2018 May 08

T&G: Amitai Yuval (Hebrew University), The Hodge decomposition theorem for manifolds with boundary

12:00pm to 1:30pm


Room 110, Manchester Buildling, Jerusalem, Israel
The Hodge decomposition theorem is the climax of a beautiful theory involving geometry, analysis and topology, which has far-reaching implications in various fields. I will present the Hodge decomposition in compact Riemannian manifolds, with or without boundary. The non-empty-boundary case is more interesting, as it requires the formulation of an appropriate boundary condition. As it turns out, the Hodge-Laplacian has two different elliptic boundary conditions generalizing the classical Dirichlet and Neumann conditions, respectively.
2018 May 10

Basic Notions - Benjamin Weiss: "All ergodic systems have the Weak Pinsker property"

4:00pm to 5:30pm


Ross 70
An ergodic system (X;B; μ; T) is said to have the weak Pinsker property if for any ε > 0 one can express the system as the direct product of two systems with the first having entropy less than ε and the second one being isomorphic to a Bernoulli system. The problem as to whether or not this property holds for all systems was open for more than forty years and has been recently settled in the affirmative in a remarkable work by Tim Austin. I will begin by describing why Jean-Paul formulated this prob- lem and its significance. Then I will give an aerial view of Tim's
2018 Jun 04

NT&AG: Hillel Firstenberg (HUJI), "Hyper-modular functions, irrationality of \zeta(3), and algebraic functions over finite fields"

2:00pm to 3:00pm


Room 70A, Ross Building, Jerusalem, Israel
Using formal power series one can define, over any field, a class of functions including algebraic and classical modular functions over C. Under simple conditions the power series will have coefficients in a subring of the field - say Z - and this plays a role in Apery's proof of the irrationality of \zeta(3). Remarkably over a finite field all such functions/power series are algebraic. I will call attention to a natural - but open - problem in this area.
2018 May 07

HD-Combinatorics: Special day on group stability

(All day)


Eilat Hall, Feldman Building, Givat Ram

This special day is part of several Mondays that will be dedicated to stability in group theory

09:00 - 11:00 Alex Lubotzky, "Group stability and approximation"

14:00 - 16:00 Lev Glebsky, "Stability and second cohomology"
2018 Jun 26

Dynamics Lunch: Jasmin Matz (Huji) ״Distribution of periodic orbits of the horocycle flow״

12:00pm to 1:00pm


Manchester lounge
An old result of Hedlund tells us that there are no closed orbits for the horocycle flow on a compact Riemann surface M. The situation is different if M is non-compact in which case there is a one-parameter family of periodic orbits for every cusp of M. I want to talk about a result by Sarnak concerning the distribution of the such orbits in each of these families when their length goes to infinity. It turns out that these orbits become equidistributed in M and the rate of convergence can in fact be quantified in terms of spectral properties of the Eisenstein series on M.
2018 May 03

Basic Notions - Alex Lubotzky: "Group stability and approximation"

4:00pm to 5:30pm


Ross 70
An old problem (Going back to Turing, Ulam and others) asks about the "stability" of solutions in some algebraic contexts. We will discuss this general problem in the context group theory: Given an "almost homomorphism" between two groups, is it close to a homomorphism?
2018 May 22

Barak Weiss (TAU): New examples for the horocycle flow on the moduli space of translation surfaces

2:15pm to 3:15pm

A longstanding open question concerning the horocycle flow on moduli space of translation surfaces, is whether one can classify the invariant measures and orbit-closures for this action. Related far-reaching results of Eskin, Mirzakhani and Mohammadi indicated that the answer might be positive. However, in recent work with Jon Chaika and John Smillie, we find unexpected examples of orbit-closures; e.g. orbit closures which are not generic for any measure, and others which have fractional Hausdorff dimension. Such examples exist even in genus 2.
2018 Jun 11

Combinatorics: Chris Cox (CMU) "Nearly orthogonal vectors"

11:00am to 12:30pm


IIAS, Eilat hall, Feldman bldg, Givat Ram
Speaker: Chris Cox, CMU Title -- Nearly orthogonal vectors Abstract -- How can $d+k$ vectors in $\mathbb{R}^d$ be arranged so that they are as close to orthogonal as possible? In particular, define $\theta(d,k):=\min_X\max_{x
2018 Jun 18

Combinatorics -- Erdos lecture cancelled; instead (NOTE THE TIME!) :

10:30am to 12:30pm


IIAS, Eilat hall, Feldman bldg (top floor), Givat Ram
Speaker: Ilan Newman and Yuri Rabinovich, U.Haifa Title: Sparsifiers - Part I (Part II from 2pm to 4pm, same day and place) Abstract: Time permitting, we plan to discuss the following topics (in this order): 1. * Additive Sparsification and VC dimension * Multiplicative Sparsification * Examples: cut weights, cut-dimension of L_1 metrics, general metrics, and their high-dimensional analogues 2. * Multiplicative Sparsification and Triangular Rank; * Karger-Benczur sparsification of cuts weights 3. * Batson-Spielman-Srivastava sparsification
2018 Jun 25

Combinatorics: Roman Glebov (HU) "Perfect Matchings in Random Subgraphs of Regular Bipartite Graphs"

11:00am to 12:30pm


IIAS, room 130, Feldman bldg, Givat Ram
Speaker: Roman Glebov (HU) Title: Perfect Matchings in Random Subgraphs of Regular Bipartite Graphs Abstract: Consider the random process in which the edges of a graph $G$ are added one by one in a random order. A classical result states that if $G$ is the complete graph $K_{2n}$ or the complete bipartite graph $K_{n,n}$, then typically a perfect matching appears at the moment at which the last isolated vertex disappears. We extend this result to arbitrary $k$-regular bipartite graphs $G$ on $2n$ vertices for all $k=\Omega(n)$.
2018 Apr 29

GAME THEORY AND MATHEMATICAL ECONOMICS RESEARCH SEMINAR:Michal Feldman, Tel Aviv University "Interdependent Values without Single-Crossing (Joint work with Alon Eden, Amos Fiat and Kira Goldner)"

1:30pm to 2:30pm


Elath Hall, 2nd floor, Feldman Building, Edmond Safra Campus


We consider a setting where an auctioneer sells a single item to n potential agents with {\em interdependent values}. That is, each agent has her own private signal, and the valuation of each agent is a function of all n private signals. This captures settings such as valuations for oil fields, broadcast rights, art, etc.