Mathematician working in the Aalto University, Finland

Who?

Hello! I am Senior Lecturer at the Department of Mathematics and Systems Analysis in the Aalto University in Espoo, Finland. My email address is tuomas.sahlsten 'at' aalto.fi.
Below is a brief overview of my past career. See also my CV in the Academy of Finland guidelines.

Career

2021-: 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 have many body quantum system of qubits, which have been isolated
to avoid external influences to the system. However, it is not possible to completely isolate the system and eventually there will be a thermalization and
a loss of information. 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? 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? The hope would be to shed light into the
Eigenstate Thermalization Hypothesis by Deutsch and Srednicki
and phenomenon of Quantum Many-Body Scarring.

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. This work has been supported by the EU (Horizon 2020/Marie Skłodowska-Curie Actions), University of Manchester and Magnus Ehrnrooth Foundation.

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 and
any course material I have developed.

Borys Kuca (graduated 2021). Joint with S. Prendiville and D. Robertson.

I was also involved in the supervision of Clément Hege during Spring 2019.

Past courses

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

Springs 2017, 2018, 2019, 2020: Mathematics 0C2 (Foundation year course in calculus and algebra), University of Manchester.

Autumn 2017: Metric Spaces online module on Blackboard, University of Manchester

Spring 2016: Additive Combinatorics and Ergodic Methods on Fractals, University of Bristol. Lecture notes PDF (latest 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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while (!deck.isInOrder()) {
print 'Iteration ' + i;
deck.shuffle();
i++;
}
print 'It took ' + i + ' iterations to sort the deck.';