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

14.4. 10:15 Ian Välimaa (Aalto University): Concentration of large random Gram matrices – M3 (M234)
This talk discusses the concentration of a Gram matrix XX^T and its off-diagonal part, where X is a large random matrix with independent and centered entries bounded by one. Such matrices play a fundamental role in high-dimensional statistics including covariance matrix estimation, dimension reduction and tensor clustering. It is well-known that, under suitable assumptions, the empirical eigenvalue distribution of the Gram matrix converges to the Marchenko-Pastur distribution. Furthermore, the extremal eigenvalues converge to the edges of the limiting distribution. In contrast, less is known about the behavior when the diagonal is removed. This talk focuses on the extremal eigenvalues of the off-diagonal part of the Gram matrix. The first half of the talk presents an asymptotically sharp, high-probability bound for these extremal eigenvalues of the off-diagonal part, while the second half outlines the proof.
14.4. 15:00 Keshav Dahiya (Indiana University): A method for computing R-matrices acting in the vector representations of quantum affine algebras (remote talk) – U250a
The theory of q-characters can be used to determine reducibility of tensor products of two representations of quantum affine algebras. In this talk, we discuss how this can be used to extract information about the R-matrix acting on this tensor product. When combined with some nice properties of the R-matrix, this information is enough to determine the R-matix (up to a choice of basis) in the case of vector representations.