Department of Mathematics and Systems Analysis

Research

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


Full list of members



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.

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.
For preprints check the arxiv and individual homepages.

Scientific events

Upcoming

See also this list of international events

List of past 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

Full list of our seminars


University of Helsinki: Seminar and workshops in mathematical physics 


The mathematical physics group is supported by

 

 

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