Events & Seminars

2019 Apr 04

Colloquium: Uri Shapira (Technion) - Dynamics on hybrid homogeneous spaces

2:30pm to 3:30pm

Location: 

Manchester Building (Hall 2), Hebrew University Jerusalem
Abstract: I will discuss a collection of results about lattices and their subgroups in Euclidean space which are obtained using dynamics on homogeneous spaces. The ergodic theory of group actions on spaces obtained by quotienning a Lie group by a lattice (spaces of lattice-type) or on projective spaces are extensively studied and display distinct dynamical phenomena. Motivated by classical questions in Diophantine approximation we are led to study the ergodic theory of group actions on hybrid homogeneous spaces which are half projective and half of lattice type.
2019 May 23

Colloquium: Yves Benoist (University of Paris-Sud) - Arithmeticity of discrete groups

2:30pm to 3:30pm

Location: 

Manchester Building (Hall 2), Hebrew University Jerusalem
By a theorem of Borel and Harish-Chandra,
an arithmetic group in a semisimple Lie group is a lattice.
Conversely, by a celebrated theorem of Margulis,
in a higher rank semisimple Lie group G
any irreducible lattice is an arithmetic group.
The aim of this lecture is to survey an
arithmeticity criterium for discrete subgroups
which are not assumed to be lattices.
This criterium, obtained with Miquel,
generalizes works of Selberg and Hee Oh
and solves a conjecture of Margulis. It says:
2018 Nov 29

Colloquium: Chaya Keller (Technion) - Improved lower and upper bounds on the Hadwiger-Debrunner numbers

2:30pm to 3:30pm

Location: 

Manchester Building (Hall 2), Hebrew University Jerusalem
A family of sets F is said to satisfy the (p,q)-property if among any p sets in F, some q have a non-empty intersection. Hadwiger and Debrunner (1957) conjectured that for any p > q > d there exists a constant c = c_d(p,q), such that any family of compact convex sets in R^d that satisfies the (p,q)-property, can be pierced by at most c points. Helly's Theorem is equivalent to the fact that c_d(p,p)=1 (p > d).
2018 Nov 15

Colloquium: Ari Shnidman (Boston College) - Rational points on elliptic curves in twist families

2:30pm to 3:30pm

Location: 

Manchester Building (Hall 2), Hebrew University Jerusalem
The rational solutions on an elliptic curve form a finitely generated abelian group, but the maximum number of generators needed is not known. Goldfeld conjectured that if one also fixes the j-invariant (i.e. the complex structure), then 50% of such curves should require 1 generator and 50% should have only the trivial solution. Smith has recently made substantial progress towards this conjecture in the special case of elliptic curves in Legendre form. I'll discuss recent work with Lemke Oliver, which bounds the average number of generators for general j-invariants.
2019 Jan 17

Colloquium: Lior Bary-Soroker (TAU) - Virtually all polynomials are irreducible

2:30pm to 3:30pm

Location: 

Manchester Building (Hall 2), Hebrew University Jerusalem
It has been known for almost a hundred years that most polynomials with integral coefficients are irreducible and have a big Galois group. For a few dozen years, people have been interested in whether the same holds when one considers sparse families of polynomials—notably, polynomials with plus-minus 1 coefficients. In particular, “some guy on the street” conjectures that the probability for a random plus-minus 1 coefficient polynomial to be irreducible tends to 1 as the degree tends to infinity (a much earlier conjecture of Odlyzko-Poonen is about the 0-1 coefficients model).
2018 Nov 01

Colloquium: Natan Rubin (BGU) - Crossing Lemmas, touching Jordan curves, and finding large cliques

2:30pm to 3:30pm

Location: 

Manchester Building (Hall 2), Hebrew University Jerusalem
It is a major challenge in Combinatorial Geometry to understand the intersection structure of the edges in a geometric or topological graph, in the Euclidean plane. One of the few "tight" results in this direction is the the Crossing Lemma (due to Ajtai, Chvatal, Newborn, and Szemeredi 1982, and independently Leighton 1983). It provides a relation between the number of edges in the graph and the number of crossings amongst these edges. This line of work led to several Ramsey-type questions of geometric nature.
2018 Nov 22

Colloquium: Spencer Unger (HUJI) - A constructive solution to Tarski's circle squaring problem

2:30pm to 3:30pm

Location: 

Manchester Building (Hall 2), Hebrew University Jerusalem
In 1925, Tarski asked whether a disk in R^2 can be partitioned into finitely many pieces which can be rearranged by isometries to form a square of the same area. The restriction of having a disk and a square with the same area is necessary. In 1990, Laczkovich gave a positive answer to the problem using the axiom of choice. We give a completely explicit (Borel) way to break the circle and the square into congruent pieces. This answers a question of Wagon. Our proof has three main components. The first is work of Laczkovich in Diophantine approximation.
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?

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