Colloquium

2018 Oct 18

Zabrodsky Lecture 1: Geometry of the moduli space of curves

Lecturer: 

Rahul Pandharipande (ETH Zurich)
2:30pm to 3:30pm

Location: 

Manchester House, Lecture Hall 2

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.

2018 Jun 07

Colloquium: Gabriel Conant (Notre Dame) - "Pseudofinite groups, VC-dimension, and arithmetic regularity"

2:15pm to 3:15pm

Location: 

Manchester Building (Hall 2), Hebrew University Jerusalem
Given a set X, the notion of VC-dimension provides a way to measure randomness in collections of subsets of X. Specifically, the VC-dimension of a collection S of subsets of X is the largest integer d (if it exists) such that some d-element subset Y of X is ""shattered"" by S, meaning that every subset of Y can be obtained as the intersection of Y with some element of S. In this talk, we will focus on the case that X is a group G, and S is the collection of left translates of some fixed subset A of G.
2018 May 10

Colloquium: Zemer Kosloff (Hebrew University) - "Poisson point processes, suspensions and local diffeomprhisms of the real line"

2:30pm to 3:30pm

Location: 

Manchester Building (Hall 2), Hebrew University Jerusalem
The study of the representations theoretic properties of the group of diffeormorphisms of locally compact non compact Riemmanian manifolds which equal to the identity outside a compact set is is linked to a natural quasi invariant action of the group which moves all points of a Poisson point process according to the diffeomorphism (Gelfand-Graev-Vershik and Goldin et al.). Neretin noticed that the local diffeomorphism group is a subgroup of a larger group which he called GMS and that GMS also acts in a similar manner on the Poisson point process.
2018 May 31

Tamar Ziegler (Hebrew University) - "Concatenating cubic structure and polynomial patterns in primes"

2:30pm to 3:30pm

Location: 

Manchester Building (Hall 2), Hebrew University Jerusalem
A major difficulty in finding polynomial patterns in primes is the need to understand their distribution properties at short scales. We describe how for some polynomial configurations one can overcome this problem by concatenating short scale behavior in "many directions" to long scale behavior for which tools from additive combinatorics are available.
2018 May 23

Colloquium: Janos Pach (EPFL Lausanne, IIAS and Renyi Institute Budapest) - "The Crossing Lemma"

4:15pm to 5:15pm

Location: 

Manchester Building (Hall 2), Hebrew University Jerusalem
The Crossing Lemma of Ajtai, Chvátal, Newborn, Szemerédi (1982) and Leighton (1983 )states that if a graph of n vertices and e>4n edges is drawn in the plane, then the number of crossings between its edges must be at least constant times e^3/n^2. This statement, which is asymptotically tight, has found many applications in combinatorial geometry and in additive combinatorics. However, most results that were obtained using the Crossing Lemma do not appear to be optimal, and there is a quest for improved versions of the lemma for graphs satisfying certain special properties.
2018 Jun 21

Colloquium: Erdos lecture - Canceled

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 Jun 14

Colloquium - Zuchovitzky lecture: Lior Yanovski (HUJI) "Homotopy cardinality and the l-adic analyticity of Morava-Euler characteristic"

2:30pm to 3:30pm

Location: 

Manchester Building (Hall 2), Hebrew University Jerusalem
A finite set has an interesting numerical invariant - its cardinality. There are two natural generalizations of "cardinality" to a (homotopy) invariant for (suitably finite) spaces. One is the classical Euler characteristic. The other is the Baez-Dolan "homotopy cardinality". These two invariants, both natural from a certain perspective, seem to be very different from each other yet mysteriously connected. The question of the precise relation between them was popularized by John Baez as one of the "mysteries of counting".
2018 Jun 28

Colloquium: Barry Simon (Caltech) - "More Tales of our Forefathers"

2:30pm to 3:30pm

Location: 

Manchester Building (Hall 2), Hebrew University Jerusalem
This is not a mathematics talk but it is a talk for mathematicians. Too often, we think of historical mathematicians as only names assigned to theorems. With vignettes and anecdotes, I'll convince you they were also human beings and that, as the Chinese say, "May you live in interesting times" really is a curse. Among the mathematicians with vignettes are Riemann, Newton, Poincare, von Neumann, Kato, Loewner, Krein and Noether. This talk is in two parts. The second part will be given from 4:00 to 5:00 (not 5:30) in the Basic Notions seminar.
2018 Mar 22

Colloquium: Gilles Zemor (Université de Bordeaux) - "Additive Combinatorics in Field Extensions"

3:30pm to 4:30pm

Location: 

Manchester Building (Hall 2), Hebrew University Jerusalem
Additive combinatorics enable one to characterize subsets S of elements in a group such that S+S has small cardinality. We are interested in linear analogues of these results, namely characterizing subspaces S in some algebras (mostly extension fields) such that the linear span of the set S^2 of products st, for s,t in S, has small dimension. We shall present a linear analogue of a theorem of Vosper which says that under the right conditions, a sufficiently small dimension for S^2 implies that S has a basis of elements in geometric progression.
2017 May 04

Colloquium: Jozsef Solymozi (UBC) Erdos Lecture Series, "The sum-product problem"

2:30pm to 3:30pm

Location: 

Manchester Building (Hall 2), Hebrew University Jerusalem
The incompatibility of multiplicative and additive structures in various fields and rings is an important phenomena. In this talk I will talk about a special case of it. Let us consider a finite subset of integers, A. The sum set of A is the set of pairwise sums of elements of A and the product set is the set of pairwise products. Erdős and Szemeredi conjectured that either the sum set or the product set should be large, almost quadratic in size of A. The conjecture is still open. Similar questions can be asked over any ring or field.
2017 Apr 20

Colloquium - Avraham (Rami) Aizenbud (Weizmann), "Representation count as a Meeting Point for Analysis, Arithmetic, Geometry and Algebra"

2:30pm to 3:30pm

Location: 

Manchester Building (Hall 2), Hebrew University Jerusalem
Consider the following questions: 1. How does the volume of the set f(x_1,...,x_d) < epsilon behaves when epsilon goes to 0? 2. How does the number of solutions of the equation f(x_1,...,x_d) = 0 (mod n) behaves when n goes to infinity. I will present these and other questions which looks as if they are taken from different areas of mathematics. I'll explain the relation between those questions. Then I'll explain how this relation is used in order to show the following theorem answering a question of Larsen and Lubotzky:
2018 May 03

Colloquium - Dvoretzki lecture 1: Alexei Borodin (MIT) - "Integrable probability"

2:30pm to 3:30pm

Location: 

Manchester Building (Hall 2), Hebrew University Jerusalem
The goal of the talk is to survey the emerging field of integrable probability, whose goal is to identify and analyze exactly solvable probabilistic models. The models and results are often easy to describe, yet difficult to find, and they carry essential information about broad universality classes of stochastic processes.

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