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

24.2. 10:15 Romain Usciati (Paris-Saclay): Imaginary Liouville theory: probabilistic construction and conformal structure – M3 (M234)
Imaginary Liouville theory is a close relative of Liouville theory, a mathematical model introduced by Polyakov in 1981 to describe fluctuations of the metric on a Riemann surface. Imaginary Liouville theory has deep connections to various models arising in statistical physics, including percolation and the Ising model. In this talk, we revisit the challenges of giving a rigorous probabilistic construction of the theory and present recent progress revealing its rich algebraic structure. In particular, we establish non-trivial conservation laws (known as Belavin-Polyakov-Zamolodchikov equations) that point toward an underlying integrable structure.
26.2. 9:00 Madeline Nurcombe (The University of Sydney): The ghost algebra and the dilute ghost algebra – U250a
The Temperley-Lieb (TL) algebra has a wide range of applications, from physical models of polymers and quantum spin chains, to knot theory. Its basis elements can be expressed as rectangular diagrams of non-crossing strings, with multiplication based on concatenation of diagrams. There are also one- and two-boundary TL algebras, describing physical systems with boundaries, but the two-boundary TL algebra requires its diagrams to have an even number of strings connected to each boundary. In this talk, I will introduce the ghost algebra, a two-boundary generalisation of the TL algebra that allows diagrams with odd or even numbers of strings at each boundary. Its diagrams contain ghosts: dots on the boundaries that act as bookkeeping devices to ensure associativity of multiplication. I will also introduce the dilute generalisation of the ghost algebra, and discuss the lattice models associated with these algebras.
7.4. 10:15 Philémon Bordereau (EPFL): TBA – M3 (M234)