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, quantum chaos, dynamics and fractals.

Open positions

See the general call: Doctoral Researchers in Mathematics, Operations Research, and Statistics
See the general call; Summer Interns in Mathematics, Operations Research, and Statistics (to be announced soon)

Members

Faculty

Random geometry and conformal field theory

Algebra and geometry of supersymmetric gauge theories

Oscar Kivinen

Full list of members

News

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, dynamics 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

Quantization Days 4.0, December 11-13 2023, Online.
Stochastic Sauna, December 20-21 2023 in Kumpula, Helsinki University.
Finnish Mathematical Days 2024, January 4-5 2024, Aalto University.
Twinned Workshop: New Directions in Conformal Field Theory, Hamburg University and Fields Institute, March 18-22, 2024.
IPAM Semester Program "Geometry, Statistical Mechanics, and Integrability", Spring 2024
Probabilistic Field Theories, June 17-19 2024, Aalto University.
Path integrals and friends: Conference on the interplay between physics, probability, and geometry, 3-6 September 2024 in Helsinki.
Trimester Program Probabilistic methods in quantum field theory @ HIM, Bonn, May-Aug 2025

List of past events

Mathematical Physics Seminar

Upcoming seminars

12.11. 10:15 Joona Oikarinen (Aalto): Small deviations of Gaussian multiplicative chaos and the massless Sinh--Gordon model – M3 (M234)
I will explain what Gaussian multiplicative chaos (GMC) measures are, and prove new small deviations estimates for the total mass of GMC measures. Then I will show how to use GMC to construct the path integral formulation of the massless Sinh--Gordon model on the 2-dimensional torus. Finally, I will show how the small deviations bounds can be used to derive lower and upper bounds for the free energy of the massless Sinh--Gordon model on the infinite torus. Based on joint work with Nikolay Barashkov (MPI Leipzig) and Mo Dick Wong (Durham).
19.11. 10:15 Konstantin Izyurov (University of Helsinki): Bosonization of the critical Ising correlations – M3 (M234)
I will explain an identity between scaling limits of the Ising correlations in arbitrary finitely connected planar domains, and correlations of a suitable version of a Gaussian free field, yielding explicit formulae for the former. The proof is based on (rigorously established) operator product expansions for the Ising and GFF correlation, and a limiting version of a classical identity between Szegö and Bergman kernel on Riemann surfaces. Joint work with Baran Bayraktaroglu, Tuomas Virtanen and Christian Webb.
10.12. 10:15 Eric Schippers (University of Manitoba): TBA – M3 (M234)