2017 May 17

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 Dec 13

Jerusalem Analysis Seminar: "Exponential concentration of zeroes of Gaussian stationary functions" Naomi Feldheim (Weizmann Institute)

12:00pm to 1:00pm


Ross 70
A Gaussian stationary function (GSF) is a random f: R --> R whose distribution is shift-invariant and all its finite marginals have centered multi-normal distribution. It is a simple and popular model for noise, for which the mean number of zeroes was computed already in the 1940's by Kac and Rice. However, it is far more complicated to estimate the probability of a significant deficiency or abundance in the number of zeroes in a long interval (compared to the expectation). We do so for a specific family of GSFs with additional smoothness and absolutely
2017 Mar 23

Xiaolin Zeng (TAU)

1:00pm to 2:00pm


Ross 70
Title: a random Schroedinger operator stemming from reinforced process Abstract: We will explain the relationship between a toy model to Anderson localization, called the H^{2|2} model (according to Zirnbauer) and edge reinforced random walk. The latter is a random walk in which, at each step, the walker prefers traversing previously visited edges, with a bias proportional to the number of times the edge was traversed. Recent study on this random walk showed that it is equivalent to Zirnbauer's model and we will show some consequences once this equivalence is established.
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 13

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

2:00pm to 4:00pm


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 20

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

3:00pm to 4:00pm


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


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


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.