Curriculum Vitae

Anton Fonarev

Algebraic Geometry Section,
Steklov Mathematical Institute of Russian Academy of Sciences,
8 Gubkina Str.,
Moscow, 119991,
Russia

email: avfonarev@mi-ras.ru

Born: December 26, 1989 — Moscow, Russia
Nationality: Russian
Spoken languages: Russian (native), English, French (both fluent)

Current Position

Researcher, Steklov Mathematical Institute of Russian Academy of Scieneces.

Education

2011 MSc in Mathematics, with Honours, Moscow State University, Moscow, Russia.
2014 PhD in Mathematics, Steklov Mathematical Institute, Moscow, Russia (defended on December 26).

Research interests

Algebraic geometry, derived categories of coherent sheaves.

Publications & talks

Seminar and conference talks

2010

  • Minimal Lefschetz exceptional collections for Grassmannians, Institut Fourier, Grenoble, France, December 10.

2011

  • A Diagrammatic Approach to Categorification (after M. Khovanov and A. Lauda), Steklov Mathematical Institute, Moscow, Russia, September 30.

2012

  • Minimal Lefschetz decompositions for Grassmannians, "Relation of String Theory to Gauge Theories and Moduli Problems of Branes", Moscow, Russia, September 11.

2013

  • Staircase complexes, University of Massachusetts, Amherst, USA, January 25.
  • Staircase complexes, Simons Center for Geometry and Physics, Stony Brook, USA, January 29.
  • Staircase complexes, Northeastern University, Boston, USA, February 1.
  • Mori program for dummies, Steklov Mathematical Institute, Moscow, Russia, October 18.
  • On rationality of some threefolds (after I. Panin), Steklov Mathematical Institute, Moscow, Russia, November 21.

2014

  • Introduction to Ekedahl invariants, Steklov Mathematical Institute, Moscow, Russia, April 24.
  • Exceptional vector bundles on Grassmannians, Steklov Mathematical Institute, Moscow, Russia,
  • September 23.
  • Exceptional vector bundles on Grassmannians, Laboratoire J.-V.Poncelet, Moscow, Russia, September 25.
  • Derived categories of Grassmannians, Moscow State University, Moscow, Russia, October 1.

2015

  • Derived categories of curves as components of Fano varieties, MPIM, Bonn, Germany, May 26.
  • Derived categories of curves as components of Fano varieties, "GEOQUANT 2015", Madrid, Spain, September 18.
  • Derived categories of curves as components of Fano varieties, "Categorical and Analytic Invariants in Algebraic Geometry II", IPMU, Japan, November 17.

2016

  • Vector bundles on Grassmannians, Moscow Mathematical Society, Moscow, Russia, March 16.

2017

  • Introduction to the derived categrory of sheaves, University of Geneva, Geneva, Switzerland, March 8.
  • Derived categories of Grassmannians, "Around the Gamma Conjectures", Konolfingen, Switzerland, March 10.

2018

  • Derived categories of algebraic varieties for a working mathematician, University of Geneva, Geneva, Switzerland, February 21.
  • Embedding derived categories of curves into derived categories of moduli of stable vector bundles, University of Geneva, Geneva, Switzerland, February 26.
  • Generalized staircase complexes, Steklov Mathematical Institute, Moscow, Russia, March 20.
  • On the generalised Dubrovin’s conjecture for Grassmannians, Kavli IPMU, Tokyo, Japan, November 13.

2019

  • On the generalised Dubrovin's conjecture for Grassmannians, Institut für Mathematik, Universität Augsburg, Augsburg, Germany, January 29.
  • Recent developments in derived categories of Grassmannians, "International Workshop on Derived Categories and Related Topics", Sun Yat-sen University, Guangzhou, China, May 30.
  • Derived categories of Grassmannians, recent progress, "Emerging Research in Algebraic Groups, Motives, and K-Theory", Euler International Mathematical Institute, St. Petersburg, Russia, September 13.

2020

  • Full exceptional collections on Lagrangian Grassmannians, Institut für Mathematik, Universität Augsburg, Augsburg, Germany, February 6.

2021

  • Staircase complexes: an overview, Wuppertal Topology Seminar, Wuppertal University, online, May 19.

2022

  • Generalized Dubrovin's Conjecture, "Second Conference of Maths Centers of Russia", Steklov Mathematical Institute, Moscow, Russia, November 11.

Publications and preprints

Published

  1. On minimal Lefschetz decompositions for Grassmannians, Izv. RAN. Ser. Mat., 77:5 (2013), 203–224.
  2. Exceptional vector bundles on Grassmannians, Uspekhi Mat. Nauk, 69:4(418) (2014), 189–190.
  3. On the Kuznetsov–Polishchuk Conjecture, Tr. Mat. Inst. Steklova, 290 (2015), 18–33.
  4. Irreducible Ulrich Bundles on Isotropic Grassmannians, Moscow Mathematical Journal, 16:4 (2016), 711–726.
  5. Derived categories of curves as components of Fano manifolds, joint with A. Kuznetsov, Journal of the London Mathematical Society, 97:1 (2018), 24–46.
  6. Full exceptional collections on Lagrangian Grassmannians, Int. Math. Res. Not. IMRN, 2022:2 (2022), 1081–1122.
  7. On the bounded derived category of $IGr(3, 7)$, Transform. Groups, 27 (2022), 89–112.

Accepted

  1. Bokstedt periodicity generator via K-theory, joint with D. Kaledin, to appear in Israel Journal of Mathematics.

Teaching

Lecturer

  • Introduction to commutative and homological algebra, Math in Moscow program, 2012, Spring term.
  • Introduction to commutative and homological algebra, Math in Moscow program, 2012, Fall term.
  • Introduction to commutative and homological algebra, Math in Moscow program, 2013, Spring term.
  • Algebraic Geometry: start-up course, Math in Moscow program, 2013, Fall term.
  • Combinatorics, Math in Moscow program, 2014,, Spring term.
  • Coherent sheaves on algebraic varieties, 2014, IUM, Fall term.
  • Introduction to commutative and homological algebra, Math in Moscow program, 2016, Spring term.
  • Combinatorics, Math in Moscow program, 2017, Fall term.
  • Algebraic Geometry: start-up course, Math in Moscow program, 2018, Spring term.
  • Algebraic Geometry: start-up course, Math in Moscow program, 2018, Fall term.
  • Algebraic Geometry: start-up course, Math in Moscow program, 2019, Spring term.
  • Introduction to commutative and homological algebra, Math in Moscow program, 2019, Fall term.
  • Foundations of Algebraic Geometry, Steklov Mathematical Institute, 2020, Spring term.
  • Algebra I, IUM, 2021, Fall term. YouTube
  • Algebra II, IUM, 2022, Spring term. YouTube
  • Algebra III, IUM, 2022, Fall term. YouTube