Thu, 27 Feb 2025

11:00 - 12:00
C5

n-ampleness and pseudobuildings

Silke Meißner
(University of Münster)
Abstract
Zilber showed that a strongly minimal theory is 1-ample if and only if it interprets a pseudoplane. We will see a generalisation of this result to n-ample theories and define the notion of a pseudobuilding. This is joint work in progress with Katrin Tent.
Thu, 06 Mar 2025

17:00 - 18:00
L3

Orthogonal types to the value group and descent

Mariana Vicaria
(University of Münster)
Abstract
First, I will present a simplified proof of descent for stably dominated types in ACVF. I will also state a more general version of descent for stably dominated types in any theory, dropping the hypothesis of the existence of invariant extensions. This first part is joint work with Pierre Simon.
 
In the second part, motivated by the study of the space of definable types orthogonal to the value group in a henselian valued field and their cohomology; I will present a theorem that states that over an algebraically closed base of imaginary elements,  a global invariant type is residually dominated (essentially controlled by the residue field) if and only if it is orthogonal to the value group , if and only if its reduct in ACVF is stably dominated. This is joint work with Pablo Cubides and Silvain Rideau- Kikuchi. The result extend to some valued fields with operators.
Thu, 20 Feb 2025

17:00 - 18:00
L3

Ax-Kochen/Ershov principles in positive characteristic

Franziska Jahnke
(University of Münster)
Abstract

A major open problem in the model theory of valued fields is to gain an understanding of the first-order theory of the power series field F((t)), where F denotes a finite field. For sufficiently "nice" henselian valued fields, the Ax-Kochen/Ershov philosophy allows to reduce questions of elementary equivalence and elementary embeddings to the analogous questions about the value group and residue field (or related structures). In my talk, I will present a new such principle which applies in particular to a large class of algebraic extensions of F((t)), albeit not to F((t)) itself. The talk is based on joint work with Konstantinos Kartas and Jonas van der Schaaf.

Wed, 04 Dec 2024
11:00
L4

Effective Mass of the Polaron and the Landau-Pekar-Spohn Conjecture

Chiranjib Mukherjee
(University of Münster)
Abstract

According to a conjecture by Landau-Pekar (1948) and by Spohn (1986), the effective mass of the Fröhlich Polaron should diverge in the strong coupling limit like a quartic power of the coupling constant. In a recent joint with R. Bazaes, M. Sellke and S.R.S. Varadhan, we prove this conjecture.

Tue, 15 Oct 2024
16:00
C3

Continuous selection in II1 factors

Andrea Vaccaro
(University of Münster)
Abstract

In this talk, based on a joint work with Ilijas Farah, I will present an application of an old continuous selection theorem due to Michael to the study of II1 factors. More precisely, I'll show that if two strongly continuous paths (or loops) of projections (p_t), (q_t), for t in [0,1], in a II1 factor are such that every p_t is subequivalent to q_t, then the subequivalence can be realized by a strongly continuous path (or loop) of partial isometries. I will then use an extension of this result to solve affirmatively the so-called trace problem for factorial W*-bundles whose base space is 1-dimensional.

Mon, 26 Aug 2024

14:00 - 15:00
L6

Analytic K-theory for bornological spaces

Devarshi Mukherjee
(University of Münster)
Abstract

We define a version of algebraic K-theory for bornological algebras, using the recently developed continuous K-theory by Efimov. In the commutative setting, we prove that this invariant satisfies descent for various topologies that arise in analytic geometry, generalising the results of Thomason-Trobaugh for schemes. Finally, we prove a version of the Grothendieck-Riemann-Roch Theorem for analytic spaces. Joint work with Jack Kelly and Federico Bambozzi. 

Thu, 30 May 2024

17:00 - 18:00
L3

Failure of the amalgamation property for definable types

Martin Hils
(University of Münster)
Abstract

In recent joint work with Pablo Cubides Kovacsics and Jinhe Ye on beautiful pairs in the unstable context, the amalgamation property (AP) for the class of global definable types plays a key role. In the talk, we will first indicate some important cases in which AP holds, and we will then present the construction of examples of theories, obtained in joint work with Rosario Mennuni, where AP fails.

Tue, 30 Apr 2024
11:00
L5

A priori bounds for subcritical fractional $\phi^4$ on $T^3$

Salvador Cesar Esquivel Calzada
(University of Münster)
Abstract

We study the stochastic quantisation for the fractional $\varphi^4$ theory. The model has been studied by Brydges, Mitter and Scopola in 2003 as a natural extension of $\phi^4$ theories to fractional sub-critical dimensions. The stochastic quantisation equation is given by the (formal) SPDE 

\[

(\partial_t + (-\Delta)^{s}) \varphi = - \lambda \varphi^3 + \xi\]

where $\xi$ is a space-time white noise over the three dimensional torus. The equation is sub-critical for $s > \frac{3}{4}$.

 

We derive a priori estimates in the full sub-critical regime $s>\frac{3}{4}$. These estimates rule out explosion in finite time and they imply the existence of an invariant measure with a standard Krylov-Bogoliubov argument. 

Our proof is based on the strategy developed for the parabolic case $s=1$ in [Chandra, Moinat, Weber, ARMA 2023]. In order to implement this strategy here, a new Schauder estimate for the fractional heat operator is developed. Additionally, several algebraic arguments from [Chandra, Moinat, Weber, ARMA 2023] are streamlined significantly. 

 

This is joint work with Hendrik Weber (Münster). 

Tue, 02 May 2023

16:00 - 17:00
C1

Amenable group actions on C*-algebras and the weak containment problem

Siegfried Echterhoff
(University of Münster)
Abstract

The notion of amenable actions by discrete groups on C*-algebras has been introduced by Claire Amantharaman-Delaroche more than thirty years ago, and has become a well understood theory with many applications. So it is somewhat surprising that an established theory of amenable actions by general locally compact groups has been missed until 2020. We now present a theory which extends the discrete case and unifies several notions of approximation properties of actions which have been discussed in the literature. We also present far reaching results towards the weak containment problem which asks wether an action $\alpha:G\to \Aut(A)$ is amenable if and only if the maximal and reduced crossed products coincide.

In this lecture we report on joint work with Alcides Buss and Rufus Willett.

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