Presentations

Presentation of the habilitation thesis.

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Schubert polynomials: flags and pipe-dreams*, NRU HSE Mathematical Winter School for students, Voronovo 2015

pdf (in Russian)

An introduction to Schubert calculus on complete flag varieties, Schubert polynomials and pipe-dreams. An expanded version of 2013 presentation with the same title.

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Newton-Okounkov polytopes of symplectic flag
varieties*, Conference Geometry, Topology and Integrability, Skolkovo 2014

pdf

Slides of my talk about Newton-Okounkov polytopes for flag varieties based on arXiv:1409.6097 [math.AG]. Geometric Demazure operators act on polytopes (more generally on convex chains) and take a polytope to a polytope of dimension one greater. For instance, Gelfand-Zetlin polytopes in type $A$ can be obtained by applying a suitable composition of geometric Demazure operators to a point

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Demazure operators and geometric mitosis*,
(ICM 2014 Satellite conference) Topology of torus actions and applications to geometry and combinatorics, Daejeon

pdf

Slides of my talk about geometric mitosis based on arXiv:1409.6097 [math.AG]. Geometric Demazure operators act on polytopes (more generally on convex chains) and take a polytope to a polytope of dimension one greater. For instance, Gelfand-Zetlin polytopes in type $A$ can be obtained by applying a suitable composition of geometric Demazure operators to a point

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The many faces of polytopes*, popularizing lecture from the cycle "Mathematics: difficult made easy", Moscow 2013

pdf (in Russian)

Slides of the talk about convex polygons, polyhedra and polytopes in higher dimension, and their applications (compass and ruler constructions, Euler formula, simplex-method, Newton polygons). Intended for non-mathematical audience.

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Schubert polynomials: flags and pipe-dreams*, NRU HSE Mathematical Winter School for students, Golitsyno 2013

pdf (in Russian)

An introduction to Schubert calculus on complete flag varieties, Schubert polynomials and pipe-dreams.

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Schubert calculus for equivariant algebraic cobordism*, BIRS workshop Lie algebras, torsors and cohomological invariants, Banff 2012

pdf

Slides of my talk about Schubert calculus in equivariant algebraic cobordism of complete flag varieties. This is joint work with Amalendu Krishna (arXiv:1104.1089 [math.AG]). For a connected reductive group G over a field k of zero characteristic and a k-split maximal torus T in G, the T-equivariant algebraic cobordism ring of the flag variety G/B (where B is a Borel subgroup in G) admits a Borel type presentation. There are also analogs of divided difference operators acting on this ring. These ingredients allow one to study Schubert calculus in equivariant cobordism, that is, generalized Schubert cycles (given by the classes of Bott-Samelson resolutions) and their multiplication. I will discuss results and open problems in this direction.

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Convex geometric Demazure operators*, The 5th MSJ-SI Schubert calculus, Osaka 2012

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Slides of my talk about convex geometric analogs of Demazure operators based on arXiv:1307.7234v1 [math.AG]. Geometric Demazure operators act on polytopes (more generally on convex chains) and take a polytope to a polytope of dimension one greater. For instance, Gelfand-Zetlin polytopes in type $A$ can be obtained by applying a suitable composition of geometric Demazure operators to a point

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Conics tangent to five given*, Spring School in Mathematics and Physics for students, Sevastopol 2012

pdf (in Russian)

The first part is an elementary introduction to enumerative geometry (apart from small corrections and additions it repeats the presentation *
Enumerative geometry and 3264 conics* below). The second part is a more rigorous explanation of the results in the first part using algebraic geometry.

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Enumerative geometry and 3264 conics*, NRU HSE Mathematical Winter School for students, Klyazma 2012

pdf (in Russian)

An elementary introduction to enumerative geometry.

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Gelfand-Zetlin polytopes and Demazure characters*, International Conference "50 years of IITP", Moscow 2011

pdf

An exposition of the formula for the Demazure characters of Schubert varieties in terms of the exponential sums over faces of Gelfand-Zetlin polytopes (joint work with Evgeny Smirnov and Valdlen Timorin).

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Polytopes and algebraic geometry*, NRU HSE Mathematical Winter School for students, Golitsyno 2011

pdf (in Russian)

An elementary exposition of Koushnirenko theorem.