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

14.10. 10:15 Dr. Thomas Wasserman (Aalto University): Continuous tensor categories and c=1 conformal field theories – M3 (M234)
Some twenty years ago Fuchs, Runkel and Schweigert (FRS) established a perspective on so-called rational conformal field theories (cfts) that can be summarized by the slogan full cft = vertex operator algebra + topological quantum field theory. After describing this result, I will discuss work in progress joint with André Henriques and Adria Marin Salvador exploring it beyond rationality in the setting of full cfts at central charge c=1. One important aspect of rational cft is that it involves working with categories with only finitely many simple objects or categorical basis vectors. CFTs at c=1 behave in many ways like rational cfts, but in contrast with the rational case one needs to consider categories with infinitely many simple objects rather than just finitely many. As is familiar from undergraduate courses, working with infinitely many things is better with a topology around. I will discuss a setup (due to Marin) for talking about a category with a topological space of simple objects. After this I will explain how these continuous categories help understand the moduli space of c=1 conformal field theories and what this teaches us about pushing the FRS result beyond rationality.
21.10. 10:15 Prof. Christian Webb (University of Helsinki): Fractional charge correlation functions in the sine-Gordon model and twisted fermions – M3 (M234)
The sine-Gordon model is a fascinating model of two-dimensional quantum field theory. It is not a conformal field theory, but it is believed to enjoy many interesting properties. This talk will focus on one of these properties known as bosonization. I will discuss how at the so-called free fermion point of the model, certain correlation functions of the sine-Gordon model are tau functions related to two-dimensional Dirac operators with twisting. This talk is based on joint work with Roland Bauerschmidt and Scott Mason.
28.10. 10:15 Dr. Augustin Lafay (Aalto University): TBA – M3 (M234)