# Joona Oikarinen

University of Helsinki

Department of Mathematics and Statistics

Exactum, Office B332

Pietari Kalmin Katu 5, Helsinki, 00560, Finland

email: *firstname.lastname X helsinki.fi*

I'm a Postdoctoral researcher at the University of Helsinki, Department
of Mathematics and Statistics, under the supervision of Antti Kupiainen.

I am part of the Mathematical Physics research group.

## Research interests

- The probabilistic approach to Liouville field theory.
Alexander Polyakov introduced Liouville Quantum Gravity in 1981,
an essential part of which is the Liouville (quantum) field theory.

The Liouville field theory was defined in a mathematically rigorous manner recently, by using probabilistic methods (Gaussian free field and Gaussian multiplicative chaos).

This way of defining the Liouville theory is what the physicist would call the path integral formulation. However, in the physics literature, Liouville theory is usually studied using the

Conformal Bootstrap approach. One of the main goals of the rigorous probabilistic approach to Liouville theory is to show that these two approaches are equivalent. - Aspects of constructive quantum field theory related to integrability and Gaussian multiplicative chaos

## Publications

- Stress-Energy in Liouville Conformal Field Theory on Compact Riemann Surfaces - Preprint (2021) - arXiv
- Stress-Energy in Liouville Conformal Field Theory, with Antti Kupiainen - Journal of Statistical Physics (2020) - DOI
- Smoothness of correlation functions in Liouville Conformal Field Theory - Annales Henri Poincare (2019) - DOI

## Theses

- Stress-Energy Tensor and Conformal Ward Identities in Constructive Liouville Quantum Field Theory - PhD thesis (2021)
- Probabilistic Liouville field theory on the two-dimensional sphere - MSc thesis (2017)
- Testifunktioavaruuden topologia (in Finnish) - BSc thesis (2015)

## Other

## Teaching

Teaching assistant for the following graduate level courses:- Clifford Analysis (Fall 2017)
- Quantum Fields and Probability (Spring 2018)
- Introduction to Liouville Quantum Gravity (Spring 2019)
- Chaos, Dynamics, Entropy (Classical Dynamics) (Spring 2020)
- Functional Analysis (Fall 2020)

- Raja-arvot (Limits) (Fall 2015)
- Differentiaalilaskenta (Differential calculus) (Fall 2015)
- Integraalilaskenta (Integral calculus) (Spring 2016)
- Sarjat (Series) (Spring 2016)
- Stokastiset Prosessit (Stochastic Processes) (Fall 2021)