2017
Nov
06

# Events & Seminars

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
Nov
30

2017
Oct
23

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.

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.

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.

2017
Dec
14

2017
Nov
16

2017
Nov
23

2017
Dec
11

2017
Nov
06

# High Dimensional Expanders and Group Stability, Alex Lubotkzy

9:00am to 11:00am

## Location:

Room 130

In the first talk we gave a brief outline of the contents of the course. In the rest of the semester we will get deeper into some topics. In the coming lecture ( and the next one) we will discuss Kazhdan property T and its connections with expanders and with first cohomology groups. No prior knowledge will be assumed.

2017
Nov
06

2018
Jan
08

# HD-Combinatorics: Amnon Ta-Shma, "Bias samplers and reducing overlap in random walks over graphs"

2:00pm to 4:00pm

Abstract:

The expander Chernoff bound states that random walks over expanders are good samplers, at least for a certain range of parameters. In this talk we will be interested in “Parity Samplers” that have the property that for any test set, about half of the sample sets see the test set an *even* number of times, and we will check whether random walks over expanders are good parity samplers. We will see that:

1. Random walks over expanders fare quite well with the challenge, but,

2. A sparse Random complex does much better.

The expander Chernoff bound states that random walks over expanders are good samplers, at least for a certain range of parameters. In this talk we will be interested in “Parity Samplers” that have the property that for any test set, about half of the sample sets see the test set an *even* number of times, and we will check whether random walks over expanders are good parity samplers. We will see that:

1. Random walks over expanders fare quite well with the challenge, but,

2. A sparse Random complex does much better.

2017
Oct
23