## Math Calendar

Tuesday, November 26, 2019

10:00-11:00

BBG007

Extra Number Theory Talk

Farbod Shokrieh (U Washinghton) - Graphs and Arithmetic Geometry

see description

Abstract: Graphs can be viewed as (non-archimedean) analogues of Riemann surfaces. For example, there is a notion of Jacobians for graphs. More classically, graphs can be viewed as electrical networks. I will explain the interplay between these points of view, as well as some recent application in arithmetic geometry.

16:00-17:00

MIN 014

Utrecht Geometry Center Seminar

Hadrian Heine (Utrecht University) - A universal property of real algebraic K-theory

see description

Abstract:

By work of Barwick algebraic K-theory of Waldhausen infinity categories is the initial multiplicative theory splitting cofiber sequences.

Blumberg, Gepner, Tabuada prove an analogous universal property of the algebraic K-theory of stable infinity categories, from which they uniquely characterize the Dennis trace map and cyclotomic trace map to topological Hochschild homology respectively topological cyclic homology.

We give a similar characterization of real algebraic K-theory for exact infinity categories with duality, which we define via a hermitian version of Waldhausen's S-construction.

This is joint work with Markus Spitzweck and Paula Verdugo.

Thursday, November 28, 2019

16:00-17:00

Utrecht

Applied Mathematics Seminar

Sanjeeva Balasuriya (University of Adelaide) - Quantifying Lagrangian uncertainty and robust sets from noisy unsteady Eulerian data, HFG 611

see description

Title: Quantifying Lagrangian uncertainty and robust sets from noisy unsteady Eulerian data

Abstract:

Observational velocity data in geophysical fluids is unsteady, and has uncertainties because of observational error, deviation from geostrophy, and importantly, subgrid effects owing to the spatial resolution scale of the data. Therefore, any conclusions on finite-time Lagrangian trajectories inferred from this Eulerian data will inherit an uncertainty. Allowing for a spatio-temporally dependent noise model, a stochastic differential equation framework for quantifying the statistical distribution of each eventual Lagrangian trajectory is developed. This captures the displacement's variance in each direction (`anisotropic variance') as well as an explicit optimized measure across all directions (`stochastic sensitivity'). The latter concept generates a field across all initial conditions, from which it is possible to identify evolving flow regions which are robust with respect to a user-specification of length-scale and noise-level in the data. It is expected that these will be invaluable new tools in ascribing uncertainties to various interpretations of Lagrangian coherent structures. One specific such method---finite-time Lyapunov exponents---is examined in this light, and the unexpected implication is that accuracy worsens as spatial resolution is improved.

Abstract:

Observational velocity data in geophysical fluids is unsteady, and has uncertainties because of observational error, deviation from geostrophy, and importantly, subgrid effects owing to the spatial resolution scale of the data. Therefore, any conclusions on finite-time Lagrangian trajectories inferred from this Eulerian data will inherit an uncertainty. Allowing for a spatio-temporally dependent noise model, a stochastic differential equation framework for quantifying the statistical distribution of each eventual Lagrangian trajectory is developed. This captures the displacement's variance in each direction (`anisotropic variance') as well as an explicit optimized measure across all directions (`stochastic sensitivity'). The latter concept generates a field across all initial conditions, from which it is possible to identify evolving flow regions which are robust with respect to a user-specification of length-scale and noise-level in the data. It is expected that these will be invaluable new tools in ascribing uncertainties to various interpretations of Lagrangian coherent structures. One specific such method---finite-time Lyapunov exponents---is examined in this light, and the unexpected implication is that accuracy worsens as spatial resolution is improved.

Friday, November 29, 2019

11:00-17:00

MIN 015

Minicourse on tangent distributions

Lucas Dahinden (Heidelberg) - Rigidity of topological entropy for positive contactomorphisms

see description

In this series of talks I aim to present a result in Symplectic Geometry. Historically, Symplectic Geometry developed as the geometry behind Physics because it is the right framework to define the Hamiltonian equations. Nowadays, Symplectic Geometry is a research field on its own, with many subbranches and connections to other fields.

During the minicourse, we will take a journey beginning with the definition of “symplectic”, to more and more specialized theories. We will follow the following structure:

1. Symplectic Geometry in general

2. Floer homology

3. Rabinowitz-Floer homology

4. The main result.

The proof of (4) uses the machinery introduced in (1-3), but I hope to show you that this machinery is also of independent interest by explaining ideas and mentioning other applications. The main result identifies a class of spaces on which a natural class of maps has positive topological entropy (i.e. they are chaotic in some sense).

For the non-experts: A generalization of geodesic flows on a generalization of rationally hyperbolic manifolds is always chaotic.

For the experts: In Liouville fillable contact manifolds with exponentially growing wrapped Floer homology, every positive contactomorphism has positive topological entropy.

During the minicourse, we will take a journey beginning with the definition of “symplectic”, to more and more specialized theories. We will follow the following structure:

1. Symplectic Geometry in general

2. Floer homology

3. Rabinowitz-Floer homology

4. The main result.

The proof of (4) uses the machinery introduced in (1-3), but I hope to show you that this machinery is also of independent interest by explaining ideas and mentioning other applications. The main result identifies a class of spaces on which a natural class of maps has positive topological entropy (i.e. they are chaotic in some sense).

For the non-experts: A generalization of geodesic flows on a generalization of rationally hyperbolic manifolds is always chaotic.

For the experts: In Liouville fillable contact manifolds with exponentially growing wrapped Floer homology, every positive contactomorphism has positive topological entropy.

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.

Thursday, December 5, 2019

16:00-17:00

Utrecht

Applied Mathematics Seminar

Wolf-Patrick Düll (University of Stuttgart) - Justification of the Nonlinear Schrödinger approximation of the dynamics
of two-dimensional water waves, HFG 611

see description

We consider the evolution system for two-dimensional surface water waves in an infinitely long canal of finite depth. Since the full system is too complicated for a direct analysis of the qualitative behavior of its solutions, it is important to approximate the system in different parameter regimes by suitable reduced model equations whose solutions have similar but more easily accessible qualitative properties.

A famous nonlinear reduced model is the Nonlinear Schrödinger (NLS) equation for the approximate description of the dynamics of modulated wave packet-like solutions. To understand to which extent this approximation yields correct predictions of the qualitative behavior of the original system it is important to justify the validity of the NLS approximation by estimates of the approximation error in the physically

relevant length and time scales.

In this talk, we give an overview on the NLS approximation and its justification. Special emphasis will be put on the most challenging case, namely, the proof of error estimates for the NLS approximation being valid for surface water waves with and without surface tension. These estimates are obtained by parametrizing the twodimensional

surface waves by arc length, which enables us to derive error bounds

that are uniform with respect to the strength of the surface tension, as the height of the wave packet and the surface tension go to zero.

A famous nonlinear reduced model is the Nonlinear Schrödinger (NLS) equation for the approximate description of the dynamics of modulated wave packet-like solutions. To understand to which extent this approximation yields correct predictions of the qualitative behavior of the original system it is important to justify the validity of the NLS approximation by estimates of the approximation error in the physically

relevant length and time scales.

In this talk, we give an overview on the NLS approximation and its justification. Special emphasis will be put on the most challenging case, namely, the proof of error estimates for the NLS approximation being valid for surface water waves with and without surface tension. These estimates are obtained by parametrizing the twodimensional

surface waves by arc length, which enables us to derive error bounds

that are uniform with respect to the strength of the surface tension, as the height of the wave packet and the surface tension go to zero.

Friday, December 6, 2019

13:15-14:30

Duistermaat

Tuesday, December 10, 2019

16:00-17:00

MIN 014

Thursday, December 12, 2019

15:30-16:30

KBG Pangea

The Utrecht Mathematical Colloquium

Chris Budd (University of Bath) - Non-smooth models in the Geosciences

see description

In this talk Iwill show how models of both geology and climate lead tonon-smooth dynamical systems. I will show how the theory of such systemscan then be used to help explain such diverse problems as rockfolding and the behaviour of the ice ages.

Tuesday, December 17, 2019

Tuesday, January 7, 2020

16:00-17:00

MIN 014

Thursday, January 9, 2020

16:00-17:00

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.

Thursday, January 16, 2020

16:00-17:00

Tuesday, January 21, 2020

Tuesday, January 28, 2020

16:00-17:00

MIN 014

Thursday, January 30, 2020

15:30-16:30

MIN 201

The Utrecht Mathematical Colloquium

Lior Bary-Soroker (Tel Aviv) - 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

16:00-17:00

MIN 014

Thursday, February 6, 2020

Tuesday, February 11, 2020

Thursday, February 13, 2020

Tuesday, February 18, 2020

16:00-17:00

MIN 014

Thursday, February 20, 2020

16:00-17:00

Tuesday, February 25, 2020

Thursday, February 27, 2020

16:00-17:00

Tuesday, March 3, 2020

Thursday, March 5, 2020

Tuesday, March 10, 2020

Tuesday, March 17, 2020

Tuesday, March 24, 2020

Thursday, March 26, 2020

Tuesday, March 31, 2020

Tuesday, April 7, 2020

Tuesday, April 14, 2020

Tuesday, April 21, 2020

Tuesday, April 28, 2020

Tuesday, May 5, 2020

Tuesday, May 12, 2020

Tuesday, May 19, 2020