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 Sid Maibach (Bonn): TBA – Y313
16.2. 10:00 Andrew Swan (EPFL): TBA –
17.2. 10:15 Dr. Lucas Hataishi (University of Oxford): Higher genus symmetric enveloping algebras from factorization homology – M3 (M234)
A complex algebra equipped with a conjugate-linear involution which can be faithfully represented as a norm-closed algebra of bounded operators on a Hilbert space is called a C-algebra. Examples include the algebra of continuous functions on a locally compact Hausdorff space vanishing at infinity. This is indeed the unique class of commutative C-algebras up to isomorphism. All relations between locally compact Hausdorff spaces can be translated as relation between their algebra of functions, and thus the theory of C*-algebras can be considered a generalization of the theory of locally compact spaces. It offers a framework in which to study algebras of observables in quantum field theory. In this talk, I will discuss aspects of a recent construction of 2-dimensional topological quantum field theories (TQFTs) from certain inclusions of C-algebras, which we call discrete. I will explain how this notion is an axiomatization of the fixed point subalgebra of a compact group action on a C-algebra. Starting from such an inclusion, the value of the resulting TQFT on a disk is characterized by an associated C*-algebra, called the symmetric enveloping algebra; a concrete realization of an abstract object that have appeared in the algebraic approach to conformal field theories, in the theory of quantum groups and of subfactors. The values of the TQFT on other surfaces give extensions of the symmetric enveloping algebra which come equipped with actions of the mapping class groups.
24.2. 10:15 Romain Usciati (Paris-Saclay): TBA – M3 (M234)