## Math Calendar

Tuesday, October 22, 2019

16:00-17:00

HFG 611

Utrecht Geometry Center Seminar

Yukako Kezuka (Regensburg) - Iwasawa theory and its relation to the Birch-Swinnerton-Dyer Conjecture

see description

The aim of this talk is to give an overview of the origin and the basic ideas of Iwasawa theory, and its relation to the conjecture of Birch and Swinnerton-Dyer (BSD). The BSD conjecture, which relates an analytic invariant of an elliptic curve to the arithmetic of the curve, is unquestionably one of the most important open problems in number theory today. Inspired by Kummer's attempt to solve Fermat's Last Theorem and the mysterious connection between ideal class groups and zeta values it displayed, Iwasawa developed in 1959 an idea which later evolved into one of the fundamental branches of modern number theory. Iwasawa theory has been applied to a wide circle of problems in which values of L-functions (or zeta functions) play a key role, and proved to be one of the most fruitful ways of understanding the BSD conjecture.

Thursday, October 24, 2019

16:00-17:00

BBG.7.12

Mathematical Physics Seminar

Sakura Schafer-Nameki (Oxford)-5d SCFTs, Calabi-Yau Threefold Singularities and Gauge Theories

see description

The goal of this program is to classify 5d Superconformal Field Theories (SCFTs), using M-theory on non-compact singular Calabi-Yau threefolds. Motivated by the connection between 5d and 6d SCFTs, we study this problem using elliptic three-folds. Resolutions of the singularities are mapped to gauge theories in 5d. We develop a precise map between the geometry, SCFTs and gauge theory using graphs, which encode salient non-perturbative features such as their superconformal flavor symmetry, RG-flows and BPS states.

16:00-17:00

HFG 611

Tuesday, October 29, 2019

16:00-17:00

HFG 611

Utrecht Geometry Center Seminar

Clélia Pech (University of Kent) - Geometry of rational curves on some varieties with a Lie group action

see description

In this talk I will describe a family of algebraic varieties with actions of Lie groups which are closely related to homogeneous spaces (which for instance include projective spaces, quadrics, Grassmannians). After describing the geometry and the orbit structure of these varieties, I will explain how to understand rational curves on these varieties, as well as an algebraic structure encoding the intersection theory of these curves, called the quantum cohomology ring. This is joint work with R. Gonzales, N. Perrin, and A. Samokhin.

Thursday, October 31, 2019

Tuesday, November 5, 2019

Thursday, November 7, 2019

16:00-17:00

HFG 611

Tuesday, November 12, 2019

16:00-17:00

MIN 014

Utrecht Geometry Center Seminar

Sebastian Hensel (LMU München) - Symmetries of surfaces and curve graphs

see description

Abstract: Surfaces are amongst the most ubiquitous objects in geometry

and topology. While they are very basic topological spaces, their

symmetry groups are surprisingly rich and still produce a wealth of

interesting questions.

In recent years, negatively curved geometry has turned out to be a

particularly successful tool in the study of mapping class groups. This

is facilitated by the so-called curve graph, which encodes intersection

patterns between simple closed curves on surfaces.

In this talk we will explore these connections, starting with very

classical and explicit examples, and ending with a very recent result

(joint with Jonathan Bowden and Richard Webb) which answers a question

of Burago-Ivanov-Polterovich on isotopically trivial surface homeomorphisms.

and topology. While they are very basic topological spaces, their

symmetry groups are surprisingly rich and still produce a wealth of

interesting questions.

In recent years, negatively curved geometry has turned out to be a

particularly successful tool in the study of mapping class groups. This

is facilitated by the so-called curve graph, which encodes intersection

patterns between simple closed curves on surfaces.

In this talk we will explore these connections, starting with very

classical and explicit examples, and ending with a very recent result

(joint with Jonathan Bowden and Richard Webb) which answers a question

of Burago-Ivanov-Polterovich on isotopically trivial surface homeomorphisms.

Thursday, November 14, 2019

15:30-16:30

KBG Pangea

Tuesday, November 19, 2019

16:00-17:00

MIN 014

Thursday, November 21, 2019

16:00-17:00

HFG 611

Tuesday, November 26, 2019

16:00-17:00

MIN 014

Thursday, November 28, 2019

Tuesday, December 3, 2019

16:00-17:00

MIN 014

Utrecht Geometry Center Seminar

Lucas Dahinden (Universite de Neuchatel) - Moduli spaces of Linkages

see description

Abstract:

A linkage in the plane is an n-gon with fixed sidelengths but free angles.

Question: What is the space of configurations of a given linkage?

Exercises: Answer the question for linkages whose sidelengths are

1 - (1,1,1)

2 - (3,1,1)

3 - (10,10,10,1)

4 - (20,10,10,1)

There is a surprisingly simple classification of these spaces which is based on a combinatorial formula for the Betti numbers. The technical tool is Morse theory.

Follow-up question: how many diffeomorphism types of manifolds are realizable as such a moduli space?

This question is harder than it looks if a precise answer is needed. However, we can find asymptotic bounds that show superexponential behaviour.

A linkage in the plane is an n-gon with fixed sidelengths but free angles.

Question: What is the space of configurations of a given linkage?

Exercises: Answer the question for linkages whose sidelengths are

1 - (1,1,1)

2 - (3,1,1)

3 - (10,10,10,1)

4 - (20,10,10,1)

There is a surprisingly simple classification of these spaces which is based on a combinatorial formula for the Betti numbers. The technical tool is Morse theory.

Follow-up question: how many diffeomorphism types of manifolds are realizable as such a moduli space?

This question is harder than it looks if a precise answer is needed. However, we can find asymptotic bounds that show superexponential behaviour.

Friday, December 6, 2019

Tuesday, December 10, 2019

Tuesday, December 17, 2019

Thursday, December 19, 2019

Tuesday, January 7, 2020

16:00-17:00

MIN 014

Tuesday, January 14, 2020

16:00-17:00

MIN 014

Utrecht Geometry Center Seminar

Ivan Beschastnyi (Sorbonne) - Symplectic methods in optimisation problems

see description

Abstract: The goal of this talk will be to convince the audience that the language of symplectic geometry is the most natural language for the study of minimisation problems. We will revise some basic tools from classical calculus of variations such as the Lagrange multiplier rule and Jacobi fields, explain their symplectic meaning and how those notions can be extended to a much more general setting.

Tuesday, January 21, 2020

Tuesday, January 28, 2020

16:00-17:00

MIN 014

Thursday, January 30, 2020

15:30-16:30

MIN 201

Utrecht Geometry Center Colloquium

Lior Bary-Soroker (Tel Aviv University) - Virtually all polynomials are irreducible

see description

Abstract: It has been known for almost a hundred years that most polynomials with large 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 families of polynomials with small coefficients—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). In the talk, I will discuss these types of problems, and approach to attack them using combination of combinatorics, analytic number theory, random permutations, and number theory in function fields.

16:00-17:00

Tuesday, February 4, 2020

Tuesday, February 11, 2020

Thursday, February 13, 2020

Tuesday, February 18, 2020

Thursday, February 20, 2020

16:00-17:00

Tuesday, February 25, 2020

Thursday, February 27, 2020

16:00-17:00

Tuesday, March 3, 2020

Tuesday, March 10, 2020

Tuesday, March 17, 2020

Tuesday, March 24, 2020

Tuesday, March 31, 2020

Tuesday, April 7, 2020

Tuesday, April 14, 2020