Eventss

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 mathematical disciplines, e.g. in combinatorics, graph theory and geometry. When
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 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.
2018 Oct 25

Colloquium: Karim Adiprasito (HUJI) - Combinatorics, topology and the standard conjectures beyond positivity

2:30pm to 3:30pm

Location: 

Manchester Building (Hall 2), Hebrew University Jerusalem
Consider a simplicial complex that allows for an embedding into R^d. How many faces of dimension d/2 or higher can it have? How dense can they be? This basic question goes back to Descartes. Using it and other rather fundamental combinatorial problems, I will motivate and introduce a version of Grothendieck's "standard conjectures" beyond positivity (which will be explored in detail in the Sunday Seminar). All notions used will be explained in the talk (I will make an effort to be very elementary)
2019 Jun 06

Colloquium: Ram Band (Technion) - Neumann Domains

2:30pm to 3:30pm

Location: 

Manchester Building (Hall 2), Hebrew University Jerusalem
Abstract: The nodal set of a Laplacian eigenfunction forms a partition of the underlying manifold. An alternative partition, based on the gradient field of the eigenfunction, is via the so called Neumann domains. A Neumann domain of an eigenfunction is a connected component of the intersection between the stable manifold of a certain minimum and the unstable manifold of a certain maximum. We introduce this subject, discuss various properties of Neumann domains and point out the similarities and differences between nodal domains and Neumann domains.
2018 Dec 20

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

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 classic theorem of Galvin and Shelah.
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: a discrete irreducible Zariski-dense subgroup of G that intersects cocompactly at least one
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.

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