## Joonas Turunen

I am a postdoc faculty member (Universitätsassistent) in the probability theory group of the University of Vienna, Faculty of Mathematics. I am also part of the active and lively Vienna probability community . Before arriving in Vienna, I worked as a postdoctoral researcher in mathematical physics at the ENS de Lyon, where my work was supported by a personal fellowship of the LabEx MILYON . I work on questions of random geometry arising from the interface of probability, combinatorics and statistical physics. I defended my thesis On Ising Model Coupled to Random Planar Triangulations in 2020, for which I worked in the Mathematical Physics group at the University of Helsinki. It focuses on random planar maps coupled to the Ising model, which could be viewed as a discrete model of the Liouville Quantum Gravity with matter. To get an idea of this, see my talks in Paris-Saclay (2020), in Cambridge (2018), or a short online talk . I also work on other random planar map models, both pure and decorated, and related random processes.

## Research papers

- Interfaces in the vertex-decorated Ising model on random triangulations of the disk. arXiv preprint (2020)

- Ising model on random triangulations of the disk: phase transition (with Linxiao Chen),
*Commun. Math. Phys.*Journal version, arXiv preprint**397,**793–873 (2023).

- Critical Ising model on random triangulations of the disk: enumeration and local limits (with Linxiao Chen),
*Commun. Math. Phys.*Journal version, arXiv preprint**374,**1577–1643 (2020).

## Theses

- On Ising Model Coupled to Random Planar Triangulations, doctoral thesis, 2020

- On random planar maps and their scaling limits, master's thesis, 2014

- Interpolation on L^p-spaces, bachelor's thesis, 2013

## Lecture notes

- Advanced Probability Theory, University of Vienna, 2024

## Lecturer (University of Vienna)

- Advanced Probability Theory, summer 2024

- Advanced Probability Theory, summer 2023

## Proseminar instructor (University of Vienna)

- Differential Equations and Modelling, winter 2023

## Course assistant (University of Helsinki)

- Functional analysis, fall 2019
- Probability theory II, fall 2018
- Probability theory I, fall 2018
- Stochastic Methods, fall 2017
- Stochastic methods in physics and biology, spring 2016
- Matematiikka tutuksi, autumn 2012

## Minicourse assistant (ENS de Lyon / CIRM)

- An Invitation to Analytic Combinatorics in Several Variables, ALEA Days, CIRM, march 2022

## Thesis supervisor

- Marcus Leivo, bachelor's thesis

## Talks

- Plane trees with a Wiener-Hopf factorization and an application to loop-decorated planar maps, AG Diskrete Mathematik, TU Wien, June 2024
- Loop-O(n) quadrangulations with mixed boundary conditions, (Not So) Informal Probability Seminar, University of Vienna, April 2024
- A Wiener-Hopf factorization for planar maps coupled with the O(n) loop model with mixed boundary conditions, Geometric and functional analysis seminar, Department of Mathematics and Statistics, University of Helsinki, April 2024
- Planar maps of the disk coupled with statistical physics models : Enumeration and limits, Graz Combinatorics Seminar, TU Graz, November 2023
- Statistical mechanics models on random (half-)planar maps, (Not So) Informal Probability Seminar, TU Vienna, October 2022
- Scaling limits of random planar maps with large faces and a causal core, 28th Nordic Congress of Mathematicians, Aalto University, August 2022
- Statistical mechanics models on random lattices of the half-plane, Séminaire de physique mathématique, IPhT, Paris-Saclay, June 2022
- A new family of random planar maps with large faces mixing causal and tree structures, ALEA Days, CIRM, March 2022
- Combinatorial aspects of random planar triangulations of the disk coupled with an Ising model, Rencontres ANR COMBINÉ, Online (Lyon / Paris / Bordeaux), February 2022
- Scaling limits of random planar maps with large faces and a causal structure, Mathematical physics seminar, Department of Mathematics and Statistics, University of Helsinki, October 2021
- Ising model on random triangulations with a boundary, Rentrée de l'ANR DIMERS, Sorbonne Université, September 2021
- Statistical mechanics models on random planar lattices, Postdoc days, Laboratoire de Physique, ENS de Lyon, July 2021
- Interfaces and phase transition on random triangulations coupled with the Ising model, ALÉA 2021, CIRM, March 2021
- Ising model on random half-planar triangulations: critical behavior, interfaces and phase transition, Journées Cartes au CIRM, CIRM, January 2021
- Ising model on random triangulations of the half-plane: critical behavior and phase transition, Integrable Probability and Related Fields from a Safe Distance, Department of Mathematics, MIT, October 2020
- Ising model on random triangulations with a boundary: from combinatorics to geometry, Journée Cartes du 16 octobre 2020, Institut de Maths d'Orsay, Université Paris-Saclay, October 2020
- Ising model on random triangulations of the half-plane, Bernoulli-IMS One World Symposium 2020, August 2020
- Ising model on random triangulations of the half-plane, Random Trees and Graphs Summer School, CIRM, July 2019
- Critical Ising model on infinite random triangulation of the half-plane, Young Researchers Symposium at ICMP 2018, Montréal, July 2018
- Critical Ising model on random triangulations of the disk: enumeration and limits, RGM follow up, Isaac Newton institute, Cambridge, July 2018
- Introduction to two-dimensional random geometry, Students’ seminar, Department of Mathematics and Statistics, University of Helsinki, November 2017
- Critical Ising model on infinite random triangulation of the half-plane, Mathematical physics seminar, University of Geneva, October 2017
- Boltzmann triangulations with Ising model on faces, Stochastics and statistics seminar, Department of Mathematics and Systems Analysis, Aalto University, October 2016
- Boltzmann triangulations with Ising model on faces, 46th Probability Summer School Saint-Flour, Saint-Flour, July 2016
- Boltzmann triangulations with Ising model on faces, Mathematical physics seminar, Department of Mathematics and Statistics, University of Helsinki, April 2016
- Introduction to analytic combinatorics, Students’ seminar, Department of Mathematics and Statistics, University of Helsinki, February 2016
- A bijection between labelled plane trees and rooted and pointed planar quadrangulations, Stochastic models seminar, Department of Mathematics and Statistics, University of Helsinki, March 2015

## Organization

- Path integrals and friends, University of Helsinki, September 2024 (co-organizer)

- Journée CombiTop@Lyon, ENS de Lyon, September 2021 (co-organizer)

## Some workshops I have attended

- Maps at CIRM, CIRM, January 2021
- Bernoulli-IMS One World Symposium 2020, August 2020
- Random Trees and Graphs Summer School, CIRM, July 2019
- Random maps and matrices from a geometric perspective, ENS Lyon, May 2019
- États de la recherche SMF : Statistical mechanics, Institut Henri Poincaré, Paris, December 2018
- Celebration of Mathematics: 150 Years of the Finnish Mathematical Society, University of Helsinki, November – December 2018
- International Congress on Mathematical Physics and Young Researchers Symposium, Montréal, July 2018
- RGM follow up, Isaac Newton institute, Cambridge, July 2018

## Contact

'given-name' 'dot' 'familyname' 'ät' univie 'dot' ac 'dot' at

or'given-name' 'dot' 'familyname' 'ät' alumni 'dot' helsinki 'dot' fi