2017 May 24

Mark Rudelson: Delocalization of the eigenvectors of random matrices.

2:00pm to 3:00pm


רוס 63
Abstract: Consider a random matrix with i.i.d. normal entries. Since its distribution is invariant under rotations, any normalized eigenvector is uniformly distributed over the unit sphere. For a general distribution of the entries, this is no longer true. Yet, if the size of the matrix is large, the eigenvectors are distributed approximately uniformly. This property, called delocalization, can be quantified in various senses. In these lectures, we will discuss recent results on delocalization for general random matrices.
2017 Jun 13

Topology and Geometry Seminar: Alexander Caviedes Castro (Tel-Aviv University), "Symplectic capacities and Cayley graphs"

1:00pm to 1:50pm


Ross 70A
Abstract: The Gromov non-squeezing theorem in symplectic geometry states that is not possible to embed symplectically a ball into a cylinder of smaller radius, although this can be done with a volume preserving embedding. Hence, the biggest radius of a ball that can be symplectically embedded into a symplectic manifold can be used as a way to measure the "symplectic size'' of the manifold. We call the square of this radius times the number \pi the Gromov width of the symplectic manifold. The Gromov width as a symplectic invariant is extended through the notion of "Symplectic Capacity".
2017 Nov 06

High Dimensional Expanders and Group Stability, Alex Lubotkzy

9:00am to 11:00am


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.
2018 Jan 08

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

2:00pm to 4:00pm


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 Nov 27

HD-Combinatorics: Irit Dinur, "PCPs and high dimensional expansion"

2:00pm to 4:00pm


Room 130, Feldman Building (IIAS), Givat Ram
The "PCP theorem" says that problems in NP are hard in a robust or stable way. I will give a brief intro to PCPs (and explain the acronym) and then try to outline a proof of the PCP theorem based on "agreement expansion" which is a form of high dimensional expansion. My aim is to show how high dimensional expansion is inherently present in PCP type questions.
2017 Sep 05

IIAS Seminar: Tatiana Nagnibeda - Infinite Ramanujan graphs and completely dissipative actions

4:00pm to 5:00pm


Math room 209
Speaker : Tatiana Nagnibeda (University of Geneva) Abstract: The definition of a Ramanujan graph extends naturally to infinite graphs: an infinite graph is Ramanujan if its spectral radius is not larger than (and hence equal to) the spectral radius of its universal covering tree. As with infinite families of finite graphs, it is interesting and non-trivial to understand, how much Ramanujan graphs resemble trees. I will discuss some results in this direction obtained in a joint work with Vadim Kaimanovich, by investigating ergodic properties of boundary actions of free groups.