Date of birth: November 1, 1973.

- 1990-1995: Student in Moscow State University;
- 1995-1998: Graduate student in Moscow State University and Independent University of Moscow;
- 1998: Ph.D. Thesis Vector bundles on Fano threefolds, instantons and birational transforms ;
- 1998-2002: Research fellow in Institute for Problems of Information Transmission;

from 2002: Research fellow in at Steklov Mathematical Institute.

Married, 4 children (3 daughters and 1 son).

Research interests: Algebraic geometry, Noncommutative algebraic geometry, Derived categories of coherent sheaves, Mirror Symmetry, Fano varieties.

1. The Laumon's resolution of Drinfeld's compactification is small, Mathematical Research Letters, 1997, V. 4, p. 349-364.

2. Global intersection cohomology of quasimaps' spaces, International Mathematical Research Notices, 1997, No. 7, p. 301-328 (joint work with M. Finkelberg)

3. Fano threefolds V22, preprint MPIM/97-24.

4. Noncommutative instantons and twistor transform, Communications in Mathematical Physics, 2001, No. 220, p. 385-432 (joint work with A. Kapustin and D. Orlov)

5. Quiver varieties and a noncommutative ${\Bbb P}^2$, Compositio Mathematica, 2002, V. 134, p. 283-318 (joint work with V. Baranovsky and V. Ginzburg)

6. Wilson's grassmanian and a noncommutative quadric, International Mathematical Research Notices, 2003, No. 21, p. 1155--1197 (joint work with V. Baranovsky and V. Ginzburg)

7. Derived categories of cubic and V14 threefolds Proc. V.A.Steklov Inst. Math, V. 246 (2004), p. 183--207.

8. Derived category of V12 Fano threefolds, Mat. zametki, V. 78, n. 4, 579-594.

9. Hyperplane sections and derived categories, Izvestiya RAN: Ser. Mat. 70:3 p. 23-128 (in Russian); translation in Izvestiya: Mathematics 70:3 p. 447-547.

10. Homological Projective Duality, preprint math.AG/0507292.

11. Derived categories of quadric fibrations and intersections of quadrics, Advances in Mathematics, V. 218 (2008), N. 5, 1340-1369.

12. Lefschetz decompositions and categorical resolutions of singularities, Selecta Mathematica, V. 13 (2008), N. 4, 661-696.

13. Symplectic structures on moduli spaces of sheaves via the Atiyah class, Journal of Geometry and Physics, V. 59 (2009) N. 7, 843-860 (joint work with D. Markushevich).

14. Base change for semiorthogonal decompositions, preprint math.AG/0711.1734.

15. Abel-Jacobi maps for hypersurfaces and non commutative Calabi-Yau's, preprint math.AG/0806.1154, accepted in Communications in Contemporary Mathematics (joint work with L. Manivel and D. Markushevich).

16. Derived categories of cubic fourfolds, in "Cohomological and Geometric Approaches to Rationality Problems. New Perspectives" Series: Progress in Mathematics, Vol. 282, Bogomolov, Fedor; Tschinkel, Yuri (Eds.) 2010, X, 314 p. 47 illus., Hardcover ISBN: 978-0-8176-4933-3 A BirkhÄauser book, preprint math.AG/0808.3351,

17. Derived categories of Fano threefolds, Proc. V.A.Steklov Inst. Math, V. 264 (2009), p. 110-122; preprint math.AG/0809.0225 .