2017
Nov
27

# Eventss

2017
Nov
20

# Leonard Schulman, "Analysis of a Classical Matrix Preconditioning Algorithm"

2:00pm to 3:00pm

## Location:

Room 130, Feldman Building, Givat Ram

There are several prominent computational problems for which

simple iterative methods are widely preferred in practice despite

an absence of runtime or performance analysis (or "worse", actual

evidence that more sophisticated methods have superior

performance according to the usual criteria). These situations

raise interesting challenges for the analysis of algorithms.

We are concerned in this work with one such simple method: a

classical iterative algorithm for balancing matrices via scaling

simple iterative methods are widely preferred in practice despite

an absence of runtime or performance analysis (or "worse", actual

evidence that more sophisticated methods have superior

performance according to the usual criteria). These situations

raise interesting challenges for the analysis of algorithms.

We are concerned in this work with one such simple method: a

classical iterative algorithm for balancing matrices via scaling

2017
Dec
25

# HD-Combinatorics: Shai Evra, "Bounded degree high dimensional expanders"

2:00pm to 4:00pm

In the recent theory of high dimensional expanders, the following open problem was raised by Gromov: Are there bounded degree high dimensional expanders?

For the definition of high dimensional expanders, we shall follow the pioneers of this field, and consider the notions of coboundary expanders (Linial-Meshulam) and topological expanders (Gromov).

In a recent work, building on an earlier work of Kaufman-Kazhdan-Lubotzky in dimension 2, we were able to prove the existence of bounded degree expanders according to Gromov, in every dimension.

2017
Oct
23

# HD-Combinatorics: Nati Linial, "High-dimensional permutations"

2:00pm to 4:00pm

## Location:

Israel Institute for Advanced Studies (Feldman building, Givat Ram), Eilat Hall

This is a survey talk about one of the main parts of what we call high-dimensional combinatorics. We start by equating a permutation with a permutation matrix. Namely, an nxn array of zeros and ones where every line (=row or column) contains exactly one 1. In general, a d-dimensional permutation is an array [n]x[n]x....x[n] (d+1 factors) of zeros and ones in which every line (now there are d+1 types of lines) contains exactly one 1. Many questions suggest themselves, some of which we have already solved, but many others are still wide opne. Here are a few examples:

2017
Nov
06

2018
Jan
15

2017
Nov
13

# HD-Combinatorics: Shmuel Weinberger, "L^2 cohomology"

2:00pm to 4:00pm

## Location:

Room 130, Feldman Building, Givat Ram

Abstract: I will give an introduction to the cohomology of universal covers of finite complexes. These groups are (for infinite covers) either trivial or infinite dimensional, but they have renormalized real valued Betti numbers. Their study is philosophically related to the topic of our year, and they have wonderful applications in geometry, group theory, topology etc and I hope to explain some of this.

2017
Oct
23

2017
Nov
30

2017
Nov
20

# HD-Combinatorics: Ran Levi, "Neuro-Topology: An interaction between topology and neuroscience"

3:00pm to 4:00pm

## Location:

Room 130, Feldman Building, Givat Ram

Abstract: While algebraic topology is now well established as an applicable branch of mathematics, its emergence in neuroscience is surprisingly recent. In this talk I will present a summary of an ongoing joint project with mathematician and neuroscientists. I will start with some basic facts on neuroscience and the digital reconstruction of a rat’s neocortex by the Blue Brain Project in EPFL.

2017
Sep
11

# IIAS Seminar: Nikolay Nikolov, "Gradients in group theory"

11:00am to 12:00pm

## Location:

Feldman building, Room 128

Abstract: Let G be a finitely generated group and let G>G_1>G_2 ... be a sequence of finite index normal subgroups of G with trivial intersection.

We expect that the asymptotic behaviour of various group theoretic invariants of the groups G_i should relate to algebraic, topological or measure theoretic properties of G.

A classic example of this is the Luck approximation theorem which says that the growth of the ordinary Betti numbers of sequence G_i is given by the L^2-Betti number of (the classifying space) of G.

We expect that the asymptotic behaviour of various group theoretic invariants of the groups G_i should relate to algebraic, topological or measure theoretic properties of G.

A classic example of this is the Luck approximation theorem which says that the growth of the ordinary Betti numbers of sequence G_i is given by the L^2-Betti number of (the classifying space) of G.

2018
Jan
01

# HD-Combinatorics: Alan Lew, "Spectral gaps of generalized flag complexes"

2:00pm to 4:00pm

## Location:

Eilat Hall, Feldman Building (IIAS), Givat Ram

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). Applications include:

1) A cohomology vanishing theorem for complexes without large missing faces.

2) A fractional Hall type theorem for general position sets in matroids.

1) A cohomology vanishing theorem for complexes without large missing faces.

2) A fractional Hall type theorem for general position sets in matroids.

2017
Nov
16

2017
Dec
14

2018
Jan
10

# Logic Seminar - Alex Lubotzky - "First order rigidity of high-rank arithmetic groups"

11:00am to 1:00pm

## Location:

Ross 63

The family of high rank arithmetic groups is a class of groups playing an important role in various areas of mathematics. It includes SL(n,Z), for n>2 , SL(n, Z[1/p] ) for n>1, their finite index subgroups and many more.
A number of remarkable results about them have been proven including; Mostow rigidity, Margulis Super rigidity and the Quasi-isometric rigidity.