## Math Calendar

Tuesday, September 24, 2019

Wednesday, September 25, 2019

16:00-17:00

Academy Bldg, Domplein, Utrecht

Thursday, September 26, 2019

16:00-17:00

HFG 611

Applied Mathematics Seminar

Rok Cestnik (Potsdam University) - Inferring the dynamics of oscillatory systems using recurrent neural networks

see description

Title: Inferring the dynamics of oscillatory systems using recurrent neural networks

Abstract: We investigate the predictive power of recurrent neural networks for oscillatory systems not only on the attractor but in its vicinity as well. For this, we consider systems perturbed by an external force. This allows us to not merely predict the time evolution of the system but also study its dynamical properties, such as bifurcations, dynamical response curves, characteristic exponents, etc. It is shown that they can be effectively estimated even in some regions of the state space where no input data were given. We consider several different oscillatory examples, including self-sustained, excitatory, time-delay, and chaotic systems. Furthermore, with a statistical analysis, we assess the amount of training data required for effective inference for two common recurrent neural network cells, the long short-term memory and the gated recurrent unit.

Abstract: We investigate the predictive power of recurrent neural networks for oscillatory systems not only on the attractor but in its vicinity as well. For this, we consider systems perturbed by an external force. This allows us to not merely predict the time evolution of the system but also study its dynamical properties, such as bifurcations, dynamical response curves, characteristic exponents, etc. It is shown that they can be effectively estimated even in some regions of the state space where no input data were given. We consider several different oscillatory examples, including self-sustained, excitatory, time-delay, and chaotic systems. Furthermore, with a statistical analysis, we assess the amount of training data required for effective inference for two common recurrent neural network cells, the long short-term memory and the gated recurrent unit.

Friday, September 27, 2019

16:00-17:00

HFG 611

Utrecht Geometry Center Seminar

Marina Logares (Universidad Complutense Madrid) - Poisson and symplectic geometry of Higgs bundles

see description

Higgs bundles are objects in the intersection of Geometry and Physics. Their moduli spaces have been widely studied from both points of view, for instance in relation to mirror symmetry or some quantum field theories. In particular, their symplectic geometry exhibit them as integrable systems. Moreover, these objects may admit some extra structure (logarithmic/parabolic, framed) leading to different moduli spaces which may then be Poisson or symplectic holomorphic manifolds. We are going to describe these moduli spaces of Higgs bundles with extra structure as well as the integrable systems they define. This is based in joint work and ongoning workwith I. Biswas, A. Peón Nieto and S. Szabo.

Tuesday, October 1, 2019

16:00-17:00

HFG 611

Utrecht Geometry Center Seminar

Irakli Patchkoria (Aberdeen) - On the de Rham-Witt complex of perfectoid rings

see description

Perfectoid rings are generalizations of perfect F_p-algebras and have a well-behaved cotangent complex. An example of a perfectoid ring is O_C, the ring of integers of the field of p-adic complex numbers C. This talk will concern the algebraic K-theory of perfectoid rings and will generalize Hesselholt's construction of the divided Bott class for O_C which lives in the target of a certain trace map on algebraic K_2. Our construction of the divided Bott element is purely algebraic and uses only calculations in the de Rham-Witt complex. We will try to introduce and motivate the main players in this talk and make it available for general audience. The talk will be quite algebraic. This is all joint with Christopher Davis.

Thursday, October 3, 2019

16:00-17:00

HFG 611

Applied Mathematics Seminar

Babette de Wolff (FU Berlin) - The odd number limitation for Pyragas control, revisited

see description

Title: The odd number limitation for Pyragas control, revisited

Abstract:

Pyragas control is a time delayed feedback control scheme designed to stabilize periodic orbits. From an implementation perspective, its main advantage is that the only knowledge required is the period of the target periodic orbit.

For years, it was believed that periodic solutions with an odd number of Floquet multipliers cannot be stabilized with a Pyragas control scheme (the ‘odd number limitation’). Although true for the non-autonomous case [Nakajima, 1997], the claim has later been refuted for autonomous systems [Fiedler et al, 2008].

In this talk, we will have a look at the obstructions that result in the odd-number limitation in the non-autonomous case, and the mechanisms that refute it in the autonomous case. Moreover, we will discuss some generalisations that can overcome these obstructions.

Abstract:

Pyragas control is a time delayed feedback control scheme designed to stabilize periodic orbits. From an implementation perspective, its main advantage is that the only knowledge required is the period of the target periodic orbit.

For years, it was believed that periodic solutions with an odd number of Floquet multipliers cannot be stabilized with a Pyragas control scheme (the ‘odd number limitation’). Although true for the non-autonomous case [Nakajima, 1997], the claim has later been refuted for autonomous systems [Fiedler et al, 2008].

In this talk, we will have a look at the obstructions that result in the odd-number limitation in the non-autonomous case, and the mechanisms that refute it in the autonomous case. Moreover, we will discuss some generalisations that can overcome these obstructions.

Tuesday, October 8, 2019

16:00-17:00

HFG 611

Tuesday, October 15, 2019

16:00-17:00

HFG 611

Utrecht Geometry Center Seminar

Andrew Bridy (Yale) - Automatic sequences and curves over finite fields

see description

Abstract: An amazing theorem of Christol states that a power series over a finite field is an algebraic function if and only if its coefficient sequence can be produced by a finite automaton, which is a limited model of a computer with no memory. The proof uses combinatorics and linear algebra, but hidden in the theorem there is geometric information about a curve that contains the power series in its function field. I make this explicit by demonstrating a precise link between the complexity of the automaton and the geometry of the curve.

Thursday, October 17, 2019

09:45-10:45

KBG Atlas

11:00-12:00

KBG Atlas

Vafa-Witten invariants, introduced by Vafa and Witten in 1994,have recently been defined in algebraic geometry by Tanaka and Thomas, asthe *virtual* enumeration of certain sheaves on a local surface.We study contributions of sheaves in the counting problem, that can bedescribed by flags of torsion free sheaves of rank 1 on the underlyingsurface (the *vertical* contributions). We discuss auniversality result, which allows us to explicitly compute some of thesecontributions. The results can be used to verify precise formulas, conjecturedby Göttsche and Kool, for the vertical contributions to rank 2 and 3Vafa-Witten invariants.

15:30-16:30

KBG Atlas

The study of curves, surfaces, and higher dimensional varieties in projective space involves questions about tangency, duality, divisors, sections and projections, enumerative geometry, and classification. Although projective toric varieties form but a small subset of all projective varieties, they constitute nonetheless a rich and interesting playground for the study of these questions. The fact that there is a “dictionary” between projective toric varieties and convex lattice polytopes makes it possible to use combinatorial methods to prove algebraic geometric results, and vice versa. In the talk, I will give several examples of such results.

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

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

Tuesday, November 12, 2019

16:00-17:00

MIN 014

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

Utrecht

Tuesday, November 26, 2019

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.

Tuesday, December 10, 2019

16:00-17:00

MIN 014

Tuesday, December 17, 2019

Thursday, December 19, 2019

Tuesday, January 7, 2020

Tuesday, January 14, 2020

Tuesday, January 21, 2020

Tuesday, January 28, 2020

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

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