• 2019 Aug 15

Analysis Seminar: Mira Shamis (London) "Applications of the Ky Fan inequality to random (and almost periodic) operators"

12:00pm to 1:00pm

Location:

Ross 70
Title: Applications of the Ky Fan inequality to random (and almost periodic) operators Abstract: We shall discuss the Ky Fan inequality for the eigenvalues of the sum of two Hermitian matrices. As an application, we shall derive a sharp version of a recent result of Hislop and Marx pertaining to the dependence of the integrated density of states of random Schroedinger operators on the distribution of the potential. Time permitting, we shall also discuss an application to quasiperiodic operators.
• 2019 Jun 26

Analysis Seminar - Dvoretzky lecture - Assaf Naor "The (in)compatibility of 3 and 5 dimensional Heisenberg geometry with Lebesgue spaces"

12:00pm to 1:00pm

Location:

Ross 70
Title: The (in)compatibility of 3 and 5 dimensional Heisenberg geometry with Lebesgue spaces Abstract: The 3-dimensional (discrete) Heisenberg geometry is the shortest-path metric on the infinite graph whose vertex set is the integer grid $\Z^3$ and the neighbors of each integer vector $(a,b,c)$ are the four integer vectors $$(a+ 1,b,c), (a- 1,b,c), (a,b+ 1,c+ a), (a,b- 1,c- a).$$
• 2019 Jun 19

Analysis Seminar: Daniel Ofner (HUJI) "Mesoscopic universality for orthogonal polynomial ensembles on the unit circle"

12:00pm to 1:00pm

Location:

Ross 70
Title: Mesoscopic universality for orthogonal polynomial ensembles on the unit circle
• 2019 May 29

Analysis Seminar: Lior Alon (Technion) "A central limit type conjecture for the nodal statistics of quantum graphs"

12:00pm to 1:00pm

Location:

Ross 70
Title: A central limit type conjecture for the nodal statistics of quantum graphs Abstract:
• 2019 May 22

Analysis seminar: Yoel Grinshpon "Fluctuations of linear statistics for Schroedinger operators with a random decaying potential"

12:00pm to 1:00pm

Location:

Ross 70
Title: Fluctuations of linear statistics for Schroedinger operators with a random decaying potential Abstract: Linear statistics provide a tool for the analysis of fluctuations of random measures and have been extensively studied for various models in random matrix theory. In this talk we discuss the application of the same philosophy to the analysis of the finite volume eigenvalue counting measure of one dimensional Schroedinger operators and demonstrate it with some interesting results in the case of a random decaying potential. This is joint work with Jonathan Breuer and Moshe White.
• 2019 May 15

Analysis Seminar: Matthias Keller (Potsdam) "Path integral representations for magnetic Schroedinger operators on graphs"

12:00pm to 1:00pm

Location:

Ross 70
Title: Path integral representations for magnetic Schroedinger operators on graphs Abstract: We consider the semigroup and the unitary group of magnetic Schrödinger operators on graphs. Using the ideas of the Feynman Kac formula, we develop a representation of the semigroup and the unitary group in terms of the stochastic process associated with the free Laplacian. As a consequence we derive Kato-Simon estimates for the unitary group. This is joint work with Batu Güneysu (Bonn).
• 2019 May 01

Analysis Seminar: Nir Lev (BIU) "On tiling the real line by translates of a function"

12:00pm to 1:00pm

Location:

Ross 70
Title: On tiling the real line by translates of a function Abstract: If f is a function on the real line, then a system of translates of f is said to be a << tiling >> if it constitutes a partition of unity. Which functions can tile the line by translations, and what can be said about the structure of the tiling? I will give some background on the problem and present our results obtained in joint work with Mihail Kolountzakis.
• 2019 Apr 10

Special Analysis Seminar: Dirk Hundertmark (Karlsruhe) "Cwikel's bound reloaded"

2:30pm to 3:30pm

Location:

Sprinzak 24
Title: Cwikel's bound reloaded Abstract: There are a couple of proofs by now for the famous Cwikel--Lieb--Rozenblum (CLR) bound, which is a semiclassical bound on the number of bound states for a Schr\"odinger operator, proven in the 1970s.
• 2019 Apr 10

Analysis Seminar: Gregory Berkolaiko (Texas A&M) "Nodal statistics of graph eigenfunctions"

12:00pm to 1:00pm

Location:

Ross 70
Title: Nodal statistics of graph eigenfunctions Abstract: Understanding statistical properties of zeros of Laplacian eigenfunctions is a program which is attracting much attention from mathematicians and physicists. We will discuss this program in the setting of "quantum graphs", self-adjoint differential operators acting on functions living on a metric graph. Numerical studies of quantum graphs motivated a conjecture that the distribution of nodal surplus (a suitably rescaled number of zeros of the n-th eigenfunction) has a universal form: it approaches Gaussian
• 2019 Apr 03

Analysis Seminar: Malte Gerhold (Technion) "Dilations of q-commuting unitaries"

12:00pm to 1:00pm

Location:

Ross 70
Title: Dilations of q-commuting unitaries Abstract: Let (u,v) be a pair of unitary operators on a Hilbert space H such that vu=quv for a complex number q of modulus 1. For q' another complex number of modulus 1, we determine the smallest constant c>0 for which there exists a pair of q' commuting unitaries (U,V) on a larger Hilbert space K containing H such that (u,v) is the compression of (cU,cV) to H.