I'm a mathematician working on problems motivated by physics, such as conformal field theories (CFT), integrable models, and scaling limits of random planar lattice models.
In general, I try to combine different mathematical methods to tackle problems related to mathematical physics. My research interests include (but are not limited to) constructive field theory, CFT, correlation functions, crossing probabilities, diagram algebras, Gaussian free field, integrable models, representation theory, Schramm-Loewner evolutions (SLE), quantum groups, and vertex operator algebras. I am particularly interested in understanding algebraic and geometric structures underlying critical random models and CFT.
Research interests (see also Publications):
Random planar geometry
Making sense of rough objects e.g. using the Gaussian free field and multiplicative chaos. Constructing scaling limits of random planar lattice models.
Schramm-Loewner evolutions
Understanding SLEs and their variants and relating them to critical lattice models and CFT.
Conformal Field Theory
Building rigorous foundations for 2D CFT. Making sense of CFTs as scaling limits of critical lattice models. Using tools from CFT in probabilistic problems.
Algebraic structures
Temperley-Lieb algebra, its variants, and quantum groups in relation with critical models, SLE, CFT.
Critical phenomena and integrability
Understanding statistical physics models at and near criticality. Finding exact solutions and formulas.
Biography:
Currently I work at Aalto Uni (Finland) and at Uni Bonn (Germany).
- 09/2021 ->: Academy Research Fellow, Aalto Uni, Dep. of Mathematics and Systems Analysis.
- 09/2021 - 01/2022: TT-Asst. Professor, Uni Jyväskylä, Dep. of Mathematics and Statistics.
- 02/2021 ->: TT-Asst. Professor, Aalto Uni, Dep. of Mathematics and Systems Analysis.
- 09/2019: Professor (W2, Bonn Junior Fellow), Uni Bonn, Institute for Applied Mathematics (IAM), and Hausdorff Center for Mathematics (HCM).
- 09/2016 - 08/2019: Postdoc in Prof. Stanislav Smirnov's group, Uni Geneva and NCCR SwissMAP.
02/2012 - 09/2016: PhD Student in Math. Phys. Group (Dr. Kytölä / Prof. Kupiainen), Uni Helsinki.
I did my studies & PhD (2016) at University of Helsinki, where I mostly studied mathematics (major) and theoretical physics (minor), with a glimpse of other sciences.
Education:
Department of Mathematics and Statistics
09/2016: Doctor of Philosophy (Mathematics)
02/2012: Master of Science (Mathematics)
12/2010: Bachelor of Science (Mathematics)
During 2012-2016, my graduate research was supported by the Vilho, Yrjö and Kalle Väisälä Foundation (Finnish Academy of Science and Letters), and by the Finnish National Doctoral Programme in Mathematics and its Applications (University of Helsinki).
PhD & Master Thesis Advisors:
Prof. Kalle Kytölä and Prof. Antti Kupiainen
Theses (for pdf, see Publications):
- PhD Thesis: Applications of quantum groups to conformally invariant random geometry.
- Minor Thesis (theoretical physics): Two-dimensional critical phenomena, interfaces, scaling limits, and Schramm-Loewner evolutions.
- Master's Thesis: An explicit relation between monodromy of the Knizhnik-Zamolodchikov equations and braiding of quantum sl2.
- Bachelor's Thesis: The Chinese remainder theorem.
