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 Jun 27

Colloquium

2:30pm to 3:30pm

Location: 

Manchester Building (Hall 2), Hebrew University Jerusalem
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 Jun 13

Colloquium

2:30pm to 3:30pm

Location: 

Manchester Building (Hall 2), Hebrew University Jerusalem
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 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 $$\sum_j e^{2 pi i \omega_j x}.$$

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