# Techmath - Math Seminars in Israel

*Abstract:*

We consider the classes of homeomorphisms of domains in $\\mathbb R^n$ withWe consider the classes of homeomorphisms of domains in $\mathbb R^n$ with $p$-moduli of the families of curves and surfaces integrally bounded from above and below. These classes essentially extend the well-known classes of mappings such as quasiconformal, quaiisometric, Lipschitzian, etc. In the talk, we survey the known results in this field but mainly establish new differential properties of such mappings. A collection of related open problems will also be presented.

*Abstract:*

The group ring first emerged as an auxiliary tool in grouptheory and representation theory at the end of the 19th century and becamean object of interest in itself some decades later. It can be seen as a structurejoining in an elegant manor the algebraic theories on rings and groups and, inthe case of the coefficient ring being the ring of integers, also number theoryenters the picture.

Denoting the group ring of a group G over a ring R by RG, in particularthe group of units of RG and its connection to the structure of G inspired alot of research. The coefficient ring keeping the closest connection to G arethe integers, since they keep the arithmetic information which would be lostwhen one is allowed to divide by some primes.

In this talk I will present basic results and questions about the unit groupof a group ring with special emphasis on finite subgroups of the unit groupof the integral group ring ZG, such as: Is G determined by the group ring? Are the orders of units determined by G? How close are the finite subgroupsof units in ZG to being subgroups of G?

*Abstract:*

The topological KKMS Theorem is a powerful extension of the Brouwer's Fixed-Point Theorem, which was proved by Shapley in 1973 in the context of game theory. We prove a colorful and polytopal generalization of the KKMS Theorem, and show that our theorem implies some seemingly unrelated results in discrete geometry and combinatorics involving colorful settings. For example, we apply our theorem to provide a new proof of the Colorful Caratheodory Theorem due to Barany, which asserts that if 0 is in the convex hull of n+1 sets of points in R^n, then there exists a colorful selection of points, one from each set, containing 0 in its convex hull. We further apply our theorem to obtain an upper bound on the piercing numbers in colorful d-interval families, extending results of Tardos, Kaiser and Alon for the non-colored case. Finally, we apply our theorem to questions regarding envy-free fair division of goods (e.g., cakes) among a set of players. Joint with Florian Frick.

*Abstract:*

We derive sharp eigenvalue asymptotics for Dirichlet-to-Neumann operator in the domain with edges and discuss obstacles for deriving the second term.

*Abstract:*

This will be the second of two talks in which we will study the recent preprint "Non-commutative peaking phenomena and a local version of the hyperrigidity conjecture", by Raphael Clouatre. Link:

https://arxiv.org/pdf/1709.01649.pdf

*Abstract:*

The study of mapping class groups has benefitted immensely from the action on the Gromov-hyperbolic space called the curve complex. The study of outer automorphisms is heavily inspired by the advances in understanding of mapping class groups. There are multiple ways to associate a 'curve complex' to Out(F_n). In this talk, I will present some such simplicial complexes on which Out(F_n) acts. I will also talk about joint work with Derrick Wigglesworth classifying the loxodromic elements for a particular Out(F_n) complex called the cyclic splitting complex.

*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:*

A model geometry for a finitely generated group is a proper geodesic metric space on which the group acts properly and cocompactly. If two groups have a common model geometry, the Milnor-Schwarz Lemma tells us that the groups are quasiisometric. In contrast, two quasi-isometric groups do not, in general, have a common model geometry.

A simple surface amalgam is obtained by taking a finite collection of compact surfaces, each with a single boundary component, and gluing them together by identifying their boundary curves. We consider the fundamental groups of such spaces and show that commensurability is determined by having a common model geometry. This gives a relatively simple family of groups that are quasi-isometric, but are neither commensurable, nor act on the same common model geometry.

This work is joint with Emily Stark.

*Abstract:*

A common question in mathematics is &quot;Can global questions be answered by local means?&quot;, this is usually referred to as the &quot;local-global principle&quot;. A famous example is the Hasse-Minkowski theorem on quadratic forms. On the other and, it is also known that the Hasse-Minkowski theorem cannot be extended to cubic forms. In this talk, I will present the local-global principle for automorphic represntations, describe its success in the cuspidal spectrum of the group GL_n and its failure in the cuspidal spectrum of the exceptional group of type G_2.

*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

*Abstract:*

A family of lines through the origin in Euclidean space is calledequiangular if any pair of lines defines the sameangle. The problem of estimating the maximum cardinality of such afamily in $R^n$ was extensively studied for the last 70years. Answering a question of Lemmens andSeidel from 1973, in this talk we show that for every fixed angle$\theta$ and sufficiently large $n$ there are at most $2n-2$ lines in$R^n$ with common angle $\theta$.Moreover, this is achievable only when $\theta =\arccos \frac{1}{3}$.Various extensions of this result to the more general settings oflines with $k$ fixed angles and of spherical codes will be discussedas well. Joint work with I. Balla, F. Drexler and P. Keevash.

*Abstract:*

The Twentieth Bi-Annual Israeli Mini-Workshops in Applied and Computational Mathematics will be held at December 28, 2017, at ORT Braude College in Karmiel. We are pleased to invite the Israeli applied mathematics community to participate in The Twentieth Israeli bi-annual Mini-Workshop in Applied and Computational Mathematics. The idea of these workshops is to create a forum for researchers, especially young faculty members and students, to get to know other members of the community, and to promote discussions as well as collaborations. Poster session: In order to highlight a wide spectrum of topics, there will be a poster session. You are welcome to submit a poster in pdf format to lavi@braude.ac.il by December 17, 2017. Registration: Participation in the workshop is free, but participants are asked to register by sending an e-mail to Anna Shmidov, math@braude.ac.il, so we can be adequately prepared for the day. Please register by 12:00 on Tuesday December 26. Location: VIP Room, EF Building. ORT Braude College. Public Transportations: There is a direct train to Karmiel main train station and from there easy a shuttles to the College. The train website: https://www.rail.co.il/en Local organizers: Aviv Gibali, Mark Elin, Lavi Karp Series founders: Raz Kupferman, Vered Rom-Kedar, Edriss S. Titi

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TBA

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*Abstract:*

In this talk, I present an analogue of the Hardy-Littlewood conjecture on the asymptotic distribution of prime constellations in the setting of short intervals in function fields of smooth projective curves over finite fields. I will discuss the definition of a "short interval" on a curve as an additive translation of the space of global sections of a sufficiently positive divisor E by a suitable rational function f, and show how this definition generalizes the definition of a short interval in the polynomial setting. I will give a sketch of the proof which includes a computation of a certain Galois group, and a counting argument, namely, Chebotarev density type theorem. This is a joint work with Tyler Foster.

**Note there are two cosecutive talks.**

*Abstract:*

I will discuss a string of discoveries aided by numerical evidence and luck regarding asymptotics of q-hypergeometric series and their relation to quantum knotinvariants (such as the Kashaev invariant of a knot, the state-integral invariants of Kashaev, and the 3D-Index of Dimofte-Gaiotto-Gukov). Joint work with Don Zagier.

*Abstract:*

Technion &amp;#8211; 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 for The Advancement of Science in IsraelThe American Foundation for Basic Research in Israel Invites 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 &amp;#8211; Israel Institute of Technology Prof. Mikhail Sodin, Tel Aviv University For More information: http://cms-math.net.technion.ac.il/batsheva-de-rothschild-seminar-on-the-hardy-type-inequalities-and-elliptic-pdes/

*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:

*Abstract:*

T.B.A.

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*Abstract:*

Markoff triples are integer solutions of the equation $x^2+y^2+z^2=3xyz$ which arose in Markoff's spectacular and fundamental work (1879) on diophantine approximation and has been henceforth ubiquitous in a tremendous variety of different fields in mathematics and beyond. After reviewing some of these, we will discuss joint work with Bourgain and Sarnak on the connectedness of the set of solutions of the Markoff equation modulo primes under the action of the group generated by Vieta involutions, showing, in particular, that for almost all primes the induced graph is connected. Similar results for composite moduli enable us to establish certain new arithmetical properties of Markoff numbers, for instance the fact that almost all of them are composite.

Time permitting, we will also discuss recent joint work with Magee and Ronan on the asymptotic formula for integer points on Markoff-Hurwitz surfaces $x_1^2+x_2^2 + \dots + x_n^2 = x_1 x_2 \dots x_n$, giving an interpretation for the exponent of growth in terms of certain conformal measure on the projective space.

*Abstract:*

TBA

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*Announcement:*

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:*

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:*

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/ **

*Announcement:*

**TBA....**

For further information please click the link below:

http://cms-math.net.technion.ac.il/summer-school-the-complex-math-of-the-real-world/