# 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

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## Group members

### Faculty

**Random geometry and conformal field theory**
**Dynamical systems and quantum chaos**

News

- 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
- 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 constructive quantum field theories, conformal field theory, random geometry, quantum chaos, dynamics and fractals. If you are interested in one of our research topics, please feel free to contact Kalle Kytölä, Eveliina Peltola or Tuomas Sahlsten.

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

## Mathematical Physics Seminar

#### Upcoming seminars

- 31.1. 10:15 Kalle Koskinen (University of Helsinki): Infinite volume states of the mean-field spherical model in a random external field – M2 (M233)
One method of introducing external randomness to a Gibbs state, as opposed to the internal randomness of the Gibbs state itself, is to perturb the Hamiltonian with a term corresponding to the coupling of a random external field to the system. For the mean-field spherical model, the corresponding perturbed model can be exactly solved, in some sense, in the infinite volume limit. In this talk, we will introduce, motivate, and present some constructions and results concerning the so-called infinite volume metastases of the mean-field spherical model in a random external field. The aim of this talk is to present the general theory of disordered systems as it pertains to this particular model, and highlight the particular aspects of this model which lead to its curious behaviour as a disordered system. This talk is based on work in a recently accepted paper to appear in the Journal of Statistical Physics.

- 7.2. 10:15 Petri Laarne (University of Helsinki): Almost sure solution of nonlinear wave equation: from donut to plane – M2 (M233)
I discuss the recent preprint [arXiv:2211.16111] of Nikolay Barashkov and I, where we show the almost sure well-posedness of a deterministic nonlinear wave equation (cubic Klein-Gordon equation) on the plane. Here "almost sur" is in respect to the \\\\phi^4 quantum field theory. I briefly introduce the invariant measure argument and outline the solution on 2D torus due to Oh and Thomann. I then explain our main contributions: extension of periodic solutions to infinite volume, and a weaker result for nonlinear Schrödinger equation. The viewpoint is functional-analytic with a dash of probability.

- 7.3. 10:15 Stephen Moore (Institute of Mathematics Polish Academy of Sciences): TBA – M2 (M233)
- 7.3. 11:15 Ethan Sussman (MIT): TBA – M2 (M233)
- 14.3. 10:15 Ethan Sussman (MIT): TBA – M2 (M233)
- 11.4. 10:15 Peter Kristel (Bonn): TBA – M2 (M233)

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