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Events
The 2nd East German Tensor Day

conference

06/12/2021 06/12/2021

The 2nd East German Tensor Day

MPI für Mathematik in den Naturwissenschaften Leipzig

E1 05 (Leibniz-Saal)

Due to the Corona pandemic this event will be canceled.
We thank you for your understanding and apologize for any inconvenience this may cause.

Tensors a higher dimensional analogues of matrices and they are a fundamental building block in modern developments of data analysis and machine learning. The goal of this one-day workshop is to foster collaboration between researchers that work in East Germany on tensors and adjacent fields. The idea is to have an in-person seminar with several one-hour talks and enough time to explore new cooperations.

Due to current Corona regulations, on-site participation is limited to 25 participants. Registrations will be considered on a first come, first serve basis. The event will be streamed, too.

Speakers

Nick Dewaele

KU Leuven

Henrik Eisenmann

MPI MIS Leipzig

Paul Görlach

Otto von Guericke University Magdeburg

Venera Khoromskaia

Max Planck Institute for Mathematics in the Sciences

Max Pfeffer

TU Chemnitz

Irem Portakal

Max Planck Institute for Mathematics in the Sciences

Dec 6, 2021
10:00	Irem Portakal (Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany) Tensors, Nash, and Other Equilibria In this ongoing joint project with Bernd Sturmfels, we explore the polynomial systems arising from Nash, correlated and dependency equilibria in Game Theory. Nash equilibria are given by a real algebraic variety in the tensor space of probability distributions of rank 1. In this case one assumes the causal independence of the actions and decisions of the players. If one drops this assumption i.e. the rank 1 condition, one encounters the correlated (Aumann, 1974) and dependency (Spohn, 2003) equilibria. For any finite game, those three equilibria always exist by the famous result of Nash in 1951. In this talk, we follow these concepts on 2-person games in which each player has two strategies and present a glance for the general case.
10:45	Coffee Break
11:00	Paul Görlach (Otto von Guericke University Magdeburg, Chemnitz, Germany) tba
11:45	Venera Khoromskaia (Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany) Tensor numerical methods in quantum chemistry: from the Hartree-Fock solvers to optical spectra of molecules Abstract
12:30	Lunch Break
13:30	Henrik Eisenmann (MPI MIS Leipzig, Leipzig, Germany) Maximum distance of a symmetric rank-two tensor to rank-one tensors We investigate the maximum distance of a symmetric rank-two tensor to rank-one tensors. An equivalent problem is given by the minimal ratio of spectral and Frobenius norm of a tensor. For matrices the distance of a rank k matrix to a rank r matrices is given by the singular value decomposition, but since there is a lack of a fitting analog of the singular value decomposition for tensors, this question is more difficult in the regime of tensors.
14:15	Nick Dewaele (KU Leuven, Leuven, Belgium) Computing the condition number of tensor decompositions through Tucker compression Several computational problems in data science and signal processing can be understood as finding a decomposition of a tensor. In contrast to matrices, tensor decompositions are often unique with minimal constraints. This property makes it possible to have a unique interpretation of the decomposition of the tensor. This is the case for decompositions like the (symmetric) tensor rank and block term decomposition. One caveat, however, is that the decomposition may be highly sensitive with respect to the tensor. This sensitivity is measured by the condition number, which determines up to what precision the decomposition can be known. We will discuss an algorithm to compute the condition number of several of tensor decompositions. In practical computations, one often represents a tensor in a minimal subspace prior to computing its decomposition. This dimensionality reduction technique, known as Tucker compression, can dramatically speed up the computation of the decomposition. Thus, it is natural to ask whether this technique changes to condition number. In recent work, we showed that the answer is negative. We illustrate how this result can be used to speed up the computation of the condition number by several orders of magnitude.
15:00	Coffee Break
15:15	Max Pfeffer (TU Chemnitz, Chemnitz, Germany) tba

Participants

Peter Benner

MPI for Dynamics of Complex Technical Systems

Arthur Bik

MPI Leipzig

Paul Breiding

Max Planck Institute for Mathematics in the Sciences

Nick Dewaele

KU Leuven

Henrik Eisenmann

MPI MIS Leipzig

Samantha Fairchild

MPI MiS

Marina Garrote-López

Max Planck Institute for Mathematics in the Sciences

Fulvio Gesmundo

MPI MiS

Paul Görlach

Otto von Guericke University Magdeburg

Thomas Kahle

Otto-von-Guericke Universität Magdeburg

Venera Khoromskaia

Max Planck Institute for Mathematics in the Sciences

Kirandeep Kour

Max Planck Institute for Dynamics of Complex Technical Systems

Raffaella Mulas

Max Planck Institute for Mathematics in the Sciences

Max Pfeffer

TU Chemnitz

Irem Portakal

Max Planck Institute for Mathematics in the Sciences

Elima Shehu

The Max Planck Institute for Mathematics in the Sciences

Miruna-Stefana Sorea

SISSA

Martin Stoll

TU Chemnitz

Bernd Sturmfels

Max Planck Institute for Mathematics in the Sciences

Simon Telen

MPI MiS

André Uschmajew

Max Planck Institute for Mathematics in the Sciences

Christiaan van de Ven

University of Trento

Nick Vannieuwenhoven

KU Leuven

Giulio Zucal

MPI MiS Leipzig

Scientific Organizers

Paul Breiding

Max Planck Institute for Mathematics in the Sciences

André Uschmajew

Max Planck Institute for Mathematics in the Sciences Homepage

Administrative Contact

Saskia Gutzschebauch

Max Planck Institute for Mathematics in the Sciences Contact by email