Alexey L. Gorodentsev
- Professor: Faculty of Mathematics
- Programme Academic Supervisor: Mathematics
- Tenured Professor (2018)
- Alexey L. Gorodentsev has been at HSE University since 2008.
Education, Degrees and Academic Titles
Lomonosov Moscow State University
Lomonosov Moscow State University
Lomonosov Moscow State University
According to the International Standard Classification of Education (ISCED) 2011, Candidate of Sciences belongs to ISCED level 8 - "doctoral or equivalent", together with PhD, DPhil, D.Lit, D.Sc, LL.D, Doctorate or similar. Candidate of Sciences allows its holders to reach the level of the Associate Professor.
Awards and Accomplishments
Best Teacher — 2020–2022, 2011–2013
Best Academic Supervisor in the category ‘Student Retention and Allegiance to HSE University’ — 2024
Best Academic Supervisor in the category ‘Student Engagement in Inter-Campus Courses’ — 2024
If you are looking for the actual content of my courses (programs, lecture notes, training aids etc) click here.
Courses (2024/2025)
- Algebra (Bachelor’s programme; Faculty of Mathematics; 1 year, 1-4 module)Rus
- Past Courses
Courses (2022/2023)
- Academic Mentor's Seminar "Algebra, Logic and Number Theory" (Master’s programme; Faculty of Mathematics field of study Mathematics, field of study Mathematics; 1 year, 1-4 module)Eng
- Algebra (Bachelor’s programme; Faculty of Mathematics; 1 year, 1-4 module)Rus
- Topological data analysis (Bachelor’s programme; Faculty of Computer Science; 3 year, 3, 4 module)Rus
Area of research
My research interests are mostly in geometry and homological algebra of vector bundles and sheaves on algebraic, analytic, and symplectic manifolds as well as applications of all this staff to mathematical physics.
- Helix theory. This is a cohomological technique for orthogonal decompositions of derived and triangulated categories in terms of exceptional bases. It was developed firstly in my PhD theses (1986/87, see also Gorodentsev A.L., Rudakov A.N. Exceptional vector bundles on projective spaces. Duke Math. J. 54 (1987) p.115-130) in order to describe exceptional vector bundles on Fano varieties. Now the helices are quite popular as one of "mirror symmetry bypasses" between algebraic geometry of coherent sheaves and differential geometry of Picard - Lefschetz pencils.
Transparencies of my KIAS Lectures on helices (May - June 2001)
The Helix theory (joint with S.A.Kuleshov; Moscow Math. J. 4:2 (2004), p.377-440)
Mukai lattices (Transparencies of my talk at the workshop GEOQUANT-2013, Wien, August 27, 2013)
ALAG. This is an abbreviation for Abelian Lagrangian Algebraic Geometry developed by A.N.Tyurin (see for example math.AG/9902027 and math.AG/9909094) as a geometrical framework for geometric quantization.
Transparencies of my KIAS Lectures on ALAG (April - May 2001)
St.Petersburg lecture on ALAG (September 2014)
English and Russian versions of "ALAG" paper explaining basic ALAG principles (joint with A.N.Tyurin).
- t-stability. A concept of stability comes from Geometric Invariant Theory where it is used to construct compact orbit spaces for algebraic group actions. t-stability generalizes this approach in a context of generic linear triangulated categories. This allows to consider moduli space problems in very general setup.
"t-stabilities and t-structures on triangulated categories" (joint with S.A.Kuleshov and A.N.Rudakov): in english and in russian.
"On finest and modular t-stabilities" (joint with S.A.Kuleshov, in english). - Syzygies of projective varieties. There are classical problems of geometry and homological algebra: how to describe a minimal free resolution for the graded coordinate algebra of projective variety in the category of modules over the polynomial ring, and what kind of extra algebraic structures does this resolution admit.
"On syzygies of highest weight orbits" (joint with A.S.Khoroshkin and A.N.Rudakov, in english). We study a minimal resolution for the coordinate algebra of projective orbit of the highest weight vector in an irreducible representation of semisimple complex Lie group. We show that the syzygies are isomorphic to the cohomologies of appropriate graded Lie superalgebra and illustrate this by several examples including the complete computation of syzygies for grassmannians Gr(2,N) in the standard Plucker embedding.
Conferences
- 2014
наука будущего (science of the future) (Санкт Петербург). Presentation: Abelian Lagrangian Algebraic Geometry (ALAG)
- 2013
ESI School and Conference Geometry and Quantization GEOQUANT 2013 (Вена). Presentation: Mukai lattices
XII международная школа по теоретической и математической физике (Севастополь). Presentation: Курс "Массивы"
XII международная школа по теоретической и математической физике (Севастополь). Presentation: Гомологическая алгебра. Введение. Проективные резольвенты. Спектральные последовательности. Комплексы Кошуля
Positions
since 2008 professor at the Faculty of Mathematics, HSE, Moscow
since 2000 senior researcher at the Mathematical Physics Group, ITEP, Moscow
since 1992 professor at the Independent University of Moscow
HSE Staff Members Receive University Awards
On January 18, several university staff members were awarded HSE medals and notes of acknowledgement from the Rector.
HSE Staff Members Awarded Status of Tenured Professor
On June 22, several HSE lecturers and staff members were awarded the status of Tenured Professor at a meeting of HSE Academic Council. Sixteen HSE staff members became Distinguished Professors at the Higher School of Economics for the first time.
Springer Nature, HSE and Skoltech to Publish Book Series in Mathematics
Moscow Lectures, a new series of books in English, is set to be published by Springer Nature. The series is issued jointly by HSE and Skoltech, and its Editor-in-Chief is Alexey Gorodentsev, Professor at the HSE Faculty of Mathematics. Twelve volumes are currently in preparation and the first volume will be published at the beginning of June 2018. The series builds on the outstanding research and education in the field of mathematics in Moscow. It is aimed at graduate and undergraduate students, as well as lecturers and researchers, across the globe.
After Turning Down Offers in New York and Berlin, Chinese Student Pursues Mathematics Training at HSE
For DaoDao Yang, a native of Dali, China, choosing a programme in mathematics came down to the decision of where he felt most challenged and most comfortable. This ultimately meant turning down offers at New York University and the Berlin Mathematical School to accept an offer from the Master’s programme at the Higher School of Economics. In an extensive interview with the HSE news service, Dao Dao recently spoke about what led him to choose HSE for his postgraduate study; his impressions of the programme, its professors and his fellow students; and his future plans.
'I’m Glad I Listened to My Heart'
A career in science and technology might sound appealing to the average Russian, but a recent survey showed that most Russians believe men are better suited for this line of work than women. The young women interviewed for this story, a mathematician and a programmer, are of a different opinion.
‘Studying with Enthusiastic People Around is Fun’
In 2015 eight graduates from the HSE Faculty of Mathematics started PhD programmes at MIT, McGill, Caltech, Pennsylvania State University and other top universities. HSE 4th year student Dmitry Pirozhkov who has got a place at Columbia University talked to the HSE News Service about how to get onto a prestigious PhD programme and about his expectations and academic plans.