Math Calendar

Tuesday, June 18, 2024
10:00-11:00
MINN-0.14
MSc presentation
Tess van Leeuwen - Homogeneous complex fractional Gaussian fields

Supervisor: Wioletta Ruszel

Second reader: Jason Frank

 Abstract: Where local boundary value problems are related to classicalderivatives, non-local problems are stated in terms of fractional derivatives.In this talk, we discuss in particular the fractional Laplacian and how it relatesto fractional Gaussian fields. We will define Gaussian random fields on Banachspaces and see that a standard Gaussian field on a Hilbert space cannotexist. A viable alternative is the concept of an abstract Wiener space,which turns out to be equivalent to a centred Gaussian field. This theory isthen applied to the fractional Laplacian to obtain the fractional Gaussianfields. Finally, we look at the examples of the Gaussian free field and thebi-Laplacian field.

12:00-13:00
HFG 610
Freudenthal topology seminar
Bernardo Uribe - Equivariant Unitary Bordism & Birational Invariants of Finite Groups

In this talk I will summarize what is known about torsion invariants on the Equivariant and Unitary Bordism groups, as well as the mysterious relation between the torsion invariants on surfaces and some birational invariants of finite groups.

Freudenthal topology seminar
Wednesday, June 19, 2024
13:00-14:00
MINN-0.17
MSc presentation
Stijn van der Wal - The Vehicle Routing Problem with Wind and Load Dependent Travel Times

Supervisors:  Dr. ir. J.M. van denAkker, Dr. S. Dirksen and P. de Bruin, MSc.

Abstract: Electric bicycle delivery in cities is often faster, more reliable and more sustainable than using cargo vans. The benefits of these vehicles comes at the price of wind and load dependency of the travel time between customers. The vehicle routing problem models this type of scheduling problem. By taking into account the non deterministic nature of wind and a discretisation of the carried load, schedules can be computed that are expected to be cheaper and on time more often than implementations that ignore these factors or see them as fixed. By sampling from an assumed distribution of wind realisations, a set of arrival time distributions can be obtained that respects the dependency of travel times. By adapting existing code from using deterministic travel times to using the samples to create travel time distributions, an algorithm was built that is shown to produce schedules that behave better in simulations than schedules produced in the deterministic setting. As few as 5 samples was shown to improve both cost and robustness and 20 samples was enough to produce schedules that had an on time percentage of over 99.9 percent in simulations.

13:00-14:00
BBG 201
AG Seminar talk
Katharina Hübner - An integral structure on the sheaf of differentials
Abstract: We explain how to define an integral structure on the sheaf of differentials $\Omega_X$ of an adic space $X$. This should be thought of as an analogue of the subsheaf $\mathcal{O}_X^+$ of the structure sheaf $\mathcal{O}_X$. This integral structure $\Omega_X^+$ can be described in terms of logarithmic differentials on a log regular model (if such a model exists). Possibly assuming resolution of singularities this gives a strategy for transferring results on log étale cohomology to tame cohomology.
Thursday, June 20, 2024
11:00-12:00
HFG611
Applied Mathematics Seminar -- Ilya Krishtal (Northern Illinois University) -- A Spectral Theory Approach to Prony’s Problem
At the end of the 18th century Prony created an algorithm that allows one to recover an s-sparse d-dimensional vector from 2s of its consecutive Fourier coefficients. This algorithm has seen numerous generalizations and appeared in various other contexts. For example, it has been found useful for understanding concepts such as compressed sensing, super-resolution, and uncertainty principles. In this talk, I will describe a relatively novel approach which regards Prony’s problem as a spectral identification problem for an unknown restriction of a known linear operator. We will see that a Prony-type algorithm applies in a very general context of Banach modules and may be used for problems such as the spectral identification in dynamical sampling and the time-varying channel identification in wireless communication. The talk is based on joint papers with A. Aldroubi and G. Pfander.
16:00-17:00
HFG 611
Applied Math Seminar
Gergely Bodo (UvA)
Title: Stochastic integration with respect to cylindrical Lévy processes in Hilbert space
 
Abstract: In this talk, we provide a complete theory of stochastic integration
with respect to arbitrary cylindrical Lévy processes in Hilbert space. Since
cylindrical Lévy processes do not have a semimartingale decomposition,
our approach relies on a limit characterisation of Lévy characteristics and
the theory of decoupled tangent sequences to introduce the notion of the
stochastic integral. Our main result gives both necessary and sufficient
conditions for a predictable Hilbert-Schmidt operator-valued process to
be integrable with respect to an arbitrary cylindrical Lévy process in a
Hilbert space. As it turns out, our integrability conditions can be explicitly
expressed in terms of the cylindrical characteristics of the integrator,
thus establishing a direct relationship between existence of the stochastic
integral and properties of the cylindrical integrator.
Friday, June 21, 2024
09:30-10:30
MINN-0.14
MSc presentation
Fien van Berkel - Iterated monodromy groups of critically fixed (anti-)rational maps

Project supervisor: Gunther Cornelissen

Daily supervisor: Mikhail Hlushchanka

Second examinor: Valentijn Karemaker

 Abstract: Iterated monodromy groups (in short, IMGs)are groups naturally associated to iterations of (anti-)rational maps on theRiemann sphere. In this thesis, we study the properties of the IMGs ofcritically fixed (anti-)rational maps; critically fixed maps being those mapswhose critical points are also fixed points. In particular, we prove that theIMGs of critically fixed (anti-)polynomials are regular branch on the subgroupof group elements with even permutational part. In the case of polynomials, wemake use of the one-to-one correspondence between the conformal conjugacyclasses of critically fixed polynomials and the isomorphism classes ofconnected planar embedded graphs. Similarly, in the case of anti-polynomials,we use that there is a one-to-one correspondence between the Möbius conjugacyclasses of critically fixed anti-rational maps and the equivalence classes ofunobstructed topological Tischler graphs. Furthermore, we discuss why the toolswe use in the case of critically fixed (anti-)polynomials are insufficient forproving the same statement in the more general case of critically fixed(anti-)rational maps.

10:00-12:00
HFG 610
Friday Fish
Sven Holtrop — Riemannian Groupoids and their Ehresmann Connections
In the first part of this talk, a new definition of Riemannian groupoids will be introduced. A Riemannian groupoid consists of a groupoid G together with a metric on G satisfying certain compatibility conditions. It will be shown that orbits of a Riemannian groupoids can be linearized using an exponential map.

The second part of the talk is about source Ehresmann connections. In particular, we will see that a Riemannian groupoid gives rise to a special type of source Ehresmann connection, called a weak Cartan connection. Using the cotangent groupoid, we can then construct an entirely new type of connection, whose dual is like a weak Cartan connection, these connections are then dubbed weak * connection.
11:00-12:00
BBG 0.61
MSc presentation Alkis Ionnidis
Higher categorical models of HoTT

Higher categorical models of HoTT

Supervisor: Paige Randall North

Second reader: Gijs Heuts

Abstract: 
Martin Löf Dependent Type Theory (MLDTT) is a formal system forconstructive mathematical reasoning. The Univalent Foundations (UF) programenhances it with the Univalence Axiom and Higher Inductive Types, and proposesit as an alternative to ZFC for the foundations of mathematics. My thesisfocuses on the categorical semantics of UF.

The semantics of the elimination principle of the identity typecorrespond to lifting properties, a fundamental component of model categories,which serve as an abstract framework for homotopy theory. It has also beenshown that Kan Complexes, or equivalently ∞-groupoids, can support a model ofUF. These findings suggest a profound connection between logic, homotopy theory& higher category theory. Over the past decade, numerous attempts have beenmade to expand on these results.

In my thesis I look into two constructions relating type theories tomodel categories and higher categories. The first asserts that if T is MLDTT,subject to certain rules, then its category of contexts is a fibration categorywhose simplicial localization is an locally cartesian closed ∞-category. Thesecond asserts that any ∞-topos can be presented by a model category thatmodels UF.

Kind regards,

Alkis Ioannidis

13:00-15:00
HFG 610
Friday Fish
Jaime Pedregal — Holonomy in generalized geometry

The study of connections on Courant algebroids is relevant for the study of metric connections on manifolds with closed skew-symmetric torsion. In this talk we will first recall the basic concepts from generalized Riemannian geometry to then introduce the notions of parallel transport and holonomy on Courant algebroids and to establish their basic properties. To get a feeling for the theory, the second half will focus on a first study of the canonical Levi-Civita connection on exact Courant algebroids, culminating in the classification of the flat ones.

Tuesday, June 25, 2024
13:00-13:45
BBG 005
Arakelov Theory Seminar
Soumya Sankar - Properties of arithmetic intersection theory
14:00-14:50
BBG 005
Arithmetic geometry talk
Brandon Alberts (Eastern Michigan University) - Tame Ramification Types in Arithmetic Statistics
We will talk about a classification for the different ways that a tame prime can ramify in a field extension. We will introduce this along with the classification for how a tame prime can ramify in a rational point on a stack introduced by Darda and Yasuda. We discuss some of the ways in which this classification is used for counting problems.
15:30-16:20
BBG 005
Arithmetic geometry talk
Juanita Duque Rosero (Boston University) - Local heights on hyperelliptic curves for quadratic Chabauty
The method of quadratic Chabauty is a powerful tool to
determine the set of rational points on curves.  A key input for this method is the values of local height functions. In this talk, we will discuss an algorithm to compute these local heights at odd primes v not equal to p for hyperelliptic curves. Through applications, we will see how this work extends the reach of quadratic Chabauty to curves previously deemed inaccessible. This is joint work with Alexander Betts, Sachi Hashimoto, and Pim Spelier.
16:30-17:20
BBG 005
Arithmetic geometry talk
Angelos Koutsianas (Aristotle University of Thessaloniki) - The modular method, old and new directions
In this talk, we will briefly discuss/recall the great success of the modularity of elliptic curves in the resolution of exponential Diophantine equations (modular method). We will see how the modular method can be used in the study of Beal conjecture (Darmon's program). New directions of the modular method using Frey abelian varieties will be presented, and will focus on the generalized Fermat equation x^p + y^p = z^5.
Wednesday, June 26, 2024
13:00-14:00
Minnaert 0.14
AG Seminar talk
Lucien Hennecart - Cohomological integrality isomorphisms
Abstract: The theory of cohomological Hall algebras has proven powerful in studying Donaldson-Thomas invariants of some 3-Calabi-Yau categories. It is in particular crucial to obtain cohomological integrality identities. Roughly speaking, the cohomological integrality results concern the finiteness of some invariants associated to the category. They also give cohomologically refined invariants. In my talk, I will give a brief overview of such results, explain their meaning, and explain how to obtain them in various contexts. I will concentrate on a new situation given by symmetric representations of reductive groups.
Thursday, June 27, 2024
09:00-19:00
Masters Thesis Presentations (Time and Location TBC)
16:00-17:00
HFG 611
Applied Math Seminar
Francesca Bartolucci (TU Delft)
Title : TBA
Abstract: TBA
Friday, June 28, 2024
09:00-19:00
Masters Thesis Presentations (Time and Location TBC)
Tuesday, July 9, 2024
12:15-13:15
PhD Defense Dirk van Bree
Thursday, September 5, 2024
16:00-17:00
MI talk Yuri Kuznetsov
Title: Recent progress in the numerical bifurcation analysis of delay differential equations
Abstract: TBA