Laboratory of Algebraic Geometry and Homological Algebra

Modern algebraic geometry has a long history, and outstanding mathematicians of the planet have been studying it for centuries. Homological algebra flourished in the XX century, but since then it has also achieved impressive comprehensive results. Those who have decided to study this topic, will face a whole world of fundamental scientific ideas, where one might even get lost.

The staff of our laboratory is ready to help students and graduate students who have decided to start such an intellectual journey. However, everyone should be ready to take their own responsibilitн, since only a combination of independent work and supervision can lead to a positive result.

The activities of our employees cover a wide range of both fundamental issues of algebraic geometry and homological algebra. Their research is also focused on specific classes of varieties, their birational structure, topological properties, a wide variety of invariants, and applications of algebraic geometry to various issues of mathematics and physics.

You can find more information about research areas of our employees by clicking on their profiles below.

News:

  • On 6th of July 2020 Stanislav Grishin, technician of our lab, successfully defended his bachelor’s thesis. Congratulations!


  • A lecture course “Discrete integrable systems and Painlevé equations” by Professor Anton Dzhamay (University of Nothern Colorado) took place on 10-19 March 2020. The videos of lectures are avaiable at:

https://www.youtube.com/watch?v=4FcpJjZJHJg&feature=youtu.be,
https://www.youtube.com/watch?v=Dv0HKAJGYSs&feature=youtu.be,
https://www.youtube.com/watch?v=r3nEjrO1ko8&feature=youtu.be


Seminars:
  • Specialized seminar by A.I. Bondal and D.V. Dubnov Applications of Homological Algebra Methods to Algebraic Geometry (fall/spring 2019/2020).

  • Applications of Algebraic and Geometric Methods to Integrable Systems and Quantum Physics Seminar (fall/spring 2019/2020).

  • Special course by A.I. Bondal and D.V. Dubnov Homological Methods for Geometry and Algebra (fall/spring 2019/2020).

  • Special course by I.V. Karzhemanov Riemann Surfaces and Algebraic Curves (fall/spring 2019/2020).

  • Special course by S.Yu. Orevkov Topology of Real Algebraic Flat Curves (fall/spring 2019/2020).

If you have questions regarding the lab, please contact us by e-mail: alggeommipt@gmail.com

Alexey Bondal

Head of Laboratory, ScD (Phys&Math)

Professional experience

Lead researcher, Steklov Institute of Mathematics; researcher, Lab for Mirror Symmetry and Automorphic Forms, Higher School of Economics

Web: https://de.wikipedia.org/wiki/Alexei_Igorewitsch_Bondal

Academic Interests
Theory of exact, Abelian, derivative, triangulated, differential graduated and higher homotopic categories; non-commutative geometry; applications of homological algebra to algebraic geometry, topology and representation theory; mathematical issues of quantum field theory and reflexive symmetry; applications of algebraic geometry and homological algebra to quantum communications theory; cellular automata such as Langton's ant; geometric and category approaches to estimating tensor ranks and the complexity of matrix products

Ilya Zhdanovskiy

Deputy Head of Laboratory, PhD (Phys&Math)

Professional experience
Associate Professor, Dept. of Higher Mathematics, Moscow Institute of Physics and Technology; researcher, Lab for Algebraic Geometry and Its Applications, Higher School of Economics

Web: https://www.researchgate.net/profile/Ilya_Zhdanovskiy
Academic Interests
Representation theory, algebraic geometry, quantum information theory, integrable systems

Stepan Orevkov

Lead researcher, PhD (Phys&Math)

Professional experience
Senior researcher at Steklov Institute of Mathematics

 Web: https://www.math.univ-toulouse.fr/~orevkov/
Academic Interests
Topology of flat real algebraic curves and surfaces, the theory of braids, complex surface mapping (as applicable to the Jacobian hypothesis)

Vassili Gorbunov

Lead researcher, PhD (Phys&Math)

Professional experience
Academic Interests
Mathematical physics, topology, quantum integrable systems

Vyacheslav Shokurov

Lead researcher, ScD (Phys&Math)

Professional experience
  • Professor, Johns Hopkins University (Baltimore, USA); lead researcher, Steklov Institute of Mathematics

    Key accomplishments: Numerical Geometry of Algebraic Varieties presentation, International Congress of Mathematicians, Berkeley, CA, USA, 1986

    Web: https://en.wikipedia.org/wiki/Vyacheslav_Shokurov

Academic Interests
Algebraic geometry

Kyoji Saito

Lead researcher, PhD (Phys&Math)

Professional experience

Professor, Research Institute for Mathematical Sciences, (Kyoto, Japan); researcher, Kavli Institute, Tokyo University (Kashiwa, Japan)

Key accomplishments: The Limit Element in the Configuration Algebra for a Discrete Group presentation, International Congress of Mathematicians, Kyoto, Japan, 1990; Mathematical Society of Japan award, 2011

Academic Interests
Reflection groups, hypersurface features, complex geometry

Ilya Karzhemanov

Researcher, PhD (Phys&Math)

Professional experience
Academic Interests
Geometry, algebra, number theory

Denis Degtyarov

Researcher

Academic Interests
Integrable systems in algebraic geometry

Svetlana Makarova

Researcher

Professional experience

Вoctorate student, MIT (Boston, USA)

Key accomplishments: Dobrushinskaya scholarship (fall 2014); Silver Nestling scholarship (fall 2014 - spring 2017); Levinson fellowship (summer 2016 and 2017); Collamore-Rogers fellowship (2016-2017)

Academic Interests
Homological algebra and its applications to algebraic geometry, including the proof of strange duality for K3 surfaces, based on birational isomorphisms (given represented by Fourier-Mukai functionaries) of stable pencil module spaces, combinatorial generation of derivative categories for quiver representation spaces with GIT factors, category-geometric approach to tensor ranks, general theory of DG and triangulated categories, and module problems

Grigory Konovalov

Technician

Professional experience
 MSc student, Skoltech (Skolkovo, Russia)
Academic Interests
Algebraic geometry (algebraic surfaces, rationality problems, Hodge theory)

Stanislav Grishin

Technician

Professional experience

BSc, Moscow Institute of Physics and Technology (Dolgoprudny, Russia)

Key accomplishments: IMC Blagoevgrad gold medal; VJIMC silver medal (Ostrava); NCUMC math competition winner (Saint Petersburg); winner of other domestic math competitions

Academic Interests
Functional analysis, general algebra

Konstantin Loginov

Researcher, PhD (Phys&Math)

Professional experience

Researcher, Steklov Institute of Mathematics

Key accomplishments: Simons Foundation scholarship (2016, 2017, 2018), Dobrushin scholarship, Presidential scholarship, Higher School of Economics

Academic Interests
Bi-rational geometry, minimal model program. Fano manifolds and their degeneracy

Dmitry Dubnov

Researcher, PhD (Phys&Math)

Professional experience



Academic Interests
Homological theory of associative algebraic representations, non-commutative algebraic geometry, symplectic groupoid theory, derivative categories of coherent pencils in algebraic varieties, associative algebraic representations, theory of t-structures and semi-orthogonal decompositions in triangulated categories, algebraic structures deformation theory, quasi-periodic process simulation, perturbation theory, fast/slow dynamic systems.

Dmitriy Stepanov

Engineer, PhD (Phys&Math)

Professional experience
Engineer, Candidate of Physical and Mathematical Sciences, Associate Professor of the Department of Higher Mathematics
Academic Interests
Algebraic geometry, singularity theory, tropical geometry

Dmitriy Rachenkov

Technician

Professional experience
Technician, MIPT master's student
Academic Interests
Сluster algebras, Painlevé equations, representation theory

Nikita Monchenko

Technician

Education
MIPT Bachelor student
Academic Interests
Exact category theory, quiver representation theory, t-structure theory.