I'm a mathematician working on problems motivated by physics, such as conformal field theories (CFT), integrable models, semiclassical limits, 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) complex geometry and Loewner theory, constructive field theory and CFT, random geometry including Schramm-Loewner evolutions (SLE), Gaussian free field (GFF), and its variants, integrable models and integrable systems, representation theory of diagram algebras, quantum groups, and vertex operator algebras, as well as combinatorial methods. 

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 GFF 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. Extending general Loewner theory. Investigating large deviations phenomena of SLE variants.

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. Relating CFT and integrability. 

Geometric aspects of CFT

Semiclassical limits, uniformization, relation to quantization. Meaning of limiting objects in complex geometry and enumerative geometry. Segal CFT and moduli spaces with boundary parameterizations.

Critical phenomena and integrability

Understanding statistical physics models at and near criticality. Finding exact solutions and formulas and perturbing them.

Algebraic structures

Temperley-Lieb algebra, its variants, and quantum groups in relation with critical models, SLE, and CFT, as well as their role for VOAs.

Education: