Events & Seminars

2018 Nov 21

Analysis Seminar: Asaf Shachar (HUJI) "Regularity via minors and applications to conformal maps"

12:00pm to 1:00pm

Location: 

Room 70, Ross Building
Title:
Regularity via minors and applications to conformal maps.
Abstract:
Let f:\mathbb{R}^n \to \mathbb{R}^n be a Sobolev map; Suppose that the k-minors of df are smooth. What can we say about the regularity of f?
This question arises naturally in the context of Liouville's theorem, which states that every weakly conformal map is smooth. I will explain the connection of the minors question to the conformal regularity problem, and describe a regularity result for maps with regular minors.
2018 Oct 18

Colloquium: Rahul Pandharipande (ETH Zürich) - Zabrodsky Lecture: Geometry of the moduli space of curves

2:30pm to 3:30pm

Location: 

Manchester Building (Hall 2), Hebrew University Jerusalem
The moduli space of curves, first appearing in the work of Riemann in the 19th century, plays an important role in geometry. After an introduction to the moduli space, I will discuss recent directions in the study of tautological classes on the moduli space following ideas and conjectures of Mumford, Faber-Zagier, and Pixton. Cohomological Field Theories (CohFTs) play an important role. The talk is about the search for a cohomology calculus for the moduli space of curves parallel to what is known for better understood geometries.
2018 Dec 06

Colloquium: Naomi Feldheim (Bar-Ilan) - A spectral perspective on stationary signals

2:30pm to 3:30pm

Location: 

Manchester Building (Hall 2), Hebrew University Jerusalem
A ``random stationary signal'', more formally known as a Gaussian stationary function, is a random function f:R-->R whose distribution is invariant under real shifts (hence stationary), and whose evaluation at any finite number of points is a centered Gaussian random vector (hence Gaussian).
The mathematical study of these random functions goes back at least 75 years, with pioneering works by Kac, Rice and Wiener, who were motivated both by applications in engineering and
by analytic questions about ``typical'' behavior in certain classes of functions.
2019 Apr 11

Colloquium: Ohad Feldheim - Lattice models of magnetism: from magnets to antiferromagnets

2:30pm to 3:30pm

Location: 

Manchester Building (Hall 2), Hebrew University Jerusalem

Abstract:
The Ising model, and its generalisation, the Potts model, are two classical graph-colouring models for magnetism and antiferromagnetism. Albeit their simple formulation, these models were instrumental in explaining many real-world magnetic phenomena and have found various applications in physics, biology and computer science. While our understanding of these models as modeling magnets has been constantly improving since the early twentieth century, little progress was made in treatment of Potts antiferromagnets.
2019 May 30

Colloquium: Alon Nishry (TAU) - Zeros of random power series

2:30pm to 3:30pm

Location: 

Manchester Building (Hall 2), Hebrew University Jerusalem

Abstract:
A central problem in complex analysis is how to describe zero sets of power series in terms of their coefficients. In general, it is difficult to obtain precise results for a given function. However, when the function is defined by a power series, whose coefficients are independent random variables, such results can be obtained. Moreover, if the coefficients are complex Gaussians, the results are especially elegant. In particular, in this talk I will discuss some different notions of "rigidity" of the zero sets.
2018 Dec 13

Erdos Lectures: Igor Pak (UCLA) - Counting integer points in polytopes

Lecturer: 

Igor Pak (UCLA)
2:30pm to 3:30pm

Location: 

Manchester Building (Hall 2), Hebrew University Jerusalem
Given a convex polytope P, what is the number of integer points in P? This problem is of great interest in combinatorics and discrete geometry, with many important applications ranging from integer programming to statistics. From a computational point of view it is hopeless in any dimensions, as the knapsack problem is a special case. Perhaps surprisingly, in bounded dimension the problem becomes tractable. How far can one go? Can one count points in projections of P, finite intersections of such projections, etc?
2018 Dec 27

Colloquium: Alexander Yom Din (Caltech) - From analysis to algebra to geometry - an example in representation theory of real groups

2:30pm to 3:30pm

Location: 

Manchester Building (Hall 2), Hebrew University Jerusalem
Representation theory of non-compact real groups, such as SL(2,R), is a fundamental discipline with uses in harmonic analysis, number theory, physics, and more. This theory is analytical in nature, but in the course of the 20th century it was algebraized and geometrized (the key contributions are by Harish-Chandra for the former and by Beilinson-Bernstein for the latter). Roughly and generally speaking, algebraization strips layers from the objects of study until we are left with a bare skeleton, amenable to symbolic manipulation.
2019 Mar 14

Colloquium: Alexander Bors (University of Western Australia) - Finite groups with a large automorphism orbit

2:30pm to 3:30pm

Location: 

Manchester Building (Hall 2), Hebrew University Jerusalem
Abstract: If X is an object such that the notion of an automorphism of X is defined (e.g.,
an algebraic structure, a graph, a topological space, etc.), then one can define an
equivalence relation ∼ on X via x ∼ y if and only if α(x) = y for some automorphism
α of X. The equivalence classes of ∼ are called the automorphism orbits of X.
Say that X is highly symmetric if and only if all elements of X lie in the same
automorphism orbit. Finite highly symmetric objects are studied across various
2019 May 02

Colloquium: Jake Solomon- Pointwise mirror symmetry

2:30pm to 3:30pm

Location: 

Manchester Building (Hall 2), Hebrew University Jerusalem

Abstract: Mirror symmetry is a correspondence between symplectic geometry on a manifold M and complex geometry on a mirror manifold W. The question of why one sort of geometry on M should be reflected in another sort of geometry on the topologically distinct manifold W, and the question of how to find W given M, are a priori highly mysterious. One attempt to explain the mysteries of mirror symmetry is the SYZ conjecture, which asserts that the mirror manifold W can be realized as the moduli space of certain objects of a category associated to M.
2018 Nov 08

Colloquium: Nathan Keller (Bar Ilan) - The junta method for hypergraphs and the Erdos-Chvatal simplex conjecture

2:30pm to 3:30pm

Location: 

Manchester Building (Hall 2), Hebrew University Jerusalem
Numerous problems in extremal hypergraph theory ask to determine the maximal size of a k-uniform hypergraph on n vertices that does not contain an 'enlarged' copy H^+ of a fixed hypergraph H. These include well-known problems such as the Erdos-Sos 'forbidding one intersection' problem and the Frankl-Furedi 'special simplex' problem.
2019 Jun 27

Colloquium Dvoretzky lecture: Assaf Naor(Princeton) - An average John theorem

2:30pm to 3:30pm

Location: 

Manchester Building (Hall 2), Hebrew University Jerusalem

Abstract: We will prove a sharp average-case variant of a classical embedding theorem of John through the theory of nonlinear spectral gaps. We will use this theorem to provide a new answer to questions of Johnson and Lindenstrauss (1983) and Bourgain (1985) on metric dimension reduction, and explain how it leads to algorithms for approximate nearest neighbor search.
2019 Jan 03

Colloquium: Nati Linial (HUJI) - Graph metrics

2:30pm to 3:30pm

A finite graph is automatically also a metric space, but is there any interesting geometry to speak of? In this lecture I will try to convey the idea that indeed there is very interesting geometry to explore here. I will say something on the local side of this as well as on the global aspects. The k-local profile of a big graph G is the following distribution. You sample uniformly at random k vertices in G and observe the subgraph that they span. Question - which distributions can occur? We know some of the answer but by and large it is very open.

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