Who?

Hello! I am Senior Lecturer and Academy Research Fellow (from September 2022) 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

  • 2022-2027: Academy Research Fellow, Department of Mathematics and Systems Analysis, Aalto University, Finland (personal Academy Research Fellowship by the Academy of Finland, Finland)
  • 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.
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Research

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:
  • Kai Hippi, PhD student for 2022-
  • Sampo Paukkonen, summer intern for 2022
  • Tuula Pulkkinen, summer intern for 2022
Past members:
  • Cliff Gilmore, Postdoc during 2018, now a postdoc in Lille and then starting as a Marie Curie Research Fellow 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
  • Borys Kuca, PhD student for 2018-2021 (jointly supervised with S. Prendiville and D. Robertson), now a postdoc in N. Frantzikinakis' group in Crete

Output

My full list of publications available in here (pdf) or ORCiD and below is the list of all my preprints hosted on arXiv:
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Teaching

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.

Current courses

PhD students

  • Kai Hippi (July 2022-, Aalto University)
  • Joe Thomas (graduated 2021, University of Manchester). Joint with E. Le Masson.
  • Connor Stevens (graduated 2021, University of Manchester)
  • Borys Kuca (graduated 2021, University of Manchester). Joint with S. Prendiville and D. Robertson.
  • I was also involved in the supervision of Clément Hege (University of Manchester) as co-supervisor for 2018-2020.

Past courses

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Outreach

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 Lp norms of eigenfunctions on large genus random surfaces, GAFA 31, 62-110 (2021)

Episode 4

Episode 3

Episode 2

Episode 1

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