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
Members
Faculty
Random geometry and conformal field theory
Algebra and geometry of supersymmetric gauge theories
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.
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.
See also this list of international events
Mathematical Physics Seminar
Upcoming seminars
- 17.11. 10:15 Andrew Swan (EPFL): How I tried and failed to prove the Polyakov conjecture – M3 (M234)
In 1975, Polyakov conjectured that the classical $O(n)$ model in two dimensions should have exponentially decaying correlations at every positive temperature, so long as $n \ge 3$. In this talk, I will describe an isomorphism theorem connecting the $O(n)$ model to a self-interacting random walk, called the Ising--Vertex Diminished Jump Process (Ising--VDJP). The walker is given an initial local-time budget at each vertex, which it consumes while waiting there. Smaller remaining budgets discourage revisits, and the walk stops when a budget is exhausted. Its jump rates are also influenced by an auxiliary Ising model coupled to the remaining budgets. The utility of the isomorphism is that it turns the spatial decay of correlations into a question about how far the walker travels before it dies.
Sadly, I was not able to prove the conjecture. But if we add a uniformly positive external field, favouring alignment in a fixed direction, a simple argument which I will explain gives exponential decay of transverse correlations for all $O(n)$ models, for all positive temperatures, on every finite or infinite graph with uniformly bounded total incident edge weight, $sup_i \sum_j W_{ij}<\infty$
University of Helsinki:
Seminar and workshops in mathematical physics
The mathematical physics group is supported by
Page content by: webmaster-math [at] list [dot] aalto [dot] fi
