## Math Calendar

Friday, October 19, 2018

11:00-13:00

HFG 610

15:00-17:00

HFG 610

The diffeomorphism group Diff(M) of a manifold M is a scary beast: it is an infinite dimensional topological group. Automorphisms of mathematical objects are inherently interesting, but this group also shows up in practical application. The diffeomorphism group of surfaces is for example closely related to the classification of three dimensional manifolds via Heegaard splittings, and the classifying space BDiff(M) of the diffeomorphism group classifies smooth M-bundles over reasonable topological spaces. It is in general difficult to determine when a bundle is trivial. Obstructions to triviality are given by pulling back cohomology classes of BDiff(M) along the classifying map. It is therefore desirable to compute the cohomology of BDiff. The Madsen-Weiss Theorem is a computation of the cohomology of BDiff(M) in the stable range. The goal of the seminar is to understand the proof of the Madsen-Weiss theorem.

Tuesday, October 23, 2018

16:00-17:00

Utrecht Geometry Center Seminar

Cristina Manolache (Imperial College London) - A splitting of the virtual class for genus one stable maps, HFG 611

see description

In order to define intersection theory on spaces with several components of different dimensions one needs to define a "virtual class". I will explain the construction of the virtual class in simple examples and then show how to split this class on components. I will discuss applications to moduli spaces of genus one stable maps.

Thursday, October 25, 2018

16:00-17:00

Utrecht

Complex Systems Seminar

Carolin Kreisbeck (UU) - Asymptotic rigidity of layered structures and applications, HFG 611

see description

Title: Asymptotic rigidity of layered structures and applications

Abstract: Rigidity results in elasticity are powerful statements that allow to derive global properties of a deformation from local ones. The classical Liouville theorem states that every local isometry of a domain corresponds to a rigid body motion. If connectedness of the set fails, clearly, global rigidity can no longer be true.

In this talk, I will present a new type of asymptotic rigidity lemma, which shows that if an elastic body contains sufficiently stiff connected components arranged into fine parallel layers, then macroscopic rigidity up to horizontal shearing prevails in the limit of vanishing layer thickness. The optimal scaling between layer thickness and stiffness can be identified using suitable bending constructions. This result constitutes a useful tool for proving homogenization results of variational problems modeling high-contrast bilayered composites. We will finally utilize it to characterize the homogenized Gamma-limits of two models inspired by nonlinear elasticity and finite crystal plasticity.

This is joint work with Fabian Christowiak (Universität Regensburg).

Tuesday, October 30, 2018

16:00-17:00

Utrecht Geometry Center Seminar

Emmanuel Kowalski (ETH Zürich) - Stories of Kloosterman sums, HFG 611

see description

Kloosterman sums are finite exponential sums which have remarkable

applications in analytic number theory, ranging from diophantine

problems to modular forms and the distribution of primes.

The talk will present the history of the study of these sums and

discuss their properties, including a number of open problems. There

will be a particular emphasis on links with algebraic geometry, and on

distribution problems for Kloosterman sums.

applications in analytic number theory, ranging from diophantine

problems to modular forms and the distribution of primes.

The talk will present the history of the study of these sums and

discuss their properties, including a number of open problems. There

will be a particular emphasis on links with algebraic geometry, and on

distribution problems for Kloosterman sums.

Thursday, November 1, 2018

16:00-17:00

Utrecht

Tuesday, November 6, 2018

16:00-17:00

Thursday, November 8, 2018

15:30-16:30

MIN 2.01

Mathematical Colloquium

Ben Schweizer (TU Dortmund) - Effective description of waves in discrete and heterogeneous media

see description

Homogenization theory predicts that waves in periodic heterogeneous media can be described, in the limit of small periodicity, by an effective wave equation. This is true as long as finite observation times are considered, but it is no longer true for large time intervals, which are relevant in many applications. On large time intervals, one observes dispersion, which means that waves of different wave-length travel with different speed. In particular, a wave pulse will, in general, change its form in the course of time. A linear wave equation with constant coefficients does not show dispersion and cannot explain the observed effect. We must instead find a dispersive model. We showed that, effectively, a linear wave equation with periodic coefficients and with a small periodicity can be replaced, in a new homogenization limit, by a linear wave equation of fourth order with constant coefficients. The predictions of this weakly dispersive model agrees perfectly with numerical results. We furthermore investigate the wave equation in a discrete spring-mass model. The discrete character of the model introduces small-scale oscillations, which result again in a dispersive long time behavior. We derive the dispersive effective wave equations also for

the discrete model. Moreover, for ring-like solution fronts that occur for localized initial data after long time, we derive the equations that dictate the evolution of the front: Our derivation provides a linearized KdV equation and an explicit representation of the corresponding initial data in Fourier space.

We present work that was obtained in collaborations with A. Lamacz, T. Dohnal, and F. Theil.

the discrete model. Moreover, for ring-like solution fronts that occur for localized initial data after long time, we derive the equations that dictate the evolution of the front: Our derivation provides a linearized KdV equation and an explicit representation of the corresponding initial data in Fourier space.

We present work that was obtained in collaborations with A. Lamacz, T. Dohnal, and F. Theil.

Tuesday, November 13, 2018

16:00-17:00

Utrecht Geometry Center Seminar

Jonathan Belletête (CEA Saclay) - A pseudo-fusion category from Temperley-Lieb algebras, HFG 611

see description

Two dimensional conformal field theories, appearing in many branches of physics, can be ( partially ) encoded into a category of representations of some vertex operator algebra; there the tensor product of representations encodes the interactions of the particles in the theory. If these interactions are sufficiently well-behaved, then this will be a Fusion category; these appear in many areas of mathematics, for instance in the representation theory of Hopf algebras, in the construction of 3D topological invariants, etc. The question is then: what if the interactions are not well-behaved? One can show easily that the defining axioms of a Fusion category are then no longer satisfied, but how should they be replaced?

The Temperley-Lieb algebras are an infinite family of associative algebras indexed by two parameters: a positive integer N and a complex number q. Physicists have argued that these algebras can be used to build 2d conformal field theories, in particular ones where the interactions are well-behaved, and ones where they are not. I will show how their categories of representations can be turned into proper tensor categories; I will discuss how these can be understood as Fusion categories in certain cases, and what happens when they can't.

Based on joint work with Yvan Saint-Aubin.

The Temperley-Lieb algebras are an infinite family of associative algebras indexed by two parameters: a positive integer N and a complex number q. Physicists have argued that these algebras can be used to build 2d conformal field theories, in particular ones where the interactions are well-behaved, and ones where they are not. I will show how their categories of representations can be turned into proper tensor categories; I will discuss how these can be understood as Fusion categories in certain cases, and what happens when they can't.

Based on joint work with Yvan Saint-Aubin.

Thursday, November 15, 2018

16:00-17:00

Utrecht

Tuesday, November 20, 2018

16:00-17:00

Thursday, November 22, 2018

16:00-17:00

Utrecht

Saturday, November 24, 2018

Tuesday, November 27, 2018

16:00-17:00

Thursday, November 29, 2018

Tuesday, December 4, 2018

16:00-17:00

Thursday, December 6, 2018

16:00-17:00

Utrecht

Tuesday, December 11, 2018

16:00-17:00

Utrecht Geometry Center Seminar

Giovanni Bazzoni (Universidad Complutense de Madrid)- Geometry and Rational Homotopy Theory

see description

This talk would like to be a celebration of the fruitful interplay between Geometry and Rational Homotopy Theory. In order to show how these two areas can work together, I will consider two concrete situations :

(a) the existence of a geometric structure on a compact manifold can be helpful in addressing problems coming from rational homotopy theory, such as the toral rank conjecture ;

(b) rational homotopy theory helps to identify compact manifolds which admit a specific geometric structure, for instance Kähler, Sasakian or Vaisman. This is particularly transparent in the case of nilmanifolds.

(a) the existence of a geometric structure on a compact manifold can be helpful in addressing problems coming from rational homotopy theory, such as the toral rank conjecture ;

(b) rational homotopy theory helps to identify compact manifolds which admit a specific geometric structure, for instance Kähler, Sasakian or Vaisman. This is particularly transparent in the case of nilmanifolds.

Thursday, December 13, 2018

Tuesday, December 18, 2018

16:00-17:00

Tuesday, January 8, 2019

Thursday, January 10, 2019

Tuesday, January 15, 2019

Tuesday, January 22, 2019

Tuesday, January 29, 2019

16:00-17:00

Thursday, January 31, 2019

Tuesday, February 5, 2019

Thursday, February 7, 2019

12:00-13:00

Utrecht

Tuesday, February 12, 2019

Thursday, February 14, 2019

Tuesday, February 19, 2019

Tuesday, February 26, 2019

Tuesday, March 5, 2019

Thursday, March 7, 2019

16:00-17:00

Utrecht

Tuesday, March 12, 2019

Thursday, March 14, 2019

Tuesday, March 19, 2019

Thursday, March 21, 2019

16:00-17:00

Utrecht

Tuesday, March 26, 2019

Thursday, March 28, 2019

Tuesday, April 2, 2019

Tuesday, April 9, 2019

Tuesday, April 16, 2019