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

10.3. 14:15 Jinwoo Sung (Chicago): A quasi-invariant group action on SLE loops – Y405
Conformal welding is an operation that encodes Jordan curves on the Riemann sphere in terms of circle homeomorphisms. Thus, composition defines a natural group action of circle homeomorphisms on Jordan curves. In this talk, I will discuss a CameronMartin type quasi-invariance result for the SLE loop measure under the right group action by WeilPetersson homeomorphisms. While this result was hinted by Carfagnini and Wang's identification of Loewner energy as the OnsagerMachlup action functional of the SLE loop measure, the group structure of SLE welding has been little understood previously. Our proof is based on the characterization of the composition operator associated with WeilPetersson circle homeomorphisms using HilbertSchmidt operators and the description of the SLE loop measure in terms of the welding of two independent quantum disks by Ang, Holden, and Sun. This is joint work with Shuo Fan (Tsinghua University and IHES).
21.3. 10:15 Tuomas Kelomäki (Aalto): TBA – M3 (M234)
8.4. 10:15 Yoh Tanimoto (University of Rome Tor Vergata): TBA – M3 (M234)
15.4. 10:15 Jiasheng Lin (Institut de Mathématiques de Jussieu-Paris Rive Gauche): TBA – M3 (M234)