Analysis

The Analysis seminar meets on Wednesdays at 12:00 at room 70 in the Ross Building.
2018 May 30

Analysis Seminar: Evgeny Strahov ( HUJI) "Product matrix processes"

12:15pm to 1:15pm

Abstract: I will discuss a family of random processes in discrete time related to products of random matrices (product matrix processes). Such processes are formed by singular values of random matrix products, and the number of factors in a random matrix product plays a role of a discrete time. I will explain that in certain cases product matrix processes are discrete-time determinantal point processes, whose correlation kernels can be expressed in terms of double contour integrals. This enables to investigate determinantal processes for products of ra ndom matrices in
2018 Jun 13

Analysis Seminar: Raz Kupferman (HUJI) "The bending energy of bucked edge-dislocations"

12:00pm to 1:00pm

Location: 

Ross building, room 70
Abstract: The study of elastic membranes carrying topological defects has a longstanding history, going back at least to the 1950s. When allowed to buckle in three-dimensional space, membranes with defects can totally relieve their in-plane strain, remaining with a bending energy, whose rigidity modulus is small compared to the stretching modulus.
2018 May 23

Analysis Seminar: Ori Gurel-Gurevich (HUJI) "Random walks on planar graphs"

12:00pm to 1:00pm

Location: 

Ross Building, Room 70
Title: Random walks on planar graphs Abstract: We will discuss several results relating the behavior of a random walk on a planar graph and the geometric properties of a nice embedding of the graph in the plane (e.g. a circle packing of the graph). An example of such a result is that for a bounded degree graph, the simple random walk is recurrent if and only if the boundary of the nice embedding is a polar set (that is, Brownian motion misses it almost surely). No prior knowledge about random walks, circle packings or Brownian motion is required.
2018 Jun 27

Analysis Seminar: Barry Simon (Caltech) "Heinävarra’s Proof of the Dobsch–Donoghue Theorem"

12:00pm to 1:00pm

Location: 

Ross Building, Room 70
Abstract: In 1934, Loewner proved a remarkable and deep theorem about matrix monotone functions. Recently, the young Finnish mathematician, Otte Heinävarra settled a 10 year old conjecture and found a 2 page proof of a theorem in Loewner theory whose only prior proof was 35 pages. I will describe his proof and use that as an excuse to discuss matrix monotone and matrix convex functions including, if time allows, my own recent proof of Loewner’s original theorem.
2018 Apr 11

Analysis Seminar: Cy Maor (Toronto) "The geodesic distance on diffeomorphism groups"

12:00pm to 1:00pm

Location: 

Ross Building, Room 70
Since the seminal work of Arnold on the Euler equations (1966), many equations in hydrodynamics were shown to be geodesic equations of diffeomorphism groups of manifolds, with respect to various Sobolev norms. This led to new ways to study these PDEs, and also initiated the study of of the geometry of those groups as (infinite dimensional) Riemannian manifolds.
2018 Jun 06

Analysis Seminar: Michal Pnueli "Dynamics in a Hamiltonian Impact System"

12:00pm to 1:00pm

Location: 

Ross Building, Room 70
Abstract: Hamiltonian impact systems are dynamical systems in which there are two main mechanisms which dictate the system’s behavior - Hamilton’s equations which govern the motion inside the impact system domain, and the billiard reflection rule which governs the motion upon reaching the domain boundary. As the dynamics in impact systems are piecewise smooth by nature due to the collisions with the boundary, many of the traditional tools used in the analysis of Hamiltonian systems cannot be applied to impact systems in a straightforward manner. This talk will present a
2018 May 02

Analysis Seminar: Bo'az Klartag "Convex geometry and waist inequalities"

12:00pm to 1:00pm

Location: 

room 70, Ross Building
Abstract: We will discuss connections between Gromov's work on isoperimetry of waists and Milman's work on the M-ellipsoid of a convex body. It is proven that any convex body K in an n-dimensional Euclidean space has a linear image K_1 of volume one satisfying the following waist inequality: Any continuous map f from K_1 to R^d has a fiber f^{-1}(t) whose (n-d)-dimensional volume is at least c^{n-d}, where c > 0 is a universal constant. Already in the case where f is linear, this constitutes a slight improvement over known results.
2018 Apr 25

Analysis Seminar: Latif Eliaz "The Essential Spectrum of Schroedinger Operators on Graphs"

12:00pm to 1:00pm

Location: 

Room 70, Ross Building

It is known that the essential spectrum of aSchrödinger operator H on\ell^2(\mathbb{N})  is equal to the union of the spectra of right limits ofH. The naturalgeneralization of this relation to \mathbb{Z}^n  is known to hold as well.In this talk we study thepossibility of generalizing this characterization of \sigma_{ess}(H)  tographs. We show that the general statement fails, while presenting natural families of models where it still holds. 

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