"Derived categories in geometry, algebra and physics"

"Formalizing Fermat"

"From Lindemann-Weierstrass to Siegel-Shidlovskii"

"Counting in hyperbolic space: number theory and geometry"

"On constructing motivic Galois groups"

"A tale of three zeta functions"

I will discuss remarkable analogies between zeta functions encountered in the following settings: number theory, algebraic curves over finite fields and geodesic flows of Riemannian manifolds.

"Classification and curvature of algebraic varieties"

A recurring theme in modern geometry is that spaces should be classified according to their curvature properties. In this talk I’ll discuss what this means from the perspective of algebraic geometry.

"Algebraic Topology and Algebraic Geometry for Data Science"

In this talk I will talk about my research areas which deal with computational algebraic topology and computational algebraic geometry. I will overview the utility of algebraic topology and algebraic geometry in data analysis and machine learning.

"Topics in the geometry of numbers"

I will present a number of results on the distribution of lattice points. Time allowing, I will also mention an application of the lattice points in mathematical physics, namely, the study of Laplace eigenfunctions on the torus, and other surfaces with arithmetic aspect. 

"Spherical surfaces and their moduli spaces"

A spherical surface is a Riemann surface with a curvature 1 metric and a finite number of conical singularities. It can always be glued from a collection of spherical triangles by isometric identification of their sides. Contrary to the hyperbolic case, when the theory is almost identical to the theory of Riemann surfaces, the case of spherical surfaces is wide open. I will speak about some recent results in the area, such as a full description of the moduli space of spherical metrics with one conical singularity on a torus (joint work with Gabrielle Mondello and Alex Eremenko), the description of possible conical angles of a spherical metric on a 2-sphere, disconnectedness of the moduli spaces and their unboundedness (joint work with Gabirelle Mondello).

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"Arithmetic schemes and Deligne—Milnor formula"

I'll discuss some instances of the interaction between algebra and topology in algebraic geometry, with particular emphasis on the Bloch conductor conjecture (and its special case, the Deligne--Milnor formula).

Minimal surfaces and the Laplace operator

Minimal surfaces are two-dimensional generalisations of geodesics, namely, they are critical points of the area functional. While it is known that all geodesics in the Euclidean space are straight lines, the theory of minimal surfaces is much more complicated. In this talk I will provide gentle introduction into the subject and explain how minimal surfaces can be described using Laplace operator and its eigenvalues.

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