2017 Nov 01

Jerusalem Analysis Seminar "When do the spectra of self-adjoint operators converge?" Siegfried Beckus (Technion)

12:00pm to 1:00pm


Ross 63

Given a self-adjoint bounded operator, its spectrum is a compact subset of the real numbers. The space of compact subsets of the real numbers is naturally equipped with the Hausdorff metric. Let $T$ be a topological (metric) space and $(A_t)$ be a family of self-adjoint, bounded operators. In the talk, we study the (Hölder-)continuity of the map assigning to each $t\in T$ the spectrum of the operator $A_t$.
2017 Mar 09

Analysis and PDEs: Leonid Parnovski (London) - Local Density of states and the spectral function for almost periodic operators

1:00pm to 2:00pm


Ross 70
I will discuss the asymptotic behaviour (both on and off the diagonal) of the spectral function of a Schroedinger operator with smooth bounded potential when energy becomes large. I formulate the conjecture that the local density of states (i.e. the spectral function on the diagonal) admits the complete asymptotic expansion and discuss the known results, mostly for almost-periodic potentials.
2016 Jun 16

Jerusalem Analysis and PDEs - Gilbert Weinstein (Ariel)

1:00pm to 2:00pm


Ross 70
Title: Harmonic maps with prescribed singularities and applications to general relativity
Abstract: We will present a general theory of existence and uniqueness for harmonic maps with prescribed singularities into Riemannian manifolds with non-positive curvature. The singularities are prescribed along submanifolds of co-dimension 2. This result generalizes one from 1996, and is motivated by a number of recent applications in general relativity including:
* a lower bound on the ADM mass in terms of charge and angular momentum for multiple black holes;
2017 May 25

Mark Rudelson: Delocalization of the eigenvectors of random matrices.

1:00pm to 2:00pm


Ross 70
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 May 10

Peli Grietzer (Harvard literature dept.)

4:00pm to 5:00pm


Ross 70.
In 1962, amateur literary theorist and professional mathematician Andrey Kolmogorov wrote: ‘A story is art only if the characters and situations it describes stand a chance of becoming
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 Jun 29

Special Seminar: Ayala Byron (HUJI) "Homogeneity of torsion-free hyperbolic groups"

2:00pm to 3:00pm


Ross 70

A (countable) group G is homogeneous if whenever g,h are tupples of the same type in G, there is an automorphism of G sending g to h.
We give a characterization of freely-indecomposable torsion-free hyperbolic groups which are homogeneous, in terms of a particular decomposition as a graph of groups - their JSJ decomposition. This is joint work with Chloe Perin.
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.