Events & Seminars

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. We will focus on two recent advances.
2019 Mar 11

Combinatorics Seminar: Yuval Filmus (Technion) "Structure of (almost) low-degree Boolean functions"

11:00am to 1:00pm

Location: 

CS bldg, room B500, Safra campus, Givat Ram
Speaker: Yuval Filmus, Technion Title: Structure of (almost) low-degree Boolean functions Abstract: Boolean function analysis studies (mostly) Boolean functions on {0,1}^n. Two basic concepts in the field are *degree* and *junta*. A function has degree d if it can be written as a degree d polynomial. A function is a d-junta if it depends on d coordinates. Clearly, a d-junta has degree d. What about the converse (for Boolean functions)? What if the Boolean function is only *close* to degree d? The questions above were answered by Nisan-Szegedy, Friedgut-Kalai-Naor, and Kindler-Safra.
2018 Oct 23

Dynamics Lunch: Amir Algom "On \alpha \beta sets."

12:00pm to 1:00pm

Location: 

Manchester faculty club
Let $\alpha, \beta$ be elements of infinite order in the circle group. A closed set K in the circle is called an \alpha \beta set if for every x\in K either x+\alpha \in K or x+\beta \in K. In 1979 Katznelson proved that there exist non-dense \alpha \beta sets, and that there exist \alpha \beta sets of arbitrarily small Hausdorff dimension. We shall discuss this result, and a more recent result of Feng and Xiong, showing that the lower box dimension of every \alpha \beta set is at least 1/2.
2019 Jan 10

Joram Seminar: Larry Guth (MIT) - Introduction to decoupling

2:30pm to 3:30pm

Location: 

Manchester Building (Hall 2), Hebrew University Jerusalem
Decoupling is a recent development in Fourier analysis. In the late 90s, Tom Wolff proposed a decoupling conjecture and made the first progress on it. The full conjecture had seemed well out of reach until a breakthrough by Jean Bourgain and Ciprian Demeter about five years ago. Decoupling has applications to problems in PDE and also to analytic number theory. One application involves exponential sums, sums of the form $$\sum_j e^{2 pi i \omega_j x}.$$
2018 Jun 28

Basic Notions: Barry Simon "More Tales of our Forefathers (Part II)"

4:00pm to 5:30pm

Location: 

Manchester Hall 2
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.
2018 Jun 27

Amitsur Symposium: Chloe Perin - "Forking independence in the free group"

2:00pm to 3:00pm

Location: 

Manchester House, Lecture Hall 2
Model theorists define, in structures whose first-order theory is "stable" (i.e. suitably nice), a notion of independence between elements. This notion coincides for example with linear independence when the structure considered is a vector space, and with algebraic independence when it is an algebraically closed field. Sela showed that the theory of the free group is stable. In a joint work with Rizos Sklinos, we give an interpretation of this model theoretic notion of independence in the free group using Grushko and JSJ decompositions.
2018 Jun 26

Amitsur Symposium: Aner Shalev - "The length and depth of finite groups, algebraic groups and Lie groups"

3:00pm to 4:00pm

Location: 

Manchester House, Lecture Hall 2
The length of a finite group G is defined to be the maximal length of an unrefinable chain of subgroups going from G to 1. This notion was studied by many authors since the 1940s. Recently there is growing interest also in the depth of G, which is the minimal length of such a chain. Moreover, similar notions were defined and studied for important families of infinite groups, such as connected algebraic groups and connected Lie groups.
2018 Jun 26

Amitsur Symposium: Malka Schaps - "Symmetric Kashivara crystals of type A in low rank"

11:30am to 12:30pm

Location: 

Manchester House, Lecture Hall 2
The basis of elements of the highest weight representations of affine Lie algebra of type A can be labeled in three different ways, my multipartitions, by piecewise linear paths in the weight space, and by canonical basis elements. The entire infinite basis is recursively generated from the highest weight vector of operators f_i from the Chevalley basis of the affine Lie algebra, and organized into a crystal called a Kashiwara crystal. We describe cases where one can move between the different labelings in a non-recursive fashion, particularly when the crystal has some symmetry.

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