Abstract: In this talk, we will explain relation between u-power torsions in Breuil--Kisin prismatic cohomology and various pathologies in p-adic cohomology theories, as well as mention some new results. Part of the talk will be based on earlier joint works with Tong Liu, we shall also report some recent ongoing projects with Ofer Gabber and Alexander Petrov separately.

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.

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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/

VBAC website: https://vbac-2025.ncag.info/

VBAC website: https://vbac-2025.ncag.info/

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Institute meeting for full professors, associate professors and assistant professors, as well as support staff of the MI.

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Host: Wioletta Ruszel 
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.

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