Department of Mathematics and Systems Analysis

Mathematical Physics

Welcome to the home page of the research group in Mathematical Physics at Aalto University. Our group conducts research in constructive quantum field theories, conformal field theory, random geometry and fractals.

Open positions

Summer Interns in Mathematics, Operations Research, and Statistics

Members

Faculty

Random geometry and conformal field theory

Algebra and geometry of supersymmetric gauge theories

Oscar Kivinen

Full list of members

News

Väisälä Prize awarded to Eveliina Peltola in December 2024
Väisälä Project Grant has been granted to Oscar Kivinen in June 2024
Oscar Kivinen has joined the faculty in fall 2023
Eveliina Peltola has received an ERC starting grant "Interplay of structures in conformal and universal random geometry" ISCoURaGe (2023-2028)
Tuomas Sahlsten has been appointed as an Academy Research Fellow (Academy of Finland), 2022-2027 [Tuomas moved to the University of Helsinki as an Associate Professor in September 2023]
Kalle Kytölä and Eveliina Peltola are members of the Finnish Centre of Excellence in Randomness and Structures (FiRST), 2022-2029
Eveliina Peltola has been appointed as an Academy Research Fellow (Academy of Finland), 2021-2025

Prospective students

Research

We provide Bachelor, Master, and Doctoral theses topics at the interface between mathematics and physics. Possible research topics include, but are not limited to, constructive quantum field theories, conformal field theory, random geometry, supersymmetric gauge theories and fractals. If you are interested in one of our research topics, please feel free to contact Kalle Kytölä, Eveliina Peltola, or Oscar Kivinen.

We also provide Summer Internships for outstanding students. These are advertised in the department's website.

Teaching

You are also welcome to take part in any of our lecture courses related to mathematical physics.

Recent publications

Individual publication records can be found on the Aalto research page, where you can also find an overview of research output for the Mathematical Physics area. For preprints check the math arxiv and individual homepages.

Scientific events

Upcoming

Trimester Program Probabilistic methods in quantum field theory @ HIM, Bonn, May-Aug 2025.

List of past events

Mathematical Physics Seminar

Upcoming seminars

30.6. 10:15 Jules Martel (Cergy Paris University): Towards a homological reconstruction of TQFTs – M3 (M234)
TQFTs are this idea of Witten that we can study quantum field theories from the point of view of the topology of state spaces and of topological transitions. Mathematically, it was formalised by Atiyah as a linearization of a cobordism category. It was concretely realized by ReshetikhinTuraev (RT) coupled with BlanchetHabbegerMasbaumVogel universal construction. The RT philosophy relies on a diagrammatic model for cobordisms (based on knot diagrams) and uses modules on quantum groups (or more generally monoidal categories) to linearly model these diagrams. This has more recently been extended so to permit the utilization of non semisimple monoidal categories as input of the construction giving rise to a new generation of TQFTs, for which a nice example is the KerlerLyubashenko (KL) construction. These constructions need abstract algebra tools applied on diagrammatic representations of manifolds, and we will try to avoid this by using homology theories, allowing a more global definition of TQFTs. In this talk I'll introduce a new philosophy to build TQFTs based on homology of configuration spaces. Representations of mapping class groups constitute an important byproduct of TQFTs, while more natural ones can be built out of twisted homologies of configuration spaces of surfaces. We will show that from this latter new framework we can recover step by step the properties of KL TQFTs associated with quantum groups and even a unifying framework. Ill stay introductory most of the talk but the constructions and their motivations will be the occasion to review joint works with: S. Bigelow, M. De Renzi, R. Detcherry or Q. Faes (depending on the time).