Tue, 30 Apr 2024

16:00 - 17:00
C2

TBD

Matteo Pagliero
(KU Leuven)
Abstract

to follow

Fri, 01 Dec 2023

12:00 - 13:15
L3

A compendium of logarithmic corrections in AdS/CFT

Nikolay Bobev
(KU Leuven)
Abstract

I will discuss logarithmic corrections to various CFT partition functions in the context of the AdS4/CFT3 correspondence for theories arising on the worldvolume of M2-branes. I will use four-dimensional gauged supergravity and heat kernel methods and present general expressions for the logarithmic corrections to the gravitational on-shell action or black hole entropy for a number of different supergravity backgrounds. I will outline several subtleties and puzzles in these calculations and contrast them with a similar analysis of logarithmic corrections performed directly in the eleven-dimensional uplift of a given four-dimensional supergravity background. This analysis suggests that four-dimensional supergravity consistent truncations are not the proper setting for studying logarithmic corrections in AdS/CFT. These results have important implications for the existence of scale-separated AdS vacua in string theory and for effective field theory in AdS more generally.

Tue, 23 Jan 2024

14:00 - 15:00
L5

On a quantitative version of Harish-Chandra's regularity theorem and singularities of representations

Yotam Hendel
(KU Leuven)
Abstract

Let G be a reductive group defined over a local field of characteristic 0 (real or p-adic). By Harish-Chandra’s regularity theorem, the character Θ_π of an irreducible representation π of G is given by a locally integrable function f_π on G. It turns out that f_π has even better integrability properties, namely, it is locally L^{1+r}-integrable for some r>0. This gives rise to a new singularity invariant of representations \e_π by considering the largest such r.

We explore \e_π, show it is bounded below only in terms of the group G, and calculate it in the case of a p-adic GL(n). To do so, we relate \e_π to the integrability of Fourier transforms of nilpotent orbital integrals appearing in the local character expansion of Θ_π. As a main technical tool, we use explicit resolutions of singularities of certain hyperplane arrangements. We obtain bounds on the multiplicities of K-types in irreducible representations of G for a p-adic G and a compact open subgroup K.

Based on a joint work with Itay Glazer and Julia Gordon.

Thu, 02 Nov 2023
15:00
L4

Generalising fat bundles and positive curvature

Alberto Rodriguez Vazquez
(KU Leuven)
Abstract

Alan Weinstein, introduced the concept of "fat bundle" as a tool to understand when the total space of a fiber bundle with totally geodesic fibers allows a metric with positive sectional curvature. 

In recent times, certain weaker notions than the condition of having a metric with positive sectional curvature have been studied due to the apparent scarcity of spaces that meet this condition. Positive kth-intermediate Ricci curvature (Rick > 0) on a Riemannian manifold Mn is a condition that bridges the gap between positive sectional curvature and positive Ricci curvature. Indeed, when k = 1, this condition corresponds to positive sectional curvature, and when k = n−1, it corresponds to positive Ricci curvature. 

In this talk, I will discuss an ongoing project with Miguel Domínguez Vázquez, David González-Álvaro, and Jason DeVito, which aims to create new examples of compact Riemannian manifolds with Ric2 > 0. We achieve this by employing a certain generalisation of the "fat bundle" concept.

Thu, 04 May 2023

16:00 - 17:00
C1

Superrigidity in von Neumann algebras

Daniel Drimbe
(KU Leuven)
Abstract

The pioneering work of Murray and von Neumann shows that any countable discrete group G gives rise in a canonical way to a group von Neumann algebra, denoted L(G). A main theme in operator algebras is to classify group von Neumann algebras, and hence, to understand how much information does L(G) remember of the underlying group G. In the amenable case, the classification problem is completed by the work of Connes from 1970s asserting that for all infinite conjugacy classes amenable groups, their von Neumann algebras are isomorphic.

In sharp contrast, in the non-amenable case, Popa's deformation rigidity/theory (2001) has led to the discovery of several instances when various properties of the group G are remembered by L(G). The goal of this talk is to survey some recent progress in this direction.

Thu, 08 Jun 2023
14:00
L3

Condition numbers of tensor decompositions

Nick Vannieuwenhoven
(KU Leuven)
Abstract

Tensor decomposition express a tensor as a linear combination of elementary tensors. They have applications in chemometrics, computer science, machine learning, psychometrics, and signal processing. Their uniqueness properties render them suitable for data analysis tasks in which the elementary tensors are the quantities of interest. However, in applications, the idealized mathematical model is corrupted by measurement errors. For a robust interpretation of the data, it is therefore imperative to quantify how sensitive these elementary tensors are to perturbations of the whole tensor. I will give an overview of recent results on the condition number of tensor decompositions, established with my collaborators C. Beltran, P. Breiding, and N. Dewaele.

Fri, 21 Oct 2022
16:00
C1

Selected aspects of the dynamical Kirchberg-Phillips theorem

Gabor Szabo
(KU Leuven)
Abstract

 I will start this talk with a brief introduction and summary of the outcome of a joint work with James Gabe. An important special case of the main result is that for any countable discrete amenable group G, any two outer G-actions on stable Kirchberg algebras are cocycle conjugate precisely when they are equivariantly KK-equivalent. In the main body of the talk, I will outline the key arguments toward a special case of the 'uniqueness theorem', which is one of the fundamental ingredients in our theory: Suppose we have two G-actions on A and B such that B is a stable Kirchberg algebra and the action on B is outer and equivariantly O_2-absorbing. Then any two cocycle embeddings from A to B are approximately unitarily equivalent. If time permits, I will provide a (very rough) sketch of how this leads to the dynamical O_2-embedding theorem, which implies that such cocycle embeddings always exist in the first place.

Tue, 18 Oct 2022
16:00
C1

Equivariant Jiang-Su stability

Lise Wouters
(KU Leuven)
Abstract

Equivariant Jiang-Su stability is an important regularity property for group actions on C*-algebras.  In this talk, I will explain this property and how it arises naturally in the context of the classification of C*-algebras and their actions. Depending on the time, I will then explain a bit more about the nature of equivariant Jiang- Su stability and the kind of techniques that are used to study it, including a recent result of Gábor Szabó and myself establishing an equivalence with equivariant property Gamma under certain conditions.
 

Tue, 08 Nov 2022

14:30 - 15:00
L3

Rational approximation of functions with branch point singularities

Astrid Herremans
(KU Leuven)
Abstract

Rational functions are able to approximate functions containing branch point singularities with a root-exponential convergence rate. These appear for example in the solution of boundary value problems on domains containing corners or edges. Results from Newman in 1964 indicate that the poles of the optimal rational approximant are exponentially clustered near the branch point singularities. Trefethen and collaborators use this knowledge to linearize the approximation problem by fixing the poles in advance, giving rise to the Lightning approximation. The resulting approximation set is however highly ill-conditioned, which raises the question of stability. We show that augmenting the approximation set with polynomial terms greatly improves stability. This observation leads to a  decoupling of the approximation problem into two regimes, related to the singular and the smooth behaviour of the function. In addition, adding polynomial terms to the approximation set can result in a significant increase in convergence speed. The convergence rate is however very sensitive to the speed at which the clustered poles approach the singularity.

Thu, 27 Jan 2022
14:00
Virtual

Approximation and discretization beyond a basis: theory and applications

Daan Huybrechs
(KU Leuven)
Abstract

Function approximation, as a goal in itself or as an ingredient in scientific computing, typically relies on having a basis. However, in many cases of interest an obvious basis is not known or is not easily found. Even if it is, alternative representations may exist with much fewer degrees of freedom, perhaps by mimicking certain features of the solution into the “basis functions" such as known singularities or phases of oscillation. Unfortunately, such expert knowledge typically doesn’t match well with the mathematical properties of a basis: it leads instead to representations which are either incomplete or overcomplete. In turn, this makes a problem potentially unsolvable or ill-conditioned. We intend to show that overcomplete representations, in spite of inherent ill-conditioning, often work wonderfully well in numerical practice. We explore a theoretical foundation for this phenomenon, use it to devise ground rules for practitioners, and illustrate how the theory and its ramifications manifest themselves in a number of applications.

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