Alexander Isaakovich Esterov

Professor:Faculty of Mathematics

Alexander Isaakovich Esterov has been at HSE since 2011.

Education and Degrees

2017
Doctor of Sciences*
2005
Candidate of Sciences* (PhD) in Geometry and Topology
Lomonosov Moscow State University
Thesis Title: Indices of 1-forms, general resultants, and Newton polyhedra
2001
Degree in Mathematics
Lomonosov Moscow State University, faculty of mechanics and mathematics

* Candidate of Sciences
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.

* Doctor of Sciences
A post-doctoral degree called Doctor of Sciences is given to reflect second advanced research qualifications or higher doctorates in ISCED 2011.

Professional Interests

algebraic geometry convex geometry singularity theory tropical geometry combinatorics

Awards and Accomplishments

Best Teacher – 2012

Young Faculty Support Program (Group of Young Academic Professionals)
Category "Future Professoriate" (2013-2014)

Student Term / Thesis Papers

Bachelor
A. Bykov «Tropical Fans of Intersection Multiplicity 1». Faculty of Mathematics, 2018
V. Romanovskii «Polynomial Mappings of Small Degree Invertible by Radicals». Faculty of Mathematics, 2017
Y. Rudko «Topology of Generic Determinantal Sets and Newton Polytopes». Faculty of Mathematics, 2017
A. Arkhipova «Signs of the Leading Coefficients of the Resultant». Faculty of Mathematics, 2016
A. Barsukov «Multivariate Generalizations of the Abel-Ruffini Theorem». Faculty of Mathematics, 2016

Full list of of student term / thesis papers

Courses (2018/2019)

Research Seminar "Convex and Algebraic Geometry 1" (Faculty of Mathematics; 1 year, 1, 2 module)Rus
Research Seminar "Polyhedra and Convex Geometry" (Faculty of Mathematics; 1 year, 1, 2 module)Rus
Past Courses

Courses (2017/2018)

Algebra (Bachelor’s programme; Faculty of Mathematics; programme "Mathematics"; 1 year, 1-4 module)Rus
Convex Optimization (Faculty of Mathematics; 1 year, 3, 4 module)Eng
Foundations of Algebra and Geometry (Bachelor’s programme; Faculty of Mathematics; 2 year, 1, 2 module)Rus
Introduction to Discrete Mathematics (Bachelor’s programme; Faculty of Mathematics; programme "Mathematics"; 1 year, 4 module)Rus
Mathematics Practical Training (Bachelor’s programme; Faculty of Mathematics; programme "Mathematics"; 1 year, 1-4 module)Rus
Research Seminar "Convex and Algebraic Geometry 1" (Faculty of Mathematics; 1 year, 1, 2 module)Eng
Research Seminar "Convex and Algebraic Geometry 2" (Faculty of Mathematics; 1 year, 3, 4 module)Eng
Research Seminar " Real Algebraic and Toric Geometry" (Faculty of Mathematics; 1 year, 1, 2 module)Eng

Courses (2016/2017)

Algebra (Bachelor’s programme; Faculty of Mathematics; 2 year, 1, 2 module)Rus
Algebra (Bachelor’s programme; Faculty of Mathematics; 1 year, 1-4 module)Rus
Introduction to Discrete Mathematics (Bachelor’s programme; Faculty of Mathematics; 1 year, 4 module)Rus
Mathematics Practical Training (Bachelor’s programme; Faculty of Mathematics; 2 year, 1-4 module)Rus
Mathematics Practical Training (Bachelor’s programme; Faculty of Mathematics; 1 year, 1-4 module)Rus

Courses (2015/2016)

Algebra (Bachelor’s programme; Faculty of Mathematics; 2 year, 1-3 module)Rus
Algebra (Bachelor’s programme; Faculty of Mathematics; 1 year, 1-4 module)Rus
Discrete Mathematics and Applications (Bachelor’s programme; Faculty of Mathematics; 1 year, 4 module)Rus
Dynamical Systems (Bachelor’s programme; Faculty of Mathematics; 2 year, 1-4 module)Rus
Introduction to Discrete Mathemetics (Bachelor’s programme; Faculty of Mathematics; 1 year, 2, 3 module)Rus
Introduction to Topology (Bachelor’s programme; Faculty of Mathematics; 1 year, 3, 4 module)Rus
Mathematics. Licenciatus (Bachelor’s programme; Faculty of Mathematics; 3 year, 4 module)Rus
Mathematics Practical Training (Bachelor’s programme; Faculty of Mathematics; 2 year, 1-4 module)Rus
Mathematics Practical Training (Bachelor’s programme; Faculty of Mathematics; 1 year, 1-4 module)Rus
Research Seminar "Convex and Algebraic Geometry 1" (Optional course (faculty); Faculty of Mathematics; 1, 2 module)Rus
Research Seminar "Convex and Algebraic Geometry 2" (Optional course (faculty); Faculty of Mathematics; 3, 4 module)Rus

Courses (2014/2015)

Algebra (Bachelor’s programme; Faculty of Mathematics; 2 year, 1-3 module)Rus
Dynamical Systems (Bachelor’s programme; Faculty of Mathematics; 2 year, 1-4 module)Rus
Elements of Number Theory 1 (Master’s programme; Faculty of Mathematics; 1 year, 1, 2 module)Rus
Introduction to Real Algebraic Geometry and Toric Varieties (Master’s programme; Faculty of Mathematics; 1 year, 1, 2 module)Rus
Mathematics. Licenciatus (Bachelor’s programme; Faculty of Mathematics; 3 year, 4 module)Rus
Mathematics Practical Training (Bachelor’s programme; Faculty of Mathematics; 2 year, 1-4 module)Rus
Research Seminar "Convex and algebraic geometry 1" (Master’s programme; Faculty of Mathematics; 1 year, 1, 2 module)Rus
Research Seminar "Convex and Algebraic Geometry 2" (Master’s programme; Faculty of Mathematics; 1 year, 3, 4 module)Rus
Supplementary Geometry 1 (Master’s programme; Faculty of Mathematics; 1 year, 1, 2 module)Eng
Supplementary Geometry 2 (Master’s programme; Faculty of Mathematics; 1 year, 3, 4 module)Eng
Tropical Geometry (Master’s programme; Faculty of Mathematics; 1 year, 3, 4 module)Rus

Courses (2013/2014)

Algebra (Bachelor’s programme; Faculty of Mathematics; 1 year, 1-4 module)Rus
Dynamical Systems (Bachelor’s programme; Faculty of Mathematics; 2 year, 1-4 module)Rus
Introduction to Discrete Mathemetics (Bachelor’s programme; Faculty of Mathematics; 1 year, 3, 4 module)Rus
Mathematics Practical Training (Bachelor’s programme; Faculty of Mathematics; 2 year, 1-4 module)Rus
Toric Varieties (Master’s programme; Faculty of Mathematics; 1 year, 1, 2 module)Eng

Courses (2012/2013)

Algebra (Bachelor’s programme; Faculty of Mathematics; 1 year, 1-4 module)Rus
Dynamic Systems (Bachelor’s programme; Faculty of Mathematics; 2 year, 1-4 module)Rus
Research Seminar "Convex Geometry 1" (Master’s programme; Faculty of Mathematics; 1 year, 1, 2 module)Rus
Research Seminar "Convex Geometry 1" (Bachelor’s programme; Faculty of Mathematics; 4 year, 1, 2 module)Rus
Research Seminar "Convex Geometry 1" (Bachelor’s programme; Faculty of Mathematics; 1 year, 1, 2 module)Rus
Research Seminar "Convex Geometry 1" (Bachelor’s programme; Faculty of Mathematics; 3 year, 1, 2 module)Rus
Research Seminar "Convex Geometry 1" (Bachelor’s programme; Faculty of Mathematics; 2 year, 1, 2 module)Rus
Research Seminar "Convex Geometry 1" (Master’s programme; Faculty of Mathematics; 2 year, 1, 2 module)Rus
Research Seminar "Convex Geometry 2" (Master’s programme; Faculty of Mathematics; field of study "010100.68 Математика", field of study "010100.68 Математика"; 1 year, 3, 4 module)Rus
Research Seminar "Convex Geometry 2" (Bachelor’s programme; Faculty of Mathematics; 4 year, 3, 4 module)Rus
Research Seminar "Convex Geometry 2" (Bachelor’s programme; Faculty of Mathematics; 1 year, 3, 4 module)Rus
Research Seminar "Convex Geometry 2" (Bachelor’s programme; Faculty of Mathematics; 3 year, 3, 4 module)Rus
Research Seminar "Convex Geometry 2" (Bachelor’s programme; Faculty of Mathematics; 2 year, 3, 4 module)Rus
Research Seminar "Convex Geometry 2" (Master’s programme; Faculty of Mathematics; 2 year, 3, 4 module)Rus

Courses (2011/2012)

Introduction to Topology (Bachelor’s programme; Faculty of Mathematics; 1 year, 4 module)Rus
Partial Differential Equations (Bachelor’s programme; Faculty of Mathematics; 4 year, 3 module)Rus
Partial Differential Equations (Bachelor’s programme; Faculty of Mathematics; 3 year, 3, 4 module)Rus
Research Seminar of the Laboratory of Algebraic Geometry and its Applications (Master’s programme; Faculty of Mathematics; 1 year, 1-4 module)Rus
Research Seminar of the Laboratory of Algebraic Geometry and its Applications (Bachelor’s programme; Faculty of Mathematics; 4 year, 1-4 module)Rus
Research Seminar of the Laboratory of Algebraic Geometry and its Applications (Bachelor’s programme; Faculty of Mathematics; 1 year, 1-4 module)Rus
Research Seminar of the Laboratory of Algebraic Geometry and its Applications (Bachelor’s programme; Faculty of Mathematics; 3 year, 1-4 module)Rus
Research Seminar of the Laboratory of Algebraic Geometry and its Applications (Bachelor’s programme; Faculty of Mathematics; 2 year, 1-4 module)Rus

Conferences

2017

Galois Meets Newton: Algebraic and Geometric aspects of Singularity Theory (Реховот). Presentation: Galois meets Newton: systems of equations solvable by radicals, and Newton polytopes of volume 4

Publications²⁰

Article Esterov A. I. Galois theory for general systems of polynomial equations // Compositio Mathematica. 2019. Vol. 155. No. 2. P. 229-245. doi
Article Alexander Esterov. Characteristic classes of affine varieties and Plücker formulas for affine morphisms // Journal of the European Mathematical Society. 2018. Vol. 20. P. 15-59. doi
Article Esterov A. I., Takeuchi K. On vanishing theorems for local systems associated to Laurent polynomials // Nagoya Mathematical Journal. 2018. Vol. 231. P. 1-22. doi
Article Esterov A. I., Arkhipova A. A. Signs of the Leading Coefficients of the Resultant // Geometric and Functional Analysis. 2017. Vol. 27. No. 1. P. 33-66. doi
Article Эстеров А. И. Степень бифуркационного множества общего полиномиального отображения // Успехи математических наук. 2017. Т. 72. № 4. С. 197-198. doi
Article Esterov A. I., Gusev G. G. Multivariate Abel–Ruffini // Mathematische Annalen. 2016. Vol. 365. No. 3. P. 1091-1110. doi
Preprint Takeuchi K., Esterov A. I., Lemahieu A. On the monodromy conjecture for non-degenerate hypersurfaces / Cornell University. Series math "arxiv.org". 2016. No. arXiv:1309.0630v4.
Article Esterov A. I., Timorin V. Changing Traditions of Mathematical Education: BSc Program in Mathematics at the National Research University Higher School of Economics // Higher Education in Russia and Beyond. 2015. No. 4(6). P. 22-23.
Article Esterov A. I., Takeuchi K. Confluent A-hypergeometric functions and rapid decay homology cycles // American Journal of Mathematics. 2015. Vol. 137. No. 2. P. 365-409. doi
Article Esterov A. I. Math Graduates’ Career Prospects in Modern Russia // Higher Education in Russia and Beyond. 2015. No. 4(6). P. 14-16.
Article Esterov A. I., Takeuchi K., Ando K. Monodromies at infinity of confluent A-hypergeometric functions // Advances in Mathematics. 2015. Vol. 272. P. 1-19. doi
Article Esterov A. I., Gusev G. G. Systems of equations with a single solution. // Journal of symbolic computation. 2015. Vol. 68-2. P. 116-130. doi
Article Esterov A. I. The discriminant of a system of equations // Advances in Mathematics. 2013. Vol. 245. P. 534-572. doi
Article Takeuchi K., Esterov A. I. Motivic Milnor fibers over complete intersection varieties and their virtual Betti numbers // International Mathematics Research Notices. 2012. No. 15. P. 3567-3613.
Article Esterov A. I. Multiplicities of degenerations of matrices and mixed volumes of Cayley polyhedra // Journal of Singularities. 2012. Vol. 6. P. 27-36. doi
Article Esterov A. I. Tropical Varieties with Polynomial Weights and Corner Loci of Piecewise Polynomials // Moscow Mathematical Journal. 2012. Vol. 12. No. 1. P. 55-76.
Article Esterov A. I. Newton polyhedra of discriminants of projections // Discrete and Computational Geometry. 2010. Vol. 44. No. 1. P. 96-148.
Article Эстеров А. И. Плотности топологических инвариантов квазипериодических субаналитических множеств // Известия РАН. Серия математическая. 2009. № 3. С. 611-626.
Article Хованский А. Г., Esterov A. I. Elimination theory and Newton polytopes // Functional Analysis and Other Mathematics. 2008. No. 1. P. 45-71.
Article Esterov A. I. Existence of mixed fiber bodies // Moscow Mathematical Journal. 2008. No. 3. P. 433-442.

Research projects

Geometry of the space of polynomials with indeterminate coefficients, MESRF МК-6223.2012.1

Topological invariants of singularities, RFBR 10-01-00678

Enumerative geometry of polytopes and polynomials, RFBR 12-01-31233\12

Timetable for today

Full timetable

Mar

2016

'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.

Feb

2012

RF president grants

Congratulations to Associate Professors of our Faculty Evgeny Feigin and Alexander Esterov upon receiving grants of the Russian Federation president for young scientists.