# Techmath - Math Seminars in Israel

*Abstract:*

This talk will investigate a certain class of continuous time Markov processes using machinery from algebraic topology. To each such process, we will associate a homological observable, the average current, which is a measurement of the net flow of probability of the system. We show that the average current quantizes in the low temperature limit. We also explain how the quantized version admits a topological description.

*Abstract:*

Statistical Learning Theory is centred on finding ways in which random data can be used to approximate an unknown random variable. At the heart of the area is the following question: Let F be a class of functions defined on a probability space (\Omega,\mu) and let Y be an unknown random variable. Find some function that is (almost) as 'close' to Y as the 'best function' in F. A crucial facet of the problem is the information one has: both Y and the underlying probability measure \mu are not known. Instead, the given data is an independent sample (X_i,Y_i)_{i=1}^N, selected according to the joint distribution of \mu and Y. One has to design a procedure that receives as input the sample (and the identity of the class F) and returns an approximating function. The success of the procedure is measured by the tradeoff between the accuracy (level of approximation) and the confidence (probability) with which that accuracy is achieved. In the talk I explore some surprising connections the problem has with high-dimensional geometry. Specifically, I explain how geometric considerations played an instrumental role in the problem's recent solution-leading to the introduction of a prediction procedure that is optimal in a very strong sense and under minimal assumptions.

*Abstract:*

TBA

*Abstract:*

For a given a finite complex K, when can I attach a cell to some iterated suspension of K so that the result satisfies Poincare duality? My talk will give partial answers to this question. I will give examples. I will also explain a connection between James Periodicity in homotopy theory to the 4-fold periodicity appearing in surgery theory.

*Abstract:*

A number of methods of the algebraic graph theory were influenced by the spectral theory of Riemann surfaces. We pay it back, and take some classical results for graphs to the continuous setting. In particular, I will talk about colorings, average distance and discrete random walks on surfaces. Based on joint works with E. DeCorte and A. Kamber.

*Abstract:*

We introduce an intersection theory problem for maps into a smooth manifold equipped with a stratification. We investigate the problem in the special case when the target is the unitary group and the domain is a circle. The first main result is an index theorem that equates a global intersection index with a finite sum of locally defined intersection indices. The local indices are integers arising from the geometry of the stratification.

The result is used to study a well-known problem in chemical physics, namely, the problem of enumerating the electronic excitations (excitons) of a molecule equipped with scattering data. We provide a lower bound for this number. The bound is shown to be sharp in a limiting case.

*Abstract:*

Let $(M,d)$ be a metric space and let $Y$ be a Banach space. Suppose that for each point $x$ of $M$ we are given a compact convex subset $F(x)$ in $Y$ of dimension at most $m$. A ``Lipschitz selection'' for the family $\{F(x): x\in M\}$ is a Lipschitz map $f$ from $M$ into $Y$ such that $f(x)$ belongs to $F(x)$ for each $x\in M$. The talk explains how one can decide whether a Lipschitz selection exists. We discuss the following ``Finiteness Principle'' for the existence of a Lipschitz selection: Suppose that on every subset $M'$ of $M$ consisting of at most $2^{m+1}$ points, $F$ has a Lipschitz selection with Lipschitz constant at most $1$. Then $F$ has a Lipschitz selection on all of $M$. Furthermore, the Lipschitz constant of this selection is bounded by a certain constant depending only on $m$. The result is joint work with Charles Fefferman.

*Abstract:*

We revisit the old construction of Gromov and Lawson that yields a Riemannian metric of positivescalar curvature on a connected sum of manifolds admitting such metrics. This is joint workwith C. Sormani and J. Basilio. Our refinement is to show that the "tunnel" constructed betweenthe two summands can be made to have arbitrarily small length and volume. We use this tocreate examples of sequences of compact manifolds with positive scalar curvature whose Gromov-Hausdorff limits do not have positive scalar curvature in a certain generalized sense.

*Abstract:*

Over the last 15 years, it has been noted that many combinatorial structures, such as real and complex hyperplane arrangements, interval greedoids, matroids, oriented matroids, and others have the structure of a left regular band, a certain kind of finite monoid. The representation theory of the associated monoid has had a major influence on understanding these objects along with related structures such as finite Coxeter groups and various Markov processes. In return, this has spurred a deeper development of the representation theory and cohomolgy theory of left regular bands and more general classes of finite monoids. In particular, the Ext modules between simple LRB modules over a field turn out to be intimately related to the cohomology of the order complex of the poset of principal right ideals of the LRB and other related simplicial complexes. These fit into the wider class of LRBs all of whose retractions (certain intervals in the poset) are isomorphic to face posets of regular CW complexes. For this class of LRBs, we can compute a quiver presentation, the global dimension of the algebra and have an analogue of the Zaslavsky Theorem on counting faces of hyperplane arrangements. Finally, a surprising connection to LeRay numbers and partially commutative LRBs will be discussed.

*Abstract:*

TBA

*Abstract:*

When the first Betti number $b_{1}(M)$ of a 3-manifold $M$ is greater than one, it follows from Thurston norm theory that if $M$ fibers over the circle, it fibers in infinitely many ways. This talk studies fiberings that are extremal in the sense that the Betti number of the fiber realises the lower bound $b_{1}(M)-1$. It is shown that in hyperbolic manifolds, such fiberings are unique up to isotopy, and can be characterised as having monodromy in a specific normal subgroup of the mapping class group.

***Double feature: please note the special time***

*Abstract:*

The talk is a special Geometry and Topology seminar.

Abstract :

When the first Betti number $b_{1}(M)$ of a 3-manifold $M$ is greater than one, it follows from Thurston norm theory that if $M$ fibers over the circle, it fibers in infinitely many ways. This talk studies fiberings that are extremal in the sense that the Betti number of the fiber realises the lower bound $b_{1}(M)-1$. It is shown that in hyperbolic manifolds, such fiberings are unique up to isotopy, and can be characterised as having monodromy in a specific normal subgroup ofthe mapping class group.

*Abstract:*

We decompose any object in the wrapped Fukaya category of a 2n-dimensional Weinstein manifold as a twisted complex built from the cocores of the n-dimensional handles in a Weinstein handle decomposition. If time permits, we will also discuss how to generalize this result to Weinstein sectors.

This is joint work with Baptiste Chantraine, Georgios Dimitroglou Rizell and Paolo Ghiggini.

*Abstract:*

T.B.A.

*Abstract:*

The aim of this talk is to present an elementary approach to Fermat's last theorem. We translate the condition of (x,y,z) being solution of Fermat's equation x^n+y^n=z^n to a robust system of p-adic recursion relations (to which we refer as &quot;zipper equations&quot;). For n=3 we will show that the zipper relations admit no solution. The talk will be followed with illustrations.

*Abstract:*

TBA

*Abstract:*

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:*

Dear colleagues, The tenth Israel CS theory day will take place at the Open University in Ra'anana on Wednesday, December 20st, 10:00-17:00. (Gathering will start at 09:30.) Check out the exciting schedule of talks, which will be delivered by 7 Israeli speakers who will cross the Atlantic to be with us, at http://www.openu.ac.il/theoryday2017 Pre-registration would be most appreciated and very helpful: https://www.fee.co.il/e38725 For directions, please see http://www.openu.ac.il/raanana/p1.html (parking in the university parking lot is free). Lehitraot, The Department of Mathematics and Computer Science at the Open University

*Announcement:*

Technion – Israel Institute of Technology

supported by the Mallat Family Fund for Research in Mathematics

and

THE ISRAEL ACADEMY OF SCIENCES AND HUMANITIESThe Batsheva de Rothschild Fund forThe Advancement of Science in IsraelThe American Foundation for Basic Research in IsraelInvites you to

#### The Batsheva de Rothschild Seminar on the Hardy-type inequalities and elliptic PDEs

7-11.01.2018

dedicated to Professor Moshe Marcus 80th birthday!

**Organizing committee:**

Prof. Dan Mangoubi, Einstein Institute of Mathematics

Prof. Yehuda Pinchover, Technion – Israel Institute of Technology

Prof. Mikhail Sodin, Tel Aviv University

For More information:

*Announcement:*

Title: TBA....

Lecture 1: April 23, 2018 at 15:30

Lecture 2: April 25, 2018 at 15:30

Lecture 3: April 26, 2018 at 15:30

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

*Announcement:*

Title: TBA....

Lecture 1: April 23, 2018 at 15:30

Lecture 2: April 25, 2018 at 15:30

Lecture 3: April 26, 2018 at 15:30

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

*Announcement:*

Title: TBA....

Lecture 1: April 23, 2018 at 15:30

Lecture 2: April 25, 2018 at 15:30

Lecture 3: April 26, 2018 at 15:30

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

*Announcement:*

Title of lectures: *Billiard paths on polygons: Where do they lead?*

LECTURE 1: Monday, April 30, 2018 at 15:30

LECTURE 2: Tuesday, May 1, 2018 at 15:30

LECTURE 3: Thursday, May 3, 2018 at 15:30

*Announcement:*

Title of lectures: *Billiard paths on polygons: Where do they lead?*

LECTURE 1: Monday, April 30, 2018 at 15:30

LECTURE 2: Tuesday, May 1, 2018 at 15:30

LECTURE 3: Thursday, May 3, 2018 at 15:30

*Announcement:*

Title of lectures: *Billiard paths on polygons: Where do they lead?*

LECTURE 1: Monday, April 30, 2018 at 15:30

LECTURE 2: Tuesday, May 1, 2018 at 15:30

LECTURE 3: Thursday, May 3, 2018 at 15:30

*Announcement:*

Technion–Israel Institute of Technology

Center for Mathematical Sciences

Supported by the Mallat Family Fund for Research in Mathematics

invite you to a workshop on the topic of

**Nonpositively Curved Groups on the Mediterranean**

**Nahsholim, 23-29.5.18**

**Organizers:**

Kim Ruane,Tufts University

Michah Sageev, Technion–Israel Institute of Technology

Daniel Wise, McGill University

**For more information:**

** http://cms-math.net.technion.ac.il/nonpositively-curved-groups-on-the-mediterranean/ **