Mathematician working in the University of Helsinki, Finland

Who?

Hello! I am an Associate Professor and Academy Research Fellow at the Department of Mathematics and Statistics in the University of Helsinki, Finland. My email address is tuomas.sahlsten 'at' helsinki.fi.
Below is a brief overview of my past career. See also my CV in the Academy of Finland guidelines.

Career

2023-: Associate Professor (Tenure-track), Department of Mathematics and Statistics, University of Helsinki, Finland.

2022-2027: Academy Research Fellow, Academy of Finland, Finland

2021-2023: Senior Lecturer, Department of Mathematics and Systems Analysis, Aalto University, Finland.

2017-2021: Lecturer in Pure Mathematics, Department of Mathematics, University of Manchester, UK.

2015-2017: Marie Curie Research Fellow, School of Mathematics, University of Bristol, UK (personal Marie Curie Fellowship by the Horizon 2020, EU)

2014-2015: Research Fellow, Einstein Institute of Mathematics, The Hebrew University of Jerusalem, Israel (employed in M. Hochman’s ERC grant)

2013-2014: Research Associate, School of Mathematics, University of Bristol, UK (P.I. in an Emil Aaltonen foundation research grant)

2012: Project Researcher, Department of Mathematical Sciences, University of Oulu, Finland (funded by a CoE in Academy of Finland)

Education

2009-2012: PhD in Mathematics, University of Helsinki, Finland. Supervisor Pertti Mattila

2006-2009: MSc and BSc in Mathematics, University of Helsinki, Finland. Supervisors Ilkka Holopainen and Pertti Mattila.

My research is currently focused on the mathematics of quantum chaos. This field tries to understand the behaviour of quantum states of dynamical systems
such as particles or more complex many body systems and how the underlying chaos affects the localization and thermalization of the quantum states of the system. These questions are motivated by mathematical models of quantum computers, where normally we have many body entangled quantum system of qubits formed of heavy atoms. The classical dynamics of each heavy atom is strongly chaotic and so it is expected (by the Eigenstate Thermalization Hypothesis by Deutsch and Srednicki) that for the many-body quantum system should thermalise and
not preserve any information of the initial state. On the other hand, in some chaotic quantum simulators (e.g. in this experiment) it has been observed to have the system return to its original quantum state (See for example this Quanta article
meant for general audience on the phenomenon). What are the mathematical mechanisms behind these phenomena? It is expected this happens due to emergence of so called Quantum Many-Body Scarring, but it is unclear mathematically how does the entanglement of chaotic systems lead to the emergence of quantum many-body scars. For example, what is the effect of adding more particles to the system or making the system larger? Does the underlying classical chaos take over the localisation arising from increasing disorder? What happens in the thermodynamic limit and how is the energy related?

While the motivation is driven by physical observations and quantum simulators, the methods are heavily based on recent advances in pure mathematics. We are developing basic mathematical single- and many body toy models around the questions of thermalization and localization.
Some example models to study include the study of eigenfunctions of the Laplacian on single-particle motions on large hyperbolic surfaces, wave scattering on large hyperbolic surfaces with many scatterers and their thermodynamic limits,
quantized coupled interval maps and toral maps, spin chains on lattices and graphs, eigenstates for coupled chaotic billiards on domains and surfaces. Some of the methods I am trying to use with my collaborators arise from tools in semiclassical analysis in mathematical physics,
chaotic dynamical systems, spectral theory of large random graphs, the spectral, geometric and topological properties of random surfaces picked in
random models on moduli space of Riemann surfaces. As of September 2022, this work is supported by the Academy of Finland, and in the past by the EU (Horizon 2020/Marie Skłodowska-Curie Actions), University of Manchester and Magnus Ehrnrooth Foundation.

Group

Current members:

Félix Lequen, postdoc for Summer 2023 - Summer 2024

Kai Hippi, PhD student from 2022-, jointly supervised with H. Ueberschär, Sorbonne University, Paris

Sampo Paukkonen, PhD student from 2023-

Past members:

Carsten Peterson, postdoc for Summer 2023, then postdocs in Paderborn University and Université Sorbonne Paris Nord

Cliff Gilmore, Postdoc during 2018, then a postdoc in Lille and now a Marie Curie Research Fellow and Maître de conférences in Clermont Auvergne

Joe Thomas, PhD student for 2018-2021 (jointly supervised with E. Le Masson), now a postdoc in Durham in M. Magee's group

Connor Stevens, PhD student for 2017-2021, now assistant quantitative analyst

Borys Kuca, PhD student for 2018-2021 (jointly supervised with S. Prendiville and D. Robertson), then postdoc in N. Frantzikinakis' group in Crete and now postdoctoral researcher at Jagiellonian University

I actively teach and supervise students in the University and enjoy the process of seeing how
students develop interest and excellence in conceptual topics they initially found difficult or not so interesting.
During my 2017-2021 tenure as a Lecturer of Pure Mathematics in the University of Manchester, I was awarded the
Fellowship of the Higher Education Academy in University Pedagogics
from AdvanceHE in the UK. Here I will list some of the course I have taught, BSc, MSc and PhD project opportunities (TBA, email me for recent projects) and
any course material I have developed.

Spring 2019, Spring 2020, Autumn 2020, Spring 2023: Analysis, Random Walks and Groups, University of Manchester and Aalto Univeristy. Lecture notes: PDF (latest version), YouTube videos from the Autumn 2020 course (YouTube playlist) and Aalto online version ()

I am running a YouTube channel, where I try to talk about the every day life of being a mathematics researcher and give any tips I have learned.

Research tips

Starting a research project

https://youtu.be/CT5XBkDutQE

Dealing with failures in research

Making a maths paper vlog

We also recorded a vlog recording the proceess of starting and working on the article G. Gilmore, E. Le Masson, T. Sahlsten, J. Thomas: Short geodesic loops and L^{p} norms of eigenfunctions on large genus random surfaces, GAFA 31, 62-110 (2021)

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i = 0;
while (!deck.isInOrder()) {
print 'Iteration ' + i;
deck.shuffle();
i++;
}
print 'It took ' + i + ' iterations to sort the deck.';