_{k}K$. Here $\Gamma$ is an acyclic

quiver. By Galois descent, we show that when $char\left(k\right)=0$

the $K/k$-forms of $A$ are classified by the cohomology pointed

set $H^{1}\left(Gal\left(K/k\right),\,S_{\Gamma}\right)$, where $S_{\Gamma}$

is a certain finite subgroup of automorphisms of the quiver. This

translates the classification of $K/k$-forms of the algebra $k\Gamma$

into a combinatorial problem. We define the notion of combinatoric

forms of a quiver $\Gamma$ and develop a combinatoric descent for

classifing these forms. We equip the combinatoric forms with algebraic

structures (which are certain tensor type path algebras), and show

that the $K/k$-forms of $k\Gamma$ are classified by evaluations

of combinatorial forms of $\Gamma$.

*Abstract:*

**Supervisor: **Assistant Professor Ram Band

**Abstract: **The Laplacian eigenvalue problem on a bounded domain admits an increasing sequence of eigenvalues and a basis of eigenfunctions. The nodal domains of an eigenfunction are the connected components on which the function has a fixed sign. Courant's theorem asserts that the number of nodal domains of the n'th eigenfunction is bounded by n. In this work, we determine the eigenfunctions and eigenvalues which attain Courant's bound in some specific domains in R^d. Our analysis involves interesting symmetry properties of the eigenfunctions and surprising lattice counting arguments.

*Abstract:*

**Adviser: **Assistant Professor Danny Neftin

**Abstract: **Let K be a number field and f ∈ K [X] . Carney, Horts h and Zieve proved that the induced map f : K −→ K is at most N to 1 outside of a finite set where N is the largest integer such that cos (2π/N) f ∈ K. In particular every f ∈ Q [X] is at most 6 to 1 outside of a finite set. They conjectured that for every rational map X → Y between d dimensional varieties over a number field the map X (K) → X (K) is at most N (d) to 1 outside of a Zariski losed subvariety. The most difficult remaining open case for curves is rational functions f : P 1 → P 1 . That is, that for every number field K there exists a constant N (K) such that for any rational function f ∈ K (X) the induced map f : P 1 (K) → P 1 (K) is at most N (K) to 1 outside of a finite set. We shall discuss advancements towards proving this conjecture.

*Abstract:*

**Abstract: ** I will consider deterministic and random perturbations of dynamical systems and stochastic processes. Under certain assumptions, the long-time evolution of the perturbed system can be described by a motion on the simplex of invariant measures of the non-perturbed system. If we have a de- scription of the simplex, the motion on it is dened by either an averaging principle, or by large deviations, or by a diusion approximation. Various classes of problems will be considered from this point of view: nite Markov chains, random perturbations of dynamical systems with multiple stable attractors, perturbations of incompressible 3D- ows with a conservation law, wave fronts in reaction diusion equations, elliptic PDEs with a small parameter, homogenization.

*Abstract:*

**Advisor**: Prof. Amos Nevo

**Abstract**: We show that averages on geometrically finite Fuchsian groups, when embedded via a representation into a space of matrices, have a homogeneous asymptotic limit when properly rescaled. This generalizes some of the results of F. Maucourant to subgroups of infinite co-volume.

*Abstract:*

**Abstract**: Suppose that for each point 𝑥 of a metric space 𝑋 we are given a compact convex set 𝐾(𝑥) in ℝ𝐷. A "Lipschitz selection" for the family {𝐾(𝑥)∶𝑥∈𝑋} is a Lipschitz map 𝐹:𝑋→ℝ𝐷 such that 𝐹(𝑥) belongs to 𝐾(𝑥) for each 𝑥 in 𝑋. The talk explains how one can decide whether a Lipschitz selection exists. The result is joint work with P. Shvartsman.

Light refreshments will be given before the talk in the lounge of the Faculty of Mathematics on the 8th floor.

*Announcement:*

We are pleased to invite you to our annual Elisha Netanyahu Memorial Lecture on the 7th of June at 17:00 in Sego 1 auditorium at Sego building. The lecturer this year is Professor Gil Kalai from the Hebrew University of Jerusalem. The title of his talk is *"Puzzles** about trees, high dimensions, elections, errors and computation". *

* *Light refreshments will be given before the talk in Faculty Lounge on the 8th floor.

Attached is the poster of the talk.

*Abstract:*

COMPLEX AND HARMONIC ANALYSIS III

In memory of

PROFESSOR URI SREBRO (Z"L)

June 4 – 8, 2017

TECHNION – Israel Institute of Technology HIT – Holon Institute of Technology

The Conference will provide a forum for discussions and exchange of new ideas, concepts and recent developments in the broad field of Modern Analysis. The topics to be addressed include (but not restricted to)

* Complex Analysis

* Harmonic Analysis and PDE

* Quasi-Conformal Mappings and Geometry

The event will take place on June 4 – 8, 2017 in the TECHNION on June 7 and in HIT June 4,5,8 in HIT.

For registration and information please contact Anaoly Goldberg at golberga@hit.ac.il

On behalf of the Organizing Committee

,

Sincerely,

Anatoly Golberg

Holon Institute of Technology

*Abstract:*

**The First Joint IMU-INdAM Conference in Analysis**

**May 29 - June 1, 2017**

**Grand Beach Hotel, Tel Aviv, Israel **

We are pleased to announce on the **First Joint Conference in Analysis** of the Israel Mathematical Union and the Istituto Nazionale di Alta Matematica "F.Severi", in cooperation with Tel Aviv University, the Technion - Israel Institute of Technology and the Galilee Research Center for Applied Mathematics, ORT Braude Academic College of Engineering, which will be held in the Grand Beach Hotel, Tel Aviv from May 29 (arrival May 28) to June 1, 2017. On May 31 there will be an excursion for the Italian guests.

We would like to ask kindly to distribute this announcement among your friends, colleagues and anyone of interest. If you have any queries please do not hesitate to contact the Organizing Committee. We are looking forward to seeing you in Tel Aviv.

*Abstract:*

The 2017 annual meeting in Akko – Israel Mathematical Union

#### 25-28/5/2017

#### Registration (mandatory)

**Schedule and Program**

https://imudotorgdotil.wordpress.com/annual-meeting/

**Plenary speakers:**

Amos Nevo (Technion-IIT)Edriss S. Titi (Weizmann Institute and Texas A&M)

**The Erdős, Nessyahu and Levitzki Prizes will be awarded**

**Zeev@80: Zeev Schuss 80 Birthday**

**Sessions and organizers:**

- Analysis – Emanuel Milman and Baptiste Devyver
- Algebra – Chen Meiri and Danny Neftin
- Applied mathematics – Nir Gavish
- Discrete mathematics – Gil Kalai and Nathan Keller
- Dynamical systems – Uri Bader and Tobias Hartnick
- Education* – Alon Pinto (*discussions in Hebrew)
- Non-linear analysis and optimization – Simeon Reich and Alexander Zaslavski
- Probability theory – Ron Ronsenthal and Nick Crawford
- Topology – Yoav Moriah and Michah Sageev

The IMU offers a limited number of discount rooms (PhD students and postdoctoral fellows: free rooms, two students/fellows in a room. Members of the IMU: 50% discount) to those who register early

For more details contact imu@imu.org.il

Organizing committee: Yehuda Pinchover, Koby Rubisntein, Amir Yehudayoff

*Abstract:*

09:00-09:10 פרופ' אלי אלחדף, דיקן הפקולטה ומרכז לימודים מתקדמים

09:15-09:25 פרופ' יהודה עגנון, מרכז התכנית הבין יחידתית במתמטיקה שימושית

09:30 הרצאות

ד"ר דני נפטין

פרופ"מ רמי בנד

ד"ר רון רוזנטל

פרופ"מ גיא רמון

פרופ"מ בני צ'וקורל

11:10 הצגת פוסטרים ותחומי מחקר

12:00 פאנל בהשתתפות: פרופ' אלי אלחדף, פרופ' מיכה שגיב, פרופ"מ עומרי ברק ונציגי הסטודנטים לתארים מתקדמים

13:00 ארוחת צהריים

*Abstract:*

In equilibrium systems there is a long tradition of modelling systems by postulating an energy and identifying stable states with local or global minimizers of this energy. In recent years, with the discovery of Wasserstein and related gradient flows, there is the potential to do the same for time-evolving systems with overdamped (non-inertial, viscosity-dominated) dynamics. Such a modelling route, however, requires an understanding of which energies (or entropies) drive a given system, which dissipation mechanisms are present, and how these two interact. Especially for the Wasserstein-based dissipations this was unclear until rather recently.

In these talks I will discuss some of the modelling arguments that underlie the use of energies, entropies, and the Wasserstein gradient flows. This understanding springs from the common connection between large deviations for stochastic particle processes on one hand, and energies, entropies, and gradient flows on the other.

In the first talk I will describe the variational structure of gradient flows, introduce generalized gradient flows, and give examples. In the second talk I will enter more deeply into the connection between gradient flows on one hand and stochastic processes on the other, in order to explain ׳where the gradient-flow structures come from׳.

-------------------

This mini-lecture series will be held 9:30-12:30 on Mon, Feb 27.

9:30 - Coffee

10:00-10:50 Lecture I (at an introductory level)

11:00-11:40 Lecture II

10:50-12:30 Lecture III

Organizers: Amy Novick-Cohen and Nir Gavish

*Abstract:*

**Advisor: **Prof. Jacob Rubinstein

**Abstract:** One of the fundamental problems in optical design is *perfect *imaging of a given set of objects or wave fronts by an optical system. An optical system is defined as a finite number of refractive and reflective surfaces and considered to be *perfect* if all the light rays from the object on one side of the system arrive to a single image on the other side of the system. In the case of a single point object we can easily solve the problem using a single optical surface called Cartesian oval. However, in the general case we need to find a set of optical surfaces that map a given set of n objects onto n respective images. In our work we study the problem for n=2 objects in two-dimensional geometry. We discuss a method of designing an optical system with two free-form surfaces that provides a –solution. We then consider a way to construct a solution with minimal degrees of freedom and extend it to wave front imaging. We will also show an application for calculating a multi-surface customized eye model by generating two twice differentiable refractive curves from wave front refraction data.

*Abstract:*

**Advisor: **Prof. Gershon Elber, CS dept

**Abstract:** Algebraic constraints arise in various applications, across domains in science and engineering. Polynomial and piece-wise polynomial (B-Spline) constraints are an important class, frequently arising in geometric modeling, computer graphics and computer aided design, due to the useful NURBs representation of the involved geometries. Subdivision based solvers use properties of the NURBs representation, enabling, under proper assumptions, to solve non-linear, multi-variate algebraic constraints - globally in a given domain, while focusing on the real roots. In this talk, we present three research results addressing problems in the field of subdivision based solvers.

The first presents a topologically guaranteed solver for algebraic problems with two degrees of freedom. The main contribution of this work is a topologically guaranteed subdivision termination criterion, enabling to terminate the subdivision process when the (yet unknown) solution in the tested sub-domain is homeomorphic to a two dimensional disk. Sufficient conditions for the disk-topology are tested via inspection of the univariate solution curve(s) on the sub-domain’s boundary, together with a condition for the injective projection on a two dimensional plane, based on the underlying implicit function and its gradients.

The second result provides a subdivision based method for detecting critical points of a given algebraic system. To find critical points, we formulate an additional algebraic system, with the semantics of searching for locations where the gradients of the input problem are linearly dependent. We formulate the new problem using function valued determinants, representing the maximal minors of the input problem’s Jacobian matrix, searching for locations where they simultaneously vanish. Consequently, an over-constrained system is obtained, involving only the original parameters. The over-constrained system is then solved as a minimization problem, such that all constrains are accounted for in a balanced manner.

The third result applies the subdivision method to the specific problem of Minkowski sum computation of free-form surfaces. As a first step, a two-DOF algebraic system is formulated, searching for parameter locations that correspond to parallel (or anti-parallel) normal vectors on the input surfaces. Only such locations can contribute to the Minkowski sum envelope surface – which is the required representation for the (typically) volumetric object given by the Minkowski sum. A purging algorithm is then executed, to further refine redundant solution locations: surface patches that admit matched normal directions, but cannot contribute to the envelope. The talk summarizes the research towards PhD in applied mathematics, under supervision of Prof. Gershon Elber.

*Abstract:*

**Abstract**: We propose a variation of the classical isomorphism problem for group rings in the context of projective representations. We formulate several weaker conditions following from our notion and give all logical connections between these condition by studying concrete examples. We introduce methods to study the problem and provide results for various classes of groups, including abelian groups, groups of central type, $p$-groups of order $p^4$ and groups of order $p^2q^2$, where $p$ and $q$ denote different primes. Joint work with Leo Margolis.

*Abstract:*

**Abstract**: Let R be a discrete valuation ring with fraction field K. It is a classical result that two nondegenerate quadratic forms over R that become isomorphic over K are already isomorphic over R. [Here, a quadratic form over R is a map q:R^n->R of the form q(x)=x^{T}Mx with M a symmetric matrix, and q is nondegenerate if M is invertible over R.] This result is a special case of a conjecture of Grothendieck and Serre concerning the etale cohomology of reductive group schemes over local regular rings. Much progress has been made recently in proving the conjecture, mostly due to Panin.I will discuss a generalization of the aforementioned result to certain degenerate quadratic and also to hermitian forms over certain (non-commutative) R-algebras. This generalization suggests that the conjecture of Grothedieck and Serre may apply to certain families of non-reductive groups arising from Bruhat-Tits theory. Certain cases of this extended conjecture were already verified and others are currently under investigation.

*Abstract:*

Amazon lets clients bid for coputing resources and publishes the uniform prices that result from this auction. Analyzing these prices and reverse engineering them revealed that prices were usually set artificially and not market driven, in contransr to Amazon's declaration.

***This lecture is intended for undergraduate students **

*Abstract:*

**Advisor:** Prof. Yoav Moriah

**Abstract:** Every closed orientable 3-dimensional manifold M admits a Heegaard splitting, i.e. a decomposition into two handlebodies which meet along their boundary. This common boundary is called a Heegaard surface in M, and is usually considered only up to isotopy in M. The genus g of the Heegaard surface is said to be the genus of the handlebodies. A Heegaard splitting gives us the Heegaard distance, which is defined using the curve complex. The fact that a Heegaard splitting is high distance has important consequences for the geometry of the 3-manifold determined by it. We will discuss two previously introduced combinatorial conditions on the Heegaard distance - the rectangle condition and the double rectangle condition - and their affect on the Heegaard distance, and hence on the geometry of the 3-manifold.

*Abstract:*

** Advisor: **Professor Alexander Nepomnyashchy.

**Abstract**: The transport induced by hydrodynamical flows often reveals anomalous properties. The anomalous transport in the case of a chaotic advection is a well-developed field. However, the anomalous properties of the advection by viscous flows in the absence of the Lagrangian chaos are much less explored.

In my talk I will introduce some basic concepts about the hydrodynamical problem and its interpretation in the framework of the theory of dynamical systems. The conception of Special Flow Introduced formerly in Ergodic Theory will help to understand the mechanisms behind the anomalous properties of the transport. I will describe the corresponding statistical properties induced by such a flow in order to draw conclusions on the original system.

*Abstract:*

**Supervisors**: Assoc. Prof. Alexander M. Leshansky and Dr. Konstantin I. Morozov, in the Faculty of Chemical Engineering

**Abstract**: Recent technological progress in micro- and nanoscale fabrication techniques allows for the construction and development of micron-scale robotic swimmers that can be potentially used for biomedical applications, such as targeted drug delivery and minimally invasive surgical procedures. An efficient technique for controlled steering of robotic microswimmers is by applying time-varying external magnetic fields. Recently, a general theory explaining the dynamics of arbitrary-shaped rigid objects in a rotating magnetic field was developed. Based on this theory, the genetic algorithm approach is applied in this study to optimize the shape of microrobots of certain symmetries. In addition, a numerical model of elastic magnetic microrobots will be presented.

*Abstract:*

**Adviser**: Prof. Dan Givoli from** t**he Interdisciplinary Program for Applied Mathematics

**Abstract: **The need to reduce the size of large discrete models is a reoccurring theme in computational mechanics in recent years. One situation which calls for such a reduction is that where the solution in some region in a high-dimensional computational domain behaves in a low-dimensional way. Typically, this situation occurs when the LowD (Low-Dimensional) model is employed as an approximation to the HighD (High-Dimensional) model in a partial region of the spatial domain. Then, one has to couple the two models on the interface between them. Fields of application where the scenario of LowD-HighD coupling is of special interest include, among others, blood-flow analysis, hydrological and geophysical flow models and elastic structures, where slender members behave in a 1D way, while joints connecting these members possess a 3D behavior. The hybrid HighD-LowD model, if designed properly, is much more efficient than the standard HighD model taken for the entire problem.

This work focuses on the coupling of two-dimensional (2D) and one-dimensional (1D) models in time-harmonic elasticity. The 2D and 1D structural regions are discretized by using 2D and 1D Finite Element (FE) formulations. Two important issues related to such hybrid 2D-1D models are: (a) the design of the hybrid model and its validation (with respect to the original problem), and (b) the way the 2D-1D coupling is done, and the coupling error generated. This research focuses on the second issue.

Several methods are adapted to the 2D-1D coupling scenario, implemented and compared numerically through a specially designed benchmark problem , as well as some more advanced problems.** **

*Abstract:*

**Advisor: **Assistant Professor Barak Fishbain

**Abstract:** Air pollution is a significant risk factor for multiple health situations. In addition, it causes many negative effects on the environment. Thus, arises the need for assessing air-quality. Air quality modeling is an essential tool this task and is in use in many studies such as air quality management and control, epidemiological studies and public health. Today, most of air-pollution modeling is based on data acquired from Air Quality Monitoring (AQM) stations. AQM provides continuous measurements and considered to be accurate; however, they are expansive to build and operate, therefore scattered sparingly. As the number of measuring sites is limited, the information obtained from those measurements is generalized with mathematical methods.Here we introduce two methods to improve the spatio-temporal coverage. The first method, a new interpolation scheme, will expand the scope of the spatial coverage in order to infer the pollution levels in the entire study area. The second is a long-term forecasting method, to implement a better and wide perspective of the temporal coverage. Many researches in air quality modeling uses interpolation schemes such as IDW or Ordinary Kriging. Yet, the mathematical basis of those schemes defines that the extremum value obtained at the measuring places (without considering edge effects). In addition, they are not considering the location of pollution source or any physicochemical characteristics of pollution, hence does not reveal the real spatial coverage. Our interpolation scheme takes into account patterns of dispersion and source location. Source detection is achieved through a novel Hough Transform-like technique.Extending the temporal coverage of the measuring array is achieved through long-term forecasting. Nowadays there are only short-term forecasting methods (24-72 hours ahead), no method exists for long-term (e.g. a year) forecasting. Discrete Time Markov Model is a well-known probabilistic model used to describe and analyze stochastic processes. Here we first define and introduce a method for long-term forecasting based on Discrete-time Markov model for a better temporal coverage.These building blocks which, will be presented in the talk, facilitate the future study of spatio-temporal interpolation methods, which improve the current state-of-the-art by devising new source-location based interpolation methods.

*Abstract:*

**Adviser**: Prof. Eddy Meir-Wolf

**Abstract: **The Onsager-Machlup functional of a Cameron-Martin path relates to the probability that the solution of a stochastic differential equation lies in a small ball (or “tube”) around the path. Its computation is typically dependent of “approximatelimits” of Wiener functionals with respect to a given measurable norm.

We will discuss certain stochastic differential equations driven by fractional Brownian motion and the paths near which their solutions typically reside

*Abstract:*

**Adviser**: Prof. Amy Novick-Cohen

**Abstract**: If we look at most materials under a microscope, we will see a network of grains and grain boundaries as well as holes, cracks, cavities and additional various defects. These features determine the microstructure of the material, whose properties are crucial in determining the various mechanical, electric, magnetic, and optical properties of the material. The microstructure is in turn influenced by the evolution of the exterior surface via the grain boundaries. To describe the evolution we assume that the grain boundaries evolve according to mean curvature motion and the exterior surfaces evolve according to surface diffusion motion. The resultant description for the motion of the grain boundaries, exterior surfaces, quadruple junctions and thermal grooves in thin/thick specimen of triangular geometry containing three grains yields a PDAE system, namely a system of partial differential algebraic equations, which we then solve numerically using an implicit finite difference scheme on staggered grids with a partially parallelized algorithm. Using the program, we identified new physical instabilities numerically. For example, we found that either annihilation of the smallest grain or hole formation at the quadruple junction could occur, depending on the model parameters. A variant algorithm for wetting/dewetting isolated a new grain-hole dewetting instability.

*Abstract:*

**Advisor: **Prof**. **Amos Nevo

**Abstract**:

We establish an error estimate for counting lattice points in Euclidean norm balls (associated to an arbitrary irreducible linear representation) for lattices in simple Lie groups of real rank at least two. Our approach utilizes refined spectral estimates based on the existence of universal pointwise bounds for spherical functions on the groups involved. In the talk I will present the principles of our method. Moreover I will give a natural example in which we found improvement of the best current bound established by Duke, Rudnick and Sarnak in 1991. The group in the example will be SL(n+1, R) for n > 2 with any lattice, and with the adjoint representation

*Abstract:*

**Adviser**: Prof. Naama Brenner

**Abstract: **Phenotypic variability is a hallmark of cell populations, even when clonal and grown under uniform conditions. This variability appears in many measured cellular properties, such as cell-size, protein content, organelle copy number and more. Cells in a population constantly grow and divide, stochastically inheriting their cellular properties to the next generation. Thus, phenotypic variability is tightly connected to long-term cellular growth and division dynamics.

Of special interest and biological relevance are highly abundant proteins, which have recently been found to exhibit properties of a global cellular variable. In particular, they accumulate smoothly throughout the entire cell cycle with a rate correlated to that of cell-size accumulation; this accumulation appears to be negatively regulated similar to cell size control. In addition, both protein and cell-size distributions across a population, as well as across generations in a

single cell, are highly non-Gaussian and display a universal shape.

We propose a modeling approach which describes the multiple interacting components of cellular phenotype and reconstructs the subtle measured properties of phenotypic variability.

These include correlations among phenotype components and across time, and the universal and non-universal statistical properties of phenotype components.

*Abstract:*

Advisor: Nir Gavish

Abstract: The non-local Cahn-Hilliard (Ohta-Kawasaki) equation manifests spatio-temporal behaviors driven by competing short-range forces and long-range Coulombic interactions. These models

are often being employed to study di-block copolymers, and for renewable energy applications that are based on complex nano-materials, such as ionic liquids and polyelectrolyte membranes. Asymmetric properties between different materials, e.g, phase-dependent permittivity and tilted free energy potential, are included in extended Ohta-Kawasaki model.

Using perturbation methods and numerical continuation methods, we study the distinct solution families of Ohta-Kawasaki equations. Specifically, we focus on spatially localized states in 1-space dimensions, and show that in gradient coupled parabolic and elliptic PDEs (phase separation coupled to electrostatics), 1D homoclinic snaking appears as not-slanted and describe the dependence of localized stripes vs. hexagons, on the domain size.

*Abstract:*

The 22nd Amitsur Memorial Symposium will be held at the University of Haifa on June 20-21.

Speakers:

A. Giambruno (Palermo)

Y. Ginosar (Haifa)

B. Kunyavski (Bar Ilan)

D. Neftin (Technion)

C. Procesi (Rome)

A. Regev (Weizmann)

E. Sayag (Ben Gurion)

T. Weigel (Milan)

S. Westreich (Bar Ilan)

Please let us know if you wish to participate in the festive dinner at the end of the first day.

email: ginosar@math.haifa.ac.il

Please forward this email to anyone who might be interested.

Hoping to see you here,

The organizing committee:

E. Aljadeff

A. Braun

Y. Ginosar

*Abstract:*

**Advisor: **Tobias Hartnick

**Abstract: **The Out(G)-action on the group cohomology H^n(G) of a group G is an important object of study in group theory. On the contrary, almost nothing is known about the corresponding Out(G)-action on the bounded group cohomology H^n_b(G). This talk will introduce bounded group cohomology and then look at the case of G=F_2 and n=2. There the dynamics of the unipotent elements in Out(F_2) on a dense subset B(F_2) of H^{^2}_b(F_2) will be presented concretely and visualized. In particular we will show that no element of B(F_2) is fixed by the Out(F_2)-action, partly answering a question of Miklós Abért.

*Abstract:*

**יום בית פתוח לתארים מתקדמים**

**09:00-09:15 דברי פתיחה / פרופ' אלי אלחדף, דיקן הפקולטה**

**09:15-09:30 פרופ' מיכאל פוליאק, מרכז הוועדה לתארים מתקדמים**

**09:30-09:45 פרופ' יהודה עגנון, מרכז התכנית הבין יחידתית במתמטיקה שימושית**

**09:45-09:55 הפסקה**

**09:55-10:55 פרופ'מ ניר גביש**

** פרופ'מ אור שליט**

** פרופ"ח אמיר יהודיוף**

** פרופ'מ אורי שפירא**

**10:55-11:10 הפסקה**

**11:10-12:45 פאנל בהשתתפות הפרופסורים: יעקב רובינשטיין, מיכה שגיב ונציגי הסטודנטים **

** לתארים מתקדמים**

**13:00 ארוחת צהריים**

*Abstract:*

**Supervisor: **Prof. Shlomo Gelaki and Prof. Emeritus Arye Johasz

**Abstract: **Let W be a purely odd finite dimensional supervector space over an algebraically closed field with characteristic zero. The category sRep(W) consisting of /\W-supermodules with even morphisms is a non-semisimple symmetric finite tensor category.

We classify braided finite tensor categories containing sRep(W) as a Lagrangian subcategory (=maximal symmetric subcategory).

*Abstract:*

**מתמטיקה: חומר הלימוד שלא נמצא בסילבוס / ד"ר נתן לוי**

לימודי המתמטיקה מפתחים כישורים חשובים אשר אינם ברי מדידה אך חיוניים בתחום המחקר והפיתוח.בהרצאה זאת נתאר מספר דוגמאות לכישורים מתמטיים הנרכשים בלימודים ויישומם בתעשייה.

**כיצד ניתן להשתמש במתמטיקה תיאורטית בעולם התעשייה? / ד"ר יונתן אפללו**

חשיבותם של כלי המתמטיקה השימושית בתעשייה היא עובדה ידועה ומוכחת.למרות זאת, לימודי המתמטיקה אינם מהווים כלים לפתרון בעיות בלבד אלא גם מאפשרים דרך לפיתוח שיטות פתרון באופן מקורי, יעיל ופרקטי.

בהרצאה, ניתן דוגמאות לבעיות הניתנות לפתרון בעזרת כלים מתמטיים ולבעיות אחרות אשר פתרונן מורכב אך אינו דורש ידע מתמטי נרחב.

*Abstract:*

This lecture deals with various recent developments concerning the old and very classical concept of topological degree for continuous maps from the circle into itself (also called winding number or index).

I will first explain how it can be extended beyond the class of continuous maps.

This led to the "accidental"discovery of a simple, but intriguing formula connecting the degree of a map to its Fourier coefficients. The relation is easily justified when the map is smooth. However, the situation turns out to be extremely delicate if one assumes only continuity, or even Holder continuity. This "marriage" is more difficult than expected and there are many difficulties in this couple such as the following question I raised:

" Can you hear the degree of a map from the circle into itself?"

I will also present estimates for the degree leading to the question :

" How much energy do you need to produce a map of given degree?".

Many simple looking problems remain open.

The initial motivation for this research came from the analysis of the Ginzburg-Landau model in Physics.

The lecture will be accessible to a wide audience, including undergraduate students

*Abstract:*

**Supervisor**: Eli Aljadeff

**Abstract: **When studying noncommutative f.d. algebras, the building blocks, in a sense, are the matrix algebras over division algebras (e.g. the real quaternions). This led to the idea of a generic division algebra such that all the division algebras are just specializations of it. In particular, many properties satisfied by the generic division algebra are inherited by all other division algebras. The generic crossed product arises in a similar manner, when we consider division algebras with a crossed product structure. In this lecture, I will talk about the place of division algebras and crossed products in the study of f.d. algebras, and how to construct their generic versions. Moreover, I will show why the center of these generic objects play such a central role, and how to compute it using field invariants

*Abstract:*

The talk will concern the distance between two polytopes defined for every hypergraph: CP, the covering polytope, which is the convex hull of the characteristic vectors of the covers, and FCP, the fractional covering polytope, which is the set of all fractional covers. Clearly, the first is contained in the second. Given a direction u in space, we can measure the distance between CP and FCP in two ways. One is the ratio t/t*, where t (resp. t*) is smallest such that t u \in CP (resp. FCP). The (better known) second distance measure is the ratio s/s*, where s (resp. s*) is smallest such that a hyperplane perpendicular to u of distance s/|u| (resp. s*/|u|) from the origin meets CP (resp. FCP).

Partially joint work with Ron Aharoni and Ron Holzman

*Abstract:*

**Supervisor**: Professor Emeritus Raphael Loewy

**Abstract: **Nonnegative matrices are important in many areas. Of particular importance are the spectral properties of square nonnegative matrices. Some spectral properties are given by the well-known Perron-Frobenius theory, which is about 100 years old. One of the most difficult problems in matrix theory is to determine the lists of $n$ complex numbers (respectively real numbers) which are the spectra of $ n \times n $ nonnegative (respectively symmetric nonnegative) matrices. In fact, this problem is open for any $ n \geq 5 $. Our work deals with the first open case, that is $ n = 5 $, for a list of real numbers. We made a significant progress towards the solution of this case. In particular, we obtain the solution when the sum of the five given numbers is zero or at least half of the largest one.

*Abstract:*

Thermoacoustics is a highly promising technology for the upcoming decades. Based on the heat transfer between a temperature gradient stack and an oscillating acoustic wave, it is expected to replace current heat pumps or heat engines, such as solar panels or air conditioners, due to its improved efficiency compared to conventional methods. However, it is yet a young research topic with many improvements and tests to come. One of the most recent improvements is the addition of a reactive component to the inert media as it creates a coating layer over the stack pore's walls and forms an additional concentration gradient as a result of its phase-exchange interaction with the active component, encouraging the oscillating amplitudes for a more desirable performance and efficiency. This thesis develops the mathematical non-dimensional approach established by the physical parameters of the system building it from the conservation of momentum, concentration and energy equations applying the required boundary conditions to solve for the velocity, concentration and temperature fluctuations, respectively. Then plugging the results into the continuity equation in order to arrive to the wave equation, which describes the pressure fluctuations along the stack. At this point, it is possible to find the acoustic work flux, which determines the efficiency of the system based on all the physical parameters involved. The results evaluation is focused on the analysis of limiting cases and approximations, such as the inviscid limit or the boundary layer approximation, and their theoretic impact on the performance. Finally, the required setup for a concentration and a temperature gradient onset is found independently in the pursuit of triggering an instable oscillation.

*Abstract:*

Following the work of Linial and Meshulam on random simplicial complexes, we introduce a model for random complexes with bounded degree and study its topology. We use spectral gap theory, in particular, Garland's method, to show homological connectivity of these random complexes. We also show an upper bound on Betti numbers of complexes with highly connected links, in the spiritof Garland's method.

*Abstract:*

Given a random Cayley graph we wish to study its limiting distribution. Marklof and Str¨ombersson used the limit distribution for Frobenius numbers in m+1 variables to prove that the diameter of a random Cayley graphs of Z/kZ with a generating set of fixed size m>1 has a limit in distribution and found that limit. In this talk we survey their result and expand the discussion to Cayley graphs of Z^n/Sigma, with a generating set of fixed size m>n, where Sigma is a sublattice of Z^n

*Abstract:*

The relation between continued fraction expansions and the geodesic flow on the quotient space SL2(R)/SL2(Z) is well studied and understood and dates back to Artin. In this talk we will discuss its positive characteristic analogue, for its similarities to the real case, and its surprising differences. Time permitting, we shall discuss some recent results.

*Abstract:*

**ACTION NOW WANDERING SEMINAR**

First meeting, Technion, 1.12.15,Butler Auditorium (near Forscheimer Faculty club)

• 9:30 cookies, small pastries and fruit from Israel's northern foothills, and refreshing drinks

• 10:00 **Uri Bader**, Weizmann

**Ozawa's proof of Gromov's polynomial growth theorem. **

Gromov's polynomial growth theorem from the early 1980's, stating that every group of polynomial growth is virtually nilpotent, is a milestone in Geometric Group Theory. In this talk I will present the entropy based, two pages proof given recently by Narutaka Ozawa.

• 11:15 **Uri Shapira**, Technion

**Stationary measures on homogeneous spaces.**

Let mu be a compactly supported measure on SL_3(R) generating a group whose Zariski closure is semi-simple. Let X be the space of all rank-2 discrete subgroups of R^3 (identified up to dilation). We describe a classification of the mu-stationary measures on X. This is part of an ongoing project with Oliver Sargent in which we classify stationary measures in situations similar to the above. The proof is an adaptation of the Benoist-Quint approach for classifying stationary measures on homogeneous spaces obtained by quotienting by a discrete subgroup. As an application we show that if v in Z^3 varies along a the quadratic surface x^2 + y^2 - z^2 then the the shapes of the 2-lattices obtained by intersecting Z^3 with the orthocomplement of v is dense in the space of shapes.

• 12:15 Lunch and informal discussions

• 14:00 **Tom Meyerovich**, Ben Gurion University

**Sofic groups, sofic entropy, stabilizers and invariant random subgroups **

Sofic groups where introduced by Gromov (under a different name), and Weiss towards the end of the millennium. This is a class of groups retaining some finiteness properties, a common generalization of amenable and residually finite groups. Entropy theory for sofic groups, initiated by L. Bowen, is developing rapidly. After recalling the concepts of soficity and entropy, I will explain some results relating them to invariant random subgroups, or equivalently stabilizer groups for measure preserving actions.

• 15:15 **Brandon Seward**, Hebrew University

**Positive entropy actions of countable groups factor onto Bernoulli shifts**

I will prove that if a free ergodic action of a countable group has positive Rokhlin entropy (or, less generally, positive sofic entropy) then it factors onto all Bernoulli shifts of lesser or equal entropy. This extends to all countable groups the well-known Sinai factor theorem from classical entropy theory. As an application, I will show that for a large class of non-amenable groups, every positive entropy free ergodic action satisfies the measurable von Neumann conjecture.

*Announcement:*

**Summer Projects in Mathematics at the Technion**

The Mathematics Department at the Technion is inviting advanced undergraduate students to experience research level mathematics in a week of projects (Sunday-Thursday, September 6-10, 2015). The projects will be mentored by members, postdocs and graduate students from the department.

Please visit the Summer Projects website for more details:

http://mathweek.net.technion.ac.il/

Organizers: Ram Band, Michah Sageev and Amir Yehudayoff.

*Abstract:*

**Supervisor: **Associate Professor Uri Bader

**Abstract: **We shall study a variant of property (EH) (defined by Bader-Finkelshtein), called weak property (EH), and its relation to triviality of certain reduced horoboundary actions. We will use this property to show that generalized Heisenberg groups act trivially on their horoboundary, both in the discrete and in the smooth case, extending the results of Bader-Finkelshtein.

*Abstract:*

**Supervisor:** Associate Professor Uri Bader

**Abstract: **It is a well known question of Gromov whether there exist groups with no fixed point free action on CAT(0) spaces. Gromov conjectured that random groups have this property. In this talk we will present groups that have no fix point free isometric actions on Hadamard manifolds. These are the Steinberg groups defined over the ring R = Fp [t] In the talk we will define the Steinberg groups and show some nice properties regarding to them. We will also describe Hadamard manifolds which are complete simply connected non-positively curved Riemaniann manifolds. In particular we will study fat triangles in these manifolds and show how to deduce fix point properties** **

*Announcement:*

**Supervisor:**

Professor Amy Novick-Cohen

**Abstract:**

If we look at most materials under a microscope, we will see a network of grains and grain boundaries as well as holes, cracks, cavities and additional various defects. These features determine the microstructure of the material, whose properties are crucial in determining the various mechanical, electric, magnetic, and optical properties of the material. The microstructure is in turn influenced by the evolution of the exterior surface via the grain boundaries.

In my lecture I shall report on 3D numerical studies of the motion of quadruple junctions and thermal grooves in thin polycrystalline films where the mean curvature motion of the grain boundaries and the surface diffusion evolution of the exterior surfaces couple along the thermal grooves. Our algorithms could also be used to study hole evolution in thin monocrystalline and polycrystalline films, where only the motion of the exterior surface needs to be considered.

To describe the physical models and their motion, we used a system of partial differential algebraic equations with boundary and initial conditions. Our numerical approach used a finite difference scheme on a staggered grid with partially parallelized numerical algorithms, the backward Euler method, and Newton’s method.. Simulations, written in MATLAB and ”C”, were able to indicate some new instabilities.

*Abstract:*

Expander graphs have played, in the last few decades, an important role in computer science, and in the last decade, also in pure mathematics. In recent years a theory of "high-dimensional expanders" is starting to emerge - i.e., simplical complexes which generalize various properties of expander graphs. This has some geometric motivations (led by Gromov) and combinatorial ones (started by Linial and Meshulam). The talk will survey the various directions of research and their applications, as well as potential applications in math and CS. Some of these lead to questions about buildings and representation theory of p-adic groups.

We will survey the work of a number of people. The works of the speaker in this direction are mainly with Tali Kaufman, David Kazhdan and Roy Meshulam.

*Abstract:*

**Abstract**: If one seeks an associative algebra which corresponds canonically to a Euclidean space E (or to any vector space with a quadratic form Q) - canonically means that we refrain from "choosing", say a basis/coordinate system - an option is the Clifford algebra of the space, defined as the associative algebra generated by E, with the relations that the square in the algebra of each vector v in E equals Q(v)1. This algebra contains a plethora of interesting members and structures.Focusing mainly on the Euclidean 4-space, we shall describe its basics and try to stroll in its garden and pick some flowers. In particular, we shall encounter objects mentioned in Maria Elena Luna-Elizarraras' lecture: the 2-dim extension of the reals by a k satisfying k^2=1, and bi-quaternions.

*Abstract:*

**Prof. Martin R. Bridson**

Whitehead Professor of Pure Mathematics Mathematical Institute

**University of Oxford**

Lecture 1: **The ubiquity and wonder of non-positive curvature**

**Time: **Monday, November 10, 2014 at 17:00

**Place: **Lecture will be held at Segoe Building, Benjamin hall (Segoe 1)

Lecture 2: **The universe of groups: Geometry, Complexity and Imposters**

**Time: **Tuesday, November 11, 2014 at 17:00

**Place:** Lecture will be held at Segoe Building, Benjamin hall (Segoe 1)

Lecture 3: **Complexity, and finite shadows of infinite groups**

**Time: **Thursday, November 13, 2014 at 17:00

**Place: **Lecture will be held at Segoe Building, Benjamin hall (Segoe 1)

Refreshments will be served before the lectures