Mathematical Institute Calendar
Tuesday, April 22, 2025
15:00-16:30
HFG707
Category Theory Seminar
Niels van der Weide - The Univalence Maxim and Univalent Double Categories
see description
Abstract:Category theory unifies mathematical concepts, aiding comparisons across structures by incorporating not just objects, but also morphisms capturing interactions between objects. It has influenced areas of computer science such as automata theory, functional programming, and semantics. Of particular importance in some applications are double categories, which are categories with two classes of morphisms, axiomatizing two different kinds of interactions between objects. These have found applications in many areas of mathematics and theoretical computer science, for instance, the study of lenses, open systems, and rewriting.
However, double categories come with a wide variety of equivalences, which makes it challenging to transport structure along equivalences. To deal with this challenge, we propose the univalence maxim: each notion of equivalence of categorical structures has a corresponding notion of univalent categorical structure which induces that notion of equivalence. We also prove corresponding univalence principles, which allow us to transport structure and properties along equivalences. In this way, the usually informal practice of reasoning modulo equivalence becomes grounded in an entirely formal logical principle.
We apply this perspective to various double categorical structures, such as (pseudo) double categories and double bicategories. Concretely, we characterize and formalize their definitions in Rocq UniMath up to chosen equivalences, which we achieve by establishing their univalence principles.
However, double categories come with a wide variety of equivalences, which makes it challenging to transport structure along equivalences. To deal with this challenge, we propose the univalence maxim: each notion of equivalence of categorical structures has a corresponding notion of univalent categorical structure which induces that notion of equivalence. We also prove corresponding univalence principles, which allow us to transport structure and properties along equivalences. In this way, the usually informal practice of reasoning modulo equivalence becomes grounded in an entirely formal logical principle.
We apply this perspective to various double categorical structures, such as (pseudo) double categories and double bicategories. Concretely, we characterize and formalize their definitions in Rocq UniMath up to chosen equivalences, which we achieve by establishing their univalence principles.
Wednesday, April 23, 2025
13:00-14:00
HFG707
Arithmetic Geometry talk
Adam Morgan (University of Cambridge) - Hasse principle for intersections of two quadrics via Kummer surfaces
see description
Abstract: I will discuss recent work with Skorobogatov establishing the Hasse principle for a broad class of degree 4 del Pezzo surfaces, conditional on finiteness of Tate--Shafarevich groups of abelian surfaces. A corollary of this work is that the Hasse principle holds for smooth complete intersections of two quadrics in P^n for n\geq 5, conditional on the same conjecture. This was previously known by work of Wittenberg assuming both finiteness of Tate--Shafarevich groups of elliptic curves and Schinzel's hypothesis (H).
I will also discuss forthcoming work with Lyczak which, again under the Tate--Shafarevich conjecture, shows that the Brauer--Manin obstruction explains all failures of the Hasse principle for certain degree 4 del Pezzo surfaces about which nothing was known previously.
14:00-16:00
HFG 7.07
Thursday, April 24, 2025
13:00-14:00
Alef Sterk (RUG) on "Extremes in dynamical systems
max-stable and max-semistable laws"
see description
Title:
Extremes in dynamical systems: max-stable and max-semistable laws
Abstract:
Extreme value theory for chaotic, deterministic dynamical systems is a rapidly expanding area of research. Given a dynamical system and a real-valued observable defined on its state space, extreme value theory studies the limit probabilistic laws for asymptotically large values attained by the observable along orbits of the system. Under suitable mixing conditions the extreme value laws are the same as those for stochastic processes of i.i.d. random variables.
Max-stable laws typically arise for probability distributions with regularly varying tails. However, in the context of dynamical systems, where the underlying invariant measure can be irregular, max-semistable distributions also have a natural place in studying extremal behaviour. In this talk I will first discuss a family of autoregressive processes with marginal distributions resembling the Cantor function. The resulting extreme value law can be proven to be a max-semistable distribution. Alternatively, we can describe the autoregressive process in terms of an iterated map with an invariant measure. Further examples of extreme value laws in dynamical systems are discussed as well.
Friday, April 25, 2025
13:00-15:00
HFG 707
Friday Fish
Álvaro del Pino Gómez - The h-principle fails for prelegendrians in elliptic distributions
see description
The main question in the topological theory of distributions asks: "Are there other classes of maximally non-integrable distributions, apart from contact structures, for which the h-principle fails?". In more down to earth terms: "Are there invariants of distributions that go beyond the obvious ones?", "Is there an interesting theory that is not just algebraic topological in nature?".
This question is at the moment wide open. All progress has gone in the opposite direction: proving that various classes of distributions are classified by their obvious algebraic topological invariants.
The aim of the talk is twofold: First, I will explain the general landscape of the field, giving an overview of what we know. Then, I will explain a recent result with Wei Zhou and Eduardo Fernández that says: There is a family of submanifolds (so called prelegendrians), adapted to a certain family of distributions (called elliptic), that do have non-obvious invariants. These invariants come from Contact Topology, thanks to the following key fact: elliptic distributions can be "contactised", producing an associated contact structure.
This question is at the moment wide open. All progress has gone in the opposite direction: proving that various classes of distributions are classified by their obvious algebraic topological invariants.
The aim of the talk is twofold: First, I will explain the general landscape of the field, giving an overview of what we know. Then, I will explain a recent result with Wei Zhou and Eduardo Fernández that says: There is a family of submanifolds (so called prelegendrians), adapted to a certain family of distributions (called elliptic), that do have non-obvious invariants. These invariants come from Contact Topology, thanks to the following key fact: elliptic distributions can be "contactised", producing an associated contact structure.
Tuesday, April 29, 2025
Wednesday, April 30, 2025
14:00-16:00
HFG 7.07
Friday, May 2, 2025
13:00-15:00
HFG 707
Friday Fish
Guillermo Sánchez - h-principles for Holomorphic Partial Differential Relations in Stein Manifolds
see description
The goal of the h-principle theory is to understand when a geometric problem is governed by the laws of differential topology. When topology (more flexible) overrides geometry (more rigid), we say that the h-principle holds in that context.
The identity principle and the resulting lack of partitions of unity endow complex geometry with great rigidity. However, there is a class of complex manifolds—Stein manifolds—in which the Oka principle, a type of h-principle for holomorphic functions, holds. The flexible properties of Stein manifolds have been exploited by F. Forstnerič and M. Slapar to establish h-principles for holomorphic immersions and submersions, and by F. Forstnerič for complex contact forms. In this talk, we will explore how these techniques can be abstracted to obtain more general h-principles in this type of complex manifolds.
The identity principle and the resulting lack of partitions of unity endow complex geometry with great rigidity. However, there is a class of complex manifolds—Stein manifolds—in which the Oka principle, a type of h-principle for holomorphic functions, holds. The flexible properties of Stein manifolds have been exploited by F. Forstnerič and M. Slapar to establish h-principles for holomorphic immersions and submersions, and by F. Forstnerič for complex contact forms. In this talk, we will explore how these techniques can be abstracted to obtain more general h-principles in this type of complex manifolds.
Tuesday, May 6, 2025
16:00-17:00
HFG 611
UGC colloquium
Jared Wunsch (Northwestern University) - Propagation of waves with low regularity
see description
The connection between solutions to wave equations and dynamics of particles, known variously in different contexts as the method of geometric optics, the WKB approximation, and Bohr's Correspondence Principle, becomes tenuous in the presence of singularities of the physical potential or underlying geometry. I will describe what we know about diffractive corrections to wave equation solutions, as well as some of their consequences in spectral and scattering theory.
UGC seminar webpage https://utrechtgeometrycentre.nl/ugc-seminar/
UGC seminar webpage https://utrechtgeometrycentre.nl/ugc-seminar/
Wednesday, May 7, 2025
14:00-16:00
HFG 7.07
Friday, May 9, 2025
11:00-16:15
JKH 2-3, Room 220
Mark Kac seminar in mathematical physics and probability with Nathanael Berestycki (U Vienna)
see description
Title: On the spectral geometry of Liouville quantum gravity.
Abstract:
In these talks we will discuss the spectral geometry of the Laplace-Beltrami operator associated to Liouville quantum gravity. Over the course of two lectures, our goals will be to:
- Explain how eigenvalues and eigenfunctions for LQG are defined;
- Show that the eigenvalues a.s. obey a Weyl law (joint work with Mo Dick Wong). This is closely related to the short time asymptotics of the LQG heat kernel;
- Discuss the second term in the Weyl law and its relation to the KPZ (Knizhnik-Polyakov-Zamolodchikov) scaling relation;
- Finally we will talk about some conjectures which suggest a rather beautiful connection to a phenomenon called quantum chaos.
Monday, May 12, 2025
Tuesday, May 13, 2025
Wednesday, May 14, 2025
08:30-17:00
Ruppert B
VBAC website: https://vbac-2025.ncag.info/
14:00-16:00
HFG 7.07
Thursday, May 15, 2025
08:30-17:00
Bolognalaan 101, room 1.204
VBAC website: https://vbac-2025.ncag.info/
Friday, May 16, 2025
Tuesday, May 20, 2025
Wednesday, May 21, 2025
Monday, May 26, 2025
13:00-14:30
To be determined
Tuesday, May 27, 2025
Wednesday, May 28, 2025
14:00-16:00
HFG 7.07
Tuesday, June 3, 2025
Tuesday, June 10, 2025
Monday, June 16, 2025
Tuesday, June 17, 2025
Tuesday, June 24, 2025
16:15-17:15
Utrecht University Hall, Domplein 29, 3512 JE Utrecht, Netherlands
Tuesday, July 1, 2025
Tuesday, July 8, 2025
Tuesday, July 15, 2025
Tuesday, July 29, 2025
Tuesday, August 12, 2025
Tuesday, August 26, 2025
Tuesday, September 9, 2025
Thursday, September 18, 2025
13:00-14:00
Title:
Extremes in dynamical systems: max-stable and max-semistable laws
Abstract:
Extreme value theory for chaotic, deterministic dynamical systems is a rapidly expanding area of research. Given a dynamical system and a real-valued observable defined on its state space, extreme value theory studies the limit probabilistic laws for asymptotically large values attained by the observable along orbits of the system. Under suitable mixing conditions the extreme value laws are the same as those for stochastic processes of i.i.d. random variables.
Max-stable laws typically arise for probability distributions with regularly varying tails. However, in the context of dynamical systems, where the underlying invariant measure can be irregular, max-semistable distributions also have a natural place in studying extremal behaviour. In this talk I will first discuss a family of autoregressive processes with marginal distributions resembling the Cantor function. The resulting extreme value law can be proven to be a max-semistable distribution. Alternatively, we can describe the autoregressive process in terms of an iterated map with an invariant measure. Further examples of extreme value laws in dynamical systems are discussed as well.
Extremes in dynamical systems: max-stable and max-semistable laws
Abstract:
Extreme value theory for chaotic, deterministic dynamical systems is a rapidly expanding area of research. Given a dynamical system and a real-valued observable defined on its state space, extreme value theory studies the limit probabilistic laws for asymptotically large values attained by the observable along orbits of the system. Under suitable mixing conditions the extreme value laws are the same as those for stochastic processes of i.i.d. random variables.
Max-stable laws typically arise for probability distributions with regularly varying tails. However, in the context of dynamical systems, where the underlying invariant measure can be irregular, max-semistable distributions also have a natural place in studying extremal behaviour. In this talk I will first discuss a family of autoregressive processes with marginal distributions resembling the Cantor function. The resulting extreme value law can be proven to be a max-semistable distribution. Alternatively, we can describe the autoregressive process in terms of an iterated map with an invariant measure. Further examples of extreme value laws in dynamical systems are discussed as well.
Tuesday, September 23, 2025
Tuesday, October 7, 2025