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2018 Dec 20

Colloquium: Assaf Rinot (Bar-Ilan) - Hindman’s theorem and uncountable Abelian groups

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2:30pm to 3:30pm

Location: 

Manchester Building (Hall 2), Hebrew University Jerusalem
In the early 1970’s, Hindman proved a beautiful theorem in
additive Ramsey theory asserting that for any partition of the set of
natural numbers into finitely many cells, there exists some infinite set
such that all of its finite sums belong to a single cell.
In this talk, we shall address generalizations of this statement to the
realm of the uncountable. Among other things, we shall present a
negative partition relation for the real line which simultaneously
generalizes a recent theorem of Hindman, Leader and Strauss, and a
2019 Apr 04

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

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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

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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

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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

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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.
2018 Oct 21

Zabrodsky Lecture 2: Cohomological Field Theories

Lecturer: 

Rahul Pandharipande (ETH Zurich)
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11:00am to 12:00pm

Location: 

Ross 70
Cohomological Field Theories (CohFTs) were introduced to keep track of the classes on the moduli spaces of curves defined by Gromov-Witten theories and their cousins. I will define CohFTs (following Kontsevich-Manin), explain the classification in the semisimple case of Givental-Teleman, and discuss the application to Pixton's relations which appear in the first lecture.
2018 Oct 18

Zabrodsky Lecture 1: Geometry of the moduli space of curves

Lecturer: 

Rahul Pandharipande (ETH Zurich)
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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. 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. My goal is to give a presentation of the progress in the past decade and the current state of the field.

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