Marie Curie-stipendier til David Jekel og Harold Nieuwboer

Formålet med Marie Skłodowska-Curie Action's Postdoctoral Fellowships er at støtte forskeres karrierer og fremme fremragende forskning. Postdoc-stipendierne er målrettet forskere med en ph.d., som ønsker at udføre deres forskningsaktiviteter i udlandet, tilegne sig nye færdigheder og udvikle deres karriere. Stipendierne hjælper forskere med at få erfaring i andre lande, discipliner og ikke-akademiske sektorer.

Hver bevilling er på lidt over 1,8 millioner kroner.

David Jekel er amerikaner og fik sin ph.d. i 2020 fra University of California, Los Angeles, hos Dimitri Shlyakhtenko. Derefter havde han en NSF-postdoc-stilling ved University of California, San Diego, hos Todd Kemp i tre år. Endelig tilbragte han et år som postdoc ved Fields Institute og York University (begge Toronto, Canada), hvor han arbejdede sammen med Ilijas Farah.

David har arbejdet som postdoc på Institut for Matematiske Fag, KU, siden 1. juni 2024, hvor han sluttede sig til operatoralgebragruppen i instituttets sektion for Analyse og Kvantum. Hans vejleder er Magdalena Musat.

Fri informationsgeometri

Davids projekt vil udvikle en informationsgeometrisk fri sandsynlighedsteori. Han beskriver projektet således: 

“Information geometry refers to the synthesis of optimal transport together with measures of information such as entropy, which has shaped much recent work in partial differential equations, optimization, and data analysis. 

Free probability is a theory of non-commuting random variables that describes the large-n behaviour of many families of n x n random matrices. Free probability has had applications in data analysis, communication, finance, and many other topics where matrices appear.  It also has deep applications to the structure of von Neumann algebras, which serve as a non-commutative analogue of probability spaces, an old and challenging subject with connections to quantum mechanics, geometric group theory, ergodic theory, and more.

Information geometry has already motivated many corresponding results in free probability theory, but several deep questions remain open concerning the relationship between optimal transport and entropy in free probability, and whether it accurately describes the large-n limit of the classical information geometry for random matrices.

This project aims to

• show that free entropy is concave along optimal transport geodesics,
• establish the existence of momentum measures in free probability,
• give an optimal control formulation of free entropy, and
• exhibit counterexamples to regularity properties for optimal transport through connections with quantum information.“

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Harold Nieuwboer modtog sin ph.d. fra University of Amsterdam (Nederlandene) i januar 2024, vejledt af Michael Walter og Eric Opdam. Hans afhandling havde titlen »Classical and quantum algorithms for scaling problems«. Før sin ph.d. studerede Harold ren matematik ved Vrije Universiteit Amsterdam (Nederlandene) og University of Cambridge (Storbritannien).

Harold startede den 1. januar 2024 som postdoc ved instituttets sektion for Analyse & Kvantum, og er tilknyttet Quantum for Life Centre. Hans vejledere er Matthias Christandl og Laura Mancinska fra Centre for the Mathematics of Quantum Theory.

AsympTensorPolytop

Harold kalder sit projekt “Asymptotic properties of moment polytopes of tensors”. Han beskriver projektet således:

”I will study the behaviour of moment polytopes of families of tensors, as well as their ability to prove bounds on (asymptotic) tensor rank and sub rank. I aim to determine the properties of the moment polytopes of the unit tensors of varying ranks, as well as matrix multiplication tensors, in particular, whether they are distinct from the generic polytopes of their respective format.

“To achieve this, I will use a combination of the various descriptions of moment polytopes, which come in representation-theoretic, symplectic-geometric, intersection-theoretic, or more combinatorial forms. In particular, I will study the behaviour of moment polytopes undertaking direct sums and Kronecker products of tensors, as well as recently obtained computational results.

“The project has the potential of proving new bounds on the complexity of various tensors, as well as furthering our understanding of Strassen's asymptotic spectrum of tensors. The techniques here can also be extended to understand other settings, such as symmetric or antisymmetric tensors (bosonic or fermionic systems), algebras and quiver representations. As a result, the AsympTensorPolytope-project will have an impact in other contexts such as the complexity of matrix multiplication, quantum information theory and combinatorics.”