Eventss

2017 Mar 02

Basic Notions: Ori Gurel Gurevich (HUJI) - On Smirnov's proof of conformal invariance of critical percolation

4:00pm to 5:00pm

Location: 

Manchester Building, Lecture Hall 2
Abstract:

Let G be an infinite connected graph. For each vertex of G we decide
randomly and independently: with probability p we paint it blue and
with probability 1-p we paint it yellow. Now, consider the subgraph of
blue vertices: does it contain an infinite connected component?

There is a critical probability p_c(G), such that if p>p_c then almost
surely there is a blue infinite connected component and if pp_c or p<p_c.

We will focus on planar graphs, specifically on the triangular
2018 Jan 11

Basic Notions: Michael Hopkins (Harvard) - Homotopy theory and algebraic vector bundles

4:00pm to 5:15pm

Location: 

Einstein 2
Abstract: This talk will describe joint work with Aravind Asok and Jean Fasel using the methods of homotopy theory to construct new examples of algebraic vector bundles. I will describe a natural conjecture which, if true, implies that over the complex numbers the classification of algebraic vector bundles over smooth affine varieties admitting an algebraic cell decomposition coincides with the classification of topological complex vector bundles.
2017 Dec 27

Jerusalem Analysis Seminar: "Optimal Gaussian Partitions", Elchanan Mossel (MIT)

12:00pm to 1:00pm

Location: 

Ross 70

 How should we partition the Gaussian space into k parts in a way that minimizes Gaussian surface area, maximize correlation or simulate a specific distribution. The problem of Gaussian partitions was studied since the 70s first as a generalization of the isoperimetric problem in the context of the heat equation. It found a renewed interest in the context of the double bubble theorem proven in geometric measure theory and due to connection to problems in theoretical computer science and social choice theory. 

2017 Apr 27

PDE and Analysis Seminar: Grzegorz Swiderski (Wroclaw)

1:00pm to 2:00pm

Location: 

Ross 70
Title: Asymptotics of Christoffel functions in an unbounded setting Abstract: Consider a measure $\mu$ supported on the real line with all moments finite. Let $(p_n : n \geq 0)$ be the corresponding sequence of orthonormal polynomials. This sequence satisfies the three-term recurrence relation \[ a_{n-1} p_{n-1}(x) + b_n p_n(x) a_n p_{n+1}(x) = x p_n(x) \quad (n > 0) \] for some sequences $a$ and $b$. One defines the $n$th Christoffel function by \[ \lambda_n(x) = \left[ \sum_{k=0}^n p_k(x)^2 \right]^{-1}. \] In the talk, under some regularity hypotheses on $a$ and $b$, we show
2017 Dec 06

Jerusalem Analysis and PDEs seminar: "Asymptotics of the ground state energy for relativistic heavy atoms and molecules" Victor Ivrii (Toronto)

12:00pm to 1:00pm

Location: 

Ross 70.
We discuss sharp asymptotics of the ground state energy for the heavy atoms and molecules in the relativistic settings, without magnetic field or with the self-generated magnetic field, and, in particular, relativistic Scott correction term and also Dirac, Schwinger and relativistic correction terms. In particular, we conclude that the Thomas-Fermi density approximates the actual density of the ground state, which opens the way to estimate the excessive negative and positive charges and the ionization energy.
2016 Nov 10

Analysis and PDEs - Maurice Duits (KTH) Title: Global fluctuations for non-colliding processes

1:00pm to 2:00pm

Location: 

Ross 70
In this talk we will discuss the global fluctuations for a class of determinantal point processes coming from large systems of non-colliding processes and non-intersecting paths. By viewing the paths as level lines these systems give rise to random (stepped) surfaces. When the number of paths is large a limit shape appears. The fluctuations for the random surfaces are believed to be universally described by the Gaussian Free Field.
2017 Mar 16

Analysis and PDEs: Mayukh Mukherjee (Technion) - Some asymptotic estimates on the geometry of Laplace eigenfunctions

1:00pm to 2:00pm

Location: 

Ross 70
Given a closed smooth Riemannian manifold M, the Laplace operator is known to possess a discrete spectrum of eigenvalues going to infinity. We are interested in the properties of the nodal sets and nodal domains of corresponding eigenfunctions in the high energy limit. We focus on some recent results on the size of nodal domains and tubular neighbourhoods of nodal sets of such high energy eigenfunctions (joint work with Bogdan Georgiev).
2017 Jun 15

Analysis and PDEs, "Quantum state transfer on graphs", G. Lippner (neu)

1:00pm to 2:00pm

Location: 

Ross 70
Title: Quantum state transfer on graphs. Abstract: Transmitting quantum information losslessly through a network of particles is an important problem in quantum computing. Mathematically this amounts to studying solutions of the discrete Schrödinger equation d/dt phi = i H phi, where H is typically the adjacency or Laplace matrix of the graph. This in turn leads to questions about subtle number-theoretic behavior of the eigenvalues of H.
2017 Nov 15

Jerusalem Analysis Seminar: "Operators and random walks", Gady Kozma (Weizmann Institute)

12:00pm to 1:00pm

Location: 

Ross 70 (NOTE LOCATION!)
Abstract: We will discuss the question: for a random walk in a random environment, when should one expect a central limit theorem, i.e. that after appropriate scaling, the random walk converges to Brownian motion? The answer will turn out to involve the spectral theory of unbounded operators. All notions will be defined in the talk. Joint work with Balint Toth.

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