Colloquium

2018 Oct 18

Colloquium: Rahul Pandharipande (ETH Zürich) - Zabrodsky Lecture: Geometry of the moduli space of curves

2:30pm to 3:30pm

Location: 

Manchester Building (Hall 2), Hebrew University Jerusalem
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.
2018 Dec 06

Colloquium: Naomi Feldheim (Bar-Ilan) - A spectral perspective on stationary signals

2:30pm to 3:30pm

Location: 

Manchester Building (Hall 2), Hebrew University Jerusalem
A ``random stationary signal'', more formally known as a Gaussian stationary function, is a random function f:R-->R whose distribution is invariant under real shifts (hence stationary), and whose evaluation at any finite number of points is a centered Gaussian random vector (hence Gaussian). The mathematical study of these random functions goes back at least 75 years, with pioneering works by Kac, Rice and Wiener, who were motivated both by applications in engineering and by analytic questions about ``typical'' behavior in certain classes of functions.
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.

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