2016 Nov 22

SPECIAL Analysis and PDEs seminar -D. Fajman "Dynamics of Spacetime — Einstein’s equations as a geometric flow."

11:00am to 12:00pm

Ross 70
Abstract:
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
$\lambda_n(x) = \left[ \sum_{k=0}^n p_k(x)^2 \right]^{-1}.$
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 Nov 22

Jerusalem Analysis Seminar: "Inverse Problems with applications to Cryo-Electron Microscopy (cryo-EM)",Roy Lederman

12:00pm to 1:00pm

Location:

Ross 70
Abstract: Cryo-EM is an imaging technology that is revolutionizing structural biology; the Nobel Prize in Chemistry 2017 was recently awarded to Jacques Dubochet, Joachim Frank and Richard Henderson “for developing cryo-electron microscopy for the high-resolution structure determination of biomolecules in solution".
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.
2016 Jul 30

לכתוב מייל למורי תכנית הנשיא על פגישה ב-14.8

10:00am to 11:00am

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.
2017 Mar 09

Analysis and PDEs: Iosif Polterovich (Montreal) - Nodal Geometry of Steklov Eigenfunctions

12:00pm to 1:00pm

Location:

Ross 70
I will present an overview of some recent progress on the study of the nodal sets of Steklov eigenfunctions. In particular, I will discuss sharp estimates on the nodal length of Steklov eigenfunctions on real-analytic Riemannian surfaces with boundary obtained in my joint
work with D. Sher and J. Toth.
2017 May 18

Mark Rudelson: Delocalization of the eigenvectors of random matrices.

1:00pm to 2:00pm

Location:

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.
2016 Mar 31

PDE & Analysis: Mark Ruselson (UMichigan) - No-gaps delocalization for general random matrices.

1:00pm to 2:30pm

Location:

Ross 70
Title: No-gaps delocalization for general random matrices.
Abstract:
2017 Dec 20

Jerusalem Analysis Seminar: "Translation invariant probability measures on the space of entire functions." Adi Glucksam

12:00pm to 1:00pm

Location:

Ross 70
20 years ago Weiss constructed a collection of non-trivial translation invariant probability measures on the space of entire functions using tools from dynamical systems. In this talk, we will present another elementary construction of such a measure, and give upper and lower bounds for the possible growth of entire functions in the support of such measures.
2016 Dec 22

Analysis and PDE's Seminar -- Percy Deift (Courant)

1:00pm to 2:00pm

Location:

Ross 70
On the Asymptotic behavior of a log gas in the bulk scaling limit in the presence of a varying external potential.
T.Bothner, P.Deift, A.Its and I.Krasovsky
Abstract: We study the partition function Z of a Coulomb gas of particles with an external potential 2v applied to the
particles in an interval of length L. When v is infinite, Z describes the gap probability for GUE eigenvalues in the bulk scaling limit,
and has been well-studied for many years. Here we study the the behavior of Z in the full (v,L) plane.
2017 May 17

Mark Rudelson: Delocalization of the eigenvectors of random matrices.

2:00pm to 3:00pm

Location:

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.