# Alexei Gorinov

- Academic Director:Doctoral School in Mathematics
- Associate Professor:Faculty of Mathematics

- Alexei Gorinov has been at HSE University since 2012.

### Education and Degrees

- 2004
Candidate of Sciences* (PhD)

- 2004
PhD in Mathematics

University of Paris 7

Thesis Title: Conical resolutions of discriminants and applications to complex and real algebraic geometry. - 1998
Degree

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.

### Student Term / Thesis Papers

- Bachelor
E. Denisova, On Complete Subvarieties of the Moduli Spaces of Curves. Faculty of Mathematics, 2019

M. Dolgikh, The Cohomology of the Space of Equations of GIT-stable Plane Quartics. Faculty of Mathematics, 2019

A. Volgin, Rational Cohomology of the Moduli Spaces of Genus 1 Curves with Marked Points. Faculty of Mathematics, 2019

D. Zhurbenko, Equivariant Rational Homotopy Type of the Moduli Spaces of Rational Curves with Marked Points. Faculty of Mathematics, 2018

I. Yakovlev, On the Volume Conjecture. Faculty of Mathematics, 2017

N. Konovalov, On the Topology of Spaces of Smooth Sections of Homogeneous Vector Bundles. Faculty of Mathematics, 2016

A. Berdnikov, Conical Resolutions and the Cohomology of the Spaces of Hypersurfaces without Complicated Singularities. Faculty of Mathematics, 2014

- Master
D. Zhurbenko, Rational Homotopy Models for the Moduli Spaces of Genus 1 Curves with Marked Points and Level Structures. Faculty of Mathematics, 2020

D. Tereshkin, Commutative Algebras which are Formal as Associative. Faculty of Mathematics, 2019

I. Yakovlev, Symplectic Rational Blowdown. Faculty of Mathematics, 2019

N. Konovalov, On the Topology of Spaces of Nonsingular Sections of Homogeneous Vector Bundles. Faculty of Mathematics, 2018

G. Kondyrev, Formalism of Traces in Derived Algebraic Geometry. Faculty of Mathematics, 2017

### Courses (2020/2021)

- Research Seminar "Homothopy Theory" (Optional course (faculty); Faculty of Mathematics; 1, 2 module)Eng
- Research Seminar "Smooth, PL and topological manifolds" (Optional course (faculty); Faculty of Mathematics; 1, 2 module)Eng
- Topics in Algebra, Geometry and Probability Theory (Postgraduate course’s programme; 2 year, 1 semester)Rus
- Past Courses

### Courses (2019/2020)

- Discrete Mathematics (Bachelor’s programme; Faculty of Mathematics; 1 year, 1, 4 module)Rus
- Research Seminar "An Introduction to Elliptic Operators" (Optional course (faculty); Faculty of Mathematics; 1, 2 module)Eng
- Research Seminar "An Introduction to Stacks" (Optional course (faculty); Faculty of Mathematics; 3, 4 module)Eng
- Research Writing (Postgraduate course’s programme; 1 year, 1 semester)Rus
- Topics in Algebra, Geometry and Probability Theory (Postgraduate course’s programme; 2 year, 1 semester)Rus

### Courses (2018/2019)

- Mathematical English (Bachelor’s programme; Faculty of Mathematics; 3 year, 3 module)Eng
- Mathematics Practical Training (Bachelor’s programme; Faculty of Mathematics; 1 year, 1-4 module)Rus
- Research Seminar "Algebraic Topology" (Optional course (faculty); Faculty of Mathematics; 3, 4 module)Eng
- Research Seminar "Homothopy Theory" (Optional course (faculty); Faculty of Mathematics; 1, 2 module)Eng
- Research Writing (Postgraduate course’s programme; 1 year, 1 semester)Rus
- Topics in Algebra, Geometry and Probability Theory (Postgraduate course’s programme; 2 year, 1 semester)Rus

### Courses (2017/2018)

- Research Seminar "An Introduction to Cohomology Theory" (Optional course (faculty); Faculty of Mathematics; 3, 4 module)Eng
- Research Seminar "Main Spectral Sequences 2" (Optional course (faculty); Faculty of Mathematics; 1, 2 module)Eng
- Research Seminar "Operads in Algebra and Geometry" (Optional course (faculty); Faculty of Mathematics; 1, 2 module)Eng
- Topology 1 (Optional course (faculty); Faculty of Mathematics; 3, 4 module)Eng

### Courses (2016/2017)

- Elliptic Operators (Optional course (faculty); Faculty of Mathematics; 3, 4 module)Eng
- Research Seminar "An Introduction to Surgery Theory" (Optional course (faculty); Faculty of Mathematics; 3, 4 module)Eng
- Research Seminar "Main Spectral Sequences" (Optional course (faculty); Faculty of Mathematics; 1, 2 module)Eng
- Topology 2 (Optional course (faculty); Faculty of Mathematics; 3, 4 module)Eng

### Courses (2015/2016)

- Research Seminar "Introduction to Seiberg-Witten Invariants" (Optional course (faculty); Faculty of Mathematics; 1, 2 module)Rus
- Singularity Theory 1 (Optional course (faculty); Faculty of Mathematics; 1, 2 module)Eng
- Singularity Theory 2 (Optional course (faculty); Faculty of Mathematics; 3, 4 module)Eng
- Topology I (Optional course (faculty); Faculty of Mathematics; 1, 2 module)Eng
- Topology II (Optional course (faculty); Faculty of Mathematics; 3, 4 module)Eng

### academic course

Selected chapters of algebra, geometry and probability theory. The course of the postgraduate school.

Elliptic operators course page

### Conferences

### Publications^{15}

- Article Gorinov A., Howard R., Johnson V., McNulty G. Maps that must be affine or conjugate affine: a problem of Vladimir Arnold //
*Arnold Mathematical Journal*. 2020. No. 6. P. 213-229. doi - Preprint Gorinov A., Nikolay Konovalov.
*Topology of spaces of regular sections and applications to automorphism groups*/ Cornell University. Series "Working papers by Cornell University". 2020. No. 1712.02578. - Preprint Gorinov A.
*A purity theorem for configuration spaces of smooth compact algebraic varieties*/ Cornell University. Series "Working papers by Cornell University". 2017. No. 1702.08428 . - Preprint Gorinov A.
*Two-sided fundamental theorem of affine geometry*/ Cornell University. Series arxiv "math". 2017. No. 1702.07701. - Preprint Gorinov A.
*Conical resolutions and the cohomology of the moduli spaces of nodal hypersurfaces*/ Cornell University. Series math "arxiv.org". 2014. No. 1402.5946. - Preprint Gorinov A.
*Division theorems for the rational cohomology of discriminant complements and applications to automorphism groups in finite characteristic*/ Cornell University. Series math "arxiv.org". 2013. No. arXiv:1303.5150 [math.AG]. - Preprint Gorinov A.
*Rational cohomology of the moduli spaces of pointed genus 1 curves*/ Cornell University. Series math "arxiv.org". 2013. No. arXiv:1303.5693 [math.AG]. - Preprint Gorinov A.
*Combinatorics of double cosets and fundamental domains for the subgroups of the modular group*/ Cornell University. Series math "arxiv.org". 2009. No. 0901.1340. - Preprint Gorinov A.
*Division theorems for the rational cohomology of certain discriminant complements*/ Cornell University. Series math "arxiv.org". 2005. No. 0511593. - Article Gorinov A. Real cohomology groups of the space of nonsingular curves of degree 5 in ${\mathbb C}P^2$ //
*Annales de la Faculté des Sciences de Toulouse*. 2005. Vol. 14. No. 3. P. 395-434. - Article Горинов А. Г. Pseudocomplex and pseudo(bi)quaternion mappings // Функциональный анализ и его приложения. 2004. № 38(2). С. 149-150.
- Article Gorinov A. The cobordism group of M¨obius manifolds in dimension 1 is zero //
*Topology and its Applications*. 2004. No. 143. P. 75-85. - Article Gorinov A., Шадчин С. В. Ces\`aro Asymptotics for the orders of $SL_k(\mathbb{Z}_n)$ and $GL_k(\mathbb{Z}_n)$ as $n\to\infty$ //
*Comptes Rendus Mathematique*. 2003. Vol. 337. P. 149-152. - Article Gorinov A. Conical resolutions of discriminant varieties and real cohomology groups of the space on nonsingular plane projective quintics //
*Doklady Mathematics*. 2003. Vol. 67. No. 3. P. 730-733. - Article Горинов А. Г. On the cohomology of double complexes // Moscow University Mathematics Bulletin. 1997. № 5. С. 40-41.

### Research interests

Topology of complex algebraic varieties, in particular configuration spaces, discriminant complements, and moduli spaces; Hodge theory; low-dimensional topology and geometric structures on manifolds

### Courses

Topology II: Introduction to Homology and Cohomology Theory - Master's level, Faculty of Mathematics; Programme: Mathematics; 1st year; Blocks 3, 4

## 'Math in Moscow Programme Was Absolutely Incredible'

Jonathan Gerhard from James Madison University spent one semester studying in Math in Moscow programme run jointly by HSE, Moscow Center for Continuous Mathematical Education, and Independent University of Moscow. During his time in Russia Jonathan took intensive maths courses, studied the Russian language and traveled to several Russian cities.