# 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**

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.

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.

For preprints check the 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

**See also this list of international events**
## Mathematical Physics Seminar

#### Upcoming seminars

- 28.5. 10:15 Stephen Moore (IMPAN): Representations of the Reflection Equation Algebra – M3 (M234)
The reflection equation was introduced in relation to quantum integrable systems with boundary condition and is closely related to the Yang-Baxter equation. The reflection equation algebra was in turn introduced to allow the algebraic study of solutions of the reflection equation, similar to the connection between quantum groups and the Yang-Baxter equation. We will describe the basic properties of the reflection equation algebra and explain the classification of its bounded *-representations. This is based on joint work with Kenny De Commer.

- 31.5. 10:15 Joonas Vättö: Segal axioms for the massless, free boson (midterm review presentation) – M3 (M234)
After a review of the geometric axiomatisation scheme to two-dimensional conformal field theories (CFTs) in the spirit of Kontsevich and Segal, I will explicitly show how to construct the chiral CFT for the free, massless boson on arbitrary compact Riemann surfaces. The construction provides a rich playground for the interplay of distant areas of mathematics (Kähler spaces, C*-algebras, geometric function theory, etc.). Time permitting, I will sketch connections to Teichmüller theory, global analysis, and the Atiyah-Singer index theory.

- 25.6. 10:15 Ryosuke Sato (Chuo University): TBA – M3 (M234)
TBA

University of Helsinki:

Seminar and workshops in mathematical physics
## The mathematical physics group is supported by

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Page content by: webmaster-math [at] list [dot] aalto [dot] fi