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

11.2. 10:15 Sami Vihko (University of Helsinki): Reconstruction of log-correlated fields from multiplicative chaos measures – M3 (M234)
We consider log-correlated Gaussian fields G on a bounded domain D \subset \R^d. These are random generalized functions, that is, random Schwartz distributions with logarithmic singularity on their covariance kernel. The Gaussian multiplicative chaos (GMC) associated to such a field is formally the exponential e^{\gamma G} with a real parameter \gamma. Rigorously the GMC is constructed as a random measure via a regularization and limiting procedure. Our main result considers the reverse problem: Given a GMC measure can we retrieve the field from it? The answer is yes. The GMC measure gives full mass to a fractal set called the \gamma-thick points of the underlying field G. Thus, it is surprising that enough information is preserved by the construction of the GMC to reconstruct the field G completely. The novelty of our result is that the dimension d is arbitrary contrary to previous result with d = 2. We can also cover the critical case \gamma = \sqrt{2d} and mildly non-Gaussian case, and if time permits, we will see what changes in this setup.
19.2. 10:15 Victor Mishnyakov (Nordita): TBA – M2 (M233)