## Math Calendar

Monday, January 22, 2018

Tuesday, January 23, 2018

12:00-13:00

HFG Library

16:00-17:00

HFG 611

Utrecht Geometry Center Seminar

Julie Desjardins (MPIM Bonn) - Square-free values of a polynomial (and elliptic curves)

see description

Abstract: Let f be a primitive separable polynomial of positive degree in Z[T]. A number theory question : is there infinitely many values f(t) with no square factors ? It is conjectured that the answer is yes, and even more precisely, that a positive proportion of the values are square-free. This is known as the square-free conjecture. In 1953, Erdös showed that for cubics there are infinitely many square-free values, and in 1967, Hooley showed positive proportion when deg=3. The conjecture is still not known for irreducible polynomials of degree greater than 3.

In this talk, we relate this problem to its main motivation: the study of the variation of the analytic rank in a family

of elliptic curves.

In this talk, we relate this problem to its main motivation: the study of the variation of the analytic rank in a family

of elliptic curves.

Thursday, January 25, 2018

16:00-17:00

HFG 611

Monday, January 29, 2018

11:00-12:00

HFG 610

Extra Talk

Adrien Sauvaget (Jussieu) - Volumes and Siegel-Veech constants of $\mathcal{H}(2g-2)$ and Hodge integrals

see description

Abstract:

The Hodge bundle is stratified according to the set of zeros of the differential. In the 80's H. Masur and W. Veech defined two numerical invariants of these strata: the volume and the Siegel-Veech constants.

<br />Based on numerical experiments, A. Eskin and A. Zorich proposed a series of conjectures for the large genus asymptotic of these invariants. By a careful analysis of the asymptotic behavior of quasi-modular forms, D. Chen, M. Moeller, and D. Zagier proved this conjecture for strata of differentials with simple zeros. We will explain how to prove that the conjecture holds in the other extreme case, i.e. for strata of differentials with a unique zero. The main ingredient is the expression of the volumes of these strata in terms of Hodge integrals on moduli spaces of curves.

<br />

Tuesday, January 30, 2018

11:00-12:00

HFG 610

Utrecht Geometry Center Seminar

Cecília Salgado (MPIM Bonn/Instituto de Matemática - UFRJ) - Elliptic fibrations on K3 surfaces and linear systems of curves on rational surfaces

see description

Abstract: We consider K3 surfaces which are double covers of rational elliptic surfaces. The former is endowed with a natural elliptic fibration, which is induced by the latter. These K3 surfaces admit other elliptic fibrations, which are necessarily induced by special linear systems on the rational elliptic surfaces. We describe these linear systems in terms of the non-symplectic (deck) involution. In particular, every conic bundle on the rational surface induces a genus 1 fibration on the K3. We classify the singular fibers of the genus 1 fibration on the K3 surface it terms of singular fibers and special curves on the conic bundle on the rational surface. This is joint work with A. Garbagnati - U. Millano.

Tuesday, February 6, 2018

Thursday, February 8, 2018

16:00-17:00

HFG 611

Tuesday, February 13, 2018

Thursday, February 15, 2018

16:00-17:00

HFG 611

Tuesday, February 20, 2018

16:00-17:00

HFG 611

Tuesday, February 27, 2018

16:00-17:00

HFG 611

Utrecht Geometry Center Seminar

Arne Smeets (Radboud Universiteit Nijmegen) - On the diophantine complexity of p-adic fields

see description

Abstract

There are various notions of the diophantine 'complexity' or 'dimension' of a given field. Given any such notion, algebraically closed fields are the simplest ones. At the next level, one usually finds the finite fields and their 'neighbours'. Yet another step up in complexity, the so-called p-adic fields come into the picture.

I will discuss the properties of p-adic fields from the point of view of one particular notion of diophantine complexity, introduced by Serge Lang in the sixties. This will lead us to the theory of polynomial equations in 'many' variables, the celebrated Ax-Kochen theorem and some model theory.

Next, I will discuss a recent improvement to the Ax-Kochen theorem obtained in joint work by Dan Loughran, Alexei Skorobogatov and the speaker. Our approach to the problem makes heavy use of birational and toroidal geometry, and builds on work of Colliot-Thélène and Denef.

There are various notions of the diophantine 'complexity' or 'dimension' of a given field. Given any such notion, algebraically closed fields are the simplest ones. At the next level, one usually finds the finite fields and their 'neighbours'. Yet another step up in complexity, the so-called p-adic fields come into the picture.

I will discuss the properties of p-adic fields from the point of view of one particular notion of diophantine complexity, introduced by Serge Lang in the sixties. This will lead us to the theory of polynomial equations in 'many' variables, the celebrated Ax-Kochen theorem and some model theory.

Next, I will discuss a recent improvement to the Ax-Kochen theorem obtained in joint work by Dan Loughran, Alexei Skorobogatov and the speaker. Our approach to the problem makes heavy use of birational and toroidal geometry, and builds on work of Colliot-Thélène and Denef.

Tuesday, March 6, 2018

16:00-17:00

HFG 611

Tuesday, March 13, 2018

16:00-17:00

HFG 611

Tuesday, March 20, 2018

16:00-17:00

HFG 611

Thursday, March 22, 2018

15:30-16:30

KBG Atlas

Tuesday, March 27, 2018

16:00-17:00

HFG 611

Tuesday, April 3, 2018

Tuesday, April 10, 2018

16:00-17:00

HFG 611

Tuesday, April 17, 2018

16:00-17:00

HFG 611

Tuesday, April 24, 2018

16:00-17:00

HFG 611

Tuesday, May 1, 2018

Tuesday, May 8, 2018

Tuesday, May 15, 2018

Thursday, May 17, 2018

16:00-17:00

HFG 611

Tuesday, May 22, 2018

Tuesday, May 29, 2018

Tuesday, June 5, 2018

16:00-17:00

HFG 611

Tuesday, June 12, 2018

Tuesday, June 19, 2018

Tuesday, June 26, 2018

Tuesday, July 3, 2018

Tuesday, July 10, 2018

Tuesday, July 17, 2018