Education

1983 - 1988: Moscow State University (M.S.);

1990 - 1993: Institute of Mathematics, Academy of Sciences of Belarus (Ph.D.).

Degrees

M.S. (1988) - from Moscow State University for the thesis ``Homological dimensions of some Banach algebras'' (supervisor Prof. A.Ya. Helemskii);

Ph.D. (1993) - from Institute of Mathematics, Minsk, for the thesis ``Cohomology of finite Chevalley groups with coefficients in some modules over fields of defining characteristic'' (supervisor Prof. A.E. Zalesskii).

Publications

52 research articles, 2 research memoirs, and a monograph (see the list below).

Positions

1988 - 1989: Research Probationer at the Institute of Mathematics, Minsk;

1989 - 1993: Junior Research Fellow, the same Institute;

1993 - 1995: Research Fellow, the same Institute;

1994 - 1995: the Royal Society Postdoctoral Fellow, Cambridge University, Cambridge, England;

1995 - 2000: Assistant Professor,University of Oregon, Eugene, Oregon;

2000 - 2006: Associate Professor, University of Oregon, Eugene, Oregon.

2006 - present: Professor, University of Oregon, Eugene, Oregon.

Research interests

Primary - representation theory of algebraic and finite groups, symmetric groups, group cohomology, Lie algebras, group rings, quantum groups, Hecke algebras, locally finite groups, permutation groups.

Secondary - algebraic combinatorics, associative algebras, Lie superalgebras.

Graduate students

Jagat Sheth (Ph.D., University of Oregon, 1999);

Aaron Phillips (Ph.D., University of Oregon, 2002).

Olly Ruff (Ph. D. University of Oregon, 2005)

David Hill (Ph. D. University of Oregon, 2007)

David Nash (present)

Research grants

1993 - 1994: grant of the International Science Foundation (Soros Foundation);

1995 - 1996: grant of the Wolkswagen Foundation (coPI's - G. Michler and A.E. Zalesskii);

1996 - 1999: NSF grant (DMS-9600124), PI;

1999 - 2002: NSF grant (DMS-9900134), PI.

2003 - 2004: NSF conference grant (DMS-0244651), PI.

2004: NSA conference grant (MSPF-03C-016), PI.

2002 - 2007: NSF grant (DMS-0139019), PI.

2007 - 2012: NSF grant (DMS-0654147), coPI.

Professional Service

2005 - 2009: Algebra editor of the Transactions and Memoirs of the American Mathematical Society.

2003 - 2006: NSA panelist.

2005, 2006: NSF panelist.

Organizing Conferences:

2003: Representations of Finite Groups (Oberwolfach, Germany)

2004: Groups and Representations (Eugene, Oregon).

2005: Representations of Groups and Algebras (AMS special session, Eugene, Oregon).

2006: Representations of Finite Groups (Oberwolfach, Germany).

2008: Combinatorics and Representation Theory (MSRI, Berkeley, half-year program).

2008: Representation Theory of Finite Groups and Related Topics (MSRI, Berkeley, half-year program).

2008: Lie Theory (MSRI, Berkeley).

2008: Combinatorial Representation Theory, section of the AMS meeting at UBC (Vancouver, Canada).

2009: Algebraic Lie Theory (Isaac Newton Institute, Cambridge, England).

2009: Lie Algebraic Systems with Origins in Physics, Cambridge, England

Visiting positions

Summer 1994: Emmy Noether Institute for Mathematical Research at Bar-Ilan University, Ramat-Gan, Israel;

Summer 1996: Institute for Experimental Mathematics, Essen, Germany;

May - July 1997: Isaac Newton Institute for Mathematical Sciences, University of Cambridge, England.

August - September 1998: University of Bielefeld, Germany.

August 2001 - June 2002: Visiting Associate Professor, University of Wisconsin-Madison (sabbatical).

August 2008 - December 2008: Visiting Professor, University of Virginia (sabbatical).

Some invited talks

1996 - Meeting of the German Mathematical Society (Jena, Germany).

1997: Representations of Algebraic Groups (Cambridge, England) - 3 lectures.

1998: Symposium on modular representation theory (University of Virginia) - 5 lectures.

1998: Algebraic Representation Theory (Aarhus, Denmark).

1998: Representation Theory and Combinatorics (Magdeburg, Germany).

1998: Representation Theory of Algebras (Bielefeld, Germany).

1999: Summer meeting of the Canadian Mathematical Society (St. John's, Canada).

2000: Combinatorics of Lie Type (University of Wisconsin--Madison).

2000: Algebra-2000, (Edmonton, Canada).

2001: Groups, Geometry, and Combinatorics (Durham, England).

2001: Legacy of Schur's 1901 Thesis (Gregynog Hall, Wales).

2001: Representation Theory of Algebraic Groups and Quantum Groups (Tokyo, Japan).

2002: Representations of Finite Groups and Related Algebras (Durham, England), 2 lectures.

2002: Representations of Algebras and Related Topics (Fields Institute, Toronto, Canada), 5 lectures.

2002: Modular Representation Theory (Korea Institute for Advanced Study, Seoul, Korea), 3 lectures.

2003: Representation Theory of Groups (Summer School in Lisbon, Portugal), 3 lectures.

2003: Finite Groups (University of Florida).

2003: Current Trends in Group Representation Theory (Banff International Research Station, Canada)

2004: AMS-IMS-SIAM Joint Summer Research Conference Representations of Algebraic Groups, Quantum Groups, and Lie algebras (Snowbird, Utah).

2004: Interaction of Finite Dimensional Algebras with other areas of Mathematics (Banff International Research Station, Canada).

2005: Group Representation Theory (Bernoulli Center, EPFL, Lausanne, Switzerland).

2005: Representation Theory (University of Bielefeld, Germany).

2005: Flavors of Group Theory (Banff International Research Station, Canada).

2007: Algebraic Lie Theory (Banff International Research Station, Canada).

2007: Geometry and Lie Theory (University of Canberra and University of Sydney, Australia)

2007: International Conference on Algebra (Tsinghua University, China)

2007: Group theory and Combinatorics (University of Florida), 3 lectures

2007: Algebra Day (Ottawa, Canada)

2007: Algebraic aspects of Lie theory (Academia Sinica, Taipei, Taiwan)

2008: Evans Talk (UC-Berkeley).

Teaching experience

Moscow Institute of Energy, 1988: 2 undergraduate semester courses in Calculus;

Moscow State University, 1988: Tutorial work with undergraduates;

University of Oregon, 1995 - present: a large variety of undergraduate and graduate courses at all levels.

Books and Memoirs

1. (with J. Brundan and R. Dipper) Quantum linear groups and representations of GL_n(F_q), Memoirs of the American Mathematical Society, 149 (2001), No 706.

2. Linear and Projective Representations of Symmetric Groups, Cambridge University Press, 2005. (Series: Cambridge Tracts in Mathematics No. 163, Hardback (ISBN-10: 0521837030 | ISBN-13: 9780521837033), 292 pages).

3. (with J. Brundan) Representations of shifted Yangians, Memoirs of the AMS, to appear.

All Publications

1. Homological dimension of Banach algebras of smooth functions is equal to infinity, Moscow University Mathematical Bulletin 0043 (1988), No 6, 48--51 (MR 90f:46115).

2.Cohomology of finite Chevalley groups with coefficients in modules with nonradical highest weights, I, Preprint No 17(417), 1990, 32 p. Institute of Mathematics, Minsk.

3. Cohomology of finite Chevalley groups with coefficients in modules with nonradical highest weights, II, Preprint No 47(447), 1990, 43 p. Institute of Mathematics, Minsk.

4. 1-cohomology of a finite special linear group with coefficients in the module of truncated polynomials, Mathematical Notes, 49 (1991), No. 6, 597--603 (MR 92m:20045).

5. On extensions of modules of truncated polynomials and external powers over finite special linear groups, Mathematical Notes, 51 (1992), No. 4, 356--363 (MR 93i:20054).

6. (with A. A. Premet) On second degree cohomology of symmetric and alternating groups, Communications in Algebra, 21(2) (1993), 583--600 (MR 94c:20087a).

7. On restrictions of irreducible modular representations of semisimple algebraic groups and symmetric groups to some natural subgroups, Russian Academy of Sciences Doklady, 48(1994), No 3, 425--427.

8. 1-cohomology of finite Chevalley groups with coefficients in modules with one-dimensional weight spaces, Communications in Algebra, 22(4)(1994), 1197--1218 (MR 95d:20089).

9. On restrictions of irreducible modular representations of semisimple algebraic groups and symmetric groups to some natural subgroups, I, Proceedings of the London Mathematical Society (3) 69(1994), 515--540 (MR 95i:20065a).

10. On Conjectures of Benson and Jantzen-Seitz about modular representations of symmetric groups, Algebras, Groups and Geometries 11(1994), 215--228 (MR 95f:20018).

11. On restrictions of irreducible modular repreprentations of semisimple algebraic groups and symmetric groups to some natural subgroups, II, Communications in Algebra 22(15) (1994), 6175--6208 (MR 95i:20065b).

12. On branching rules for modular representations of reductive groups, Mathematical Notes 56(1994), No 5, 143--145.

13. Branching rules for modular representations of symmetric groups, I, Journal of Algebra 178(1995), 493--511 (MR 96m:20019a, featured review).

14. Branching rules for modular representations of symmetric groups, II, Journal fur die reine und angewandte Mathematik 459(1995), 163--212 (MR 96m:20019b, featured review).

15. Completely splittable representations of symmetric groups, Journal of Algebra 181(1996), 584--592 (MR 97a:20017).

16. Branching rules for modular representations of symmetric groups, III, Journal of the London Mathematical Society (2) 54(1996), 25--38 (MR 96m:20019c, featured review).

17. (with V.P. Burichenko and S. Martin) On cohomology of dual Specht modules, Journal of Pure and Applied Algebra 112(1996), 157--180 (MR 97g:20018).

18. (with B. Ford) A proof of the Mullineux conjecture, Mathematische Zeitschrift 226 (1997) 2, 267--308 (MR 98k:20015a, featured review).

19. On the decomposition numbers and branching coefficients for symmetric and special linear groups, Proceedings of the London Mathematical Society (3) 75 (1997), 497--558 (MR 98g:20026).

20. Branching rules for modular representations of symmetric groups, IV, Journal of Algebra 201 (1998), 547--572 (MR 99d:20019).

21. (with J. Brundan and I.D. Suprunenko) Semisimple restrictions from GL(n) to GL(n-1), Journal fur die reine und angewandte Mathematik 500 (1998), 83--112 (MR 99h:20069).

22. Branching rules for symmetric groups and applications, in Algebraic Groups and their Representations, R.W. Carter and J. Saxl editors, NATO ASI Series C, Vol. 517, Kluwer Academic Publishers, Dordrecht/Boston/London, 1998, p. 103--130 (MR 99m:20015).

23. (with A. Baranov) Maximal ideals in modular group algebras of the finitary symmetric and alternating groups, Transactions of the American Mathematical Society 351 (1999), 595--617 (MR 99d:16028).

24. (with J. Brundan) Some remarks on branching rules and tensor products for algebraic groups, Journal of Algebra 217 (1999), 335--351 (MR: 2000f:20073).

25. (with A. Baranov and A. Zalesskii) Asymptotic results on modular representations of symmetric groups and almost simple modular group algebras, Journal of Algebra 219 (1999), 506--530 (MR 2001a:20022).

26. (with C. Bessenrodt) On Kronecker products of complex representations of the symmetric and alternating groups, Pacific Journal of Mathematics 190 (1999), 201--223 (MR 2000i:20017).

27. (with J. Brundan) Modular Littlewood-Richardson coefficients, Mathematische Zeitschrift 232 (1999), 287--320 (MR 2000i:20071).

28. (with R. Gow) Connections between the representations of the symmetric group and the symplectic group in characteristic 2, Journal of Algebra 221 (1999), 60--89 (MR 2001b:20020).

29. (with J. Sheth) On extensions of simple modules over symmetric and algebraic groups, Journal of Algebra 221(1999), 705--722. Corrigendum: Journal of Algebra 238(2001), 843--844. (MR 2001f:20091)

30. (with J. Brundan) On translation functors for general linear and symmetric groups, Proceedings of the London Mathematical Society 80 (2000), 75--106 (MR 2000j:20080).

31. (with A. Premet) The globally irreducible representations of symmetric groups, Proceedings of the American Mathematical Society 128 (2000), 647--655 (MR 2000e:20025).

32. (with J. Brundan) Lower bounds for degrees of irreducible Brauer characters of finite general linear groups, Journal of Algebra 223 (2000), 615--629 (MR 2001f:20014).

33. (with C. Bessenrodt) On tensor products of modular representations of symmetric groups, Bulletin of the London Mathematical Society 32 (2000), 292--296 (MR 2001a:20023).

34. (with C. Bessenrodt) Irreducible tensor products over alternating groups, Journal of Algebra 228 (2000), 536--550 (MR 2001b:20017).

35. (with J. Sheth) Representations of the symmetric group are reducible over simply transitive subgroups, Mathematische Zeitschrift 235 (2000), 99--109 (MR 2001i:20027).

36. (with J. Brundan) Representations of the symmetric group which are irreducible over subgroups, Journal fur die reine und angewandte Mathematik, 530 (2001), 145--190 (MR 2001m:20017).

37. (with C. Bessenrodt) On Kronecker products of spin characters of the double covers of the symmetric groups, Pacific Journal of Mathematics 198 (2001), 295--305.

38. (with J. Brundan) Hecke-Clifford superalgebras, crystals of type $A_{2\ell}$ modular branching rules for $\hat S_n$, Representation Theory 5 (2001), 317--403.

39. (with D. Nakano) On comparing the cohomology of general linear and symmetric groups, Pacific Journal of Mathematics 201 (2001), 339--355.

40. (with J. Brundan) Tensor products and restrictions in type A, pp. 67--100 in Modular Representation Theory of Finite Groups, Proceedings of a Symposium held at the University of Virginia, Charlottesville May 8-15, 1998, Michael J. Collins, Brian J. Parshall and Leonard L. Scott editors, 2001, DeGruyter.

41. (with J. Brundan and R. Dipper) Quantum linear groups and representations of GL_n(F_q), Memoirs of the American Mathematical Society, 149 (2001), No 706.

42. (with J. Sheth) Representations of the alternating group which are irreducible over subgroups, Proceedings of the London Mathematical Society 84 (2002), 194--212.

43. (with J. Brundan) Projective representations of symmetric groups via Sergeev duality, Mathematische Zeitschrift 239 (2002), 27--68.

44. (with J. Brundan) Cartan determinants and Shapovalov forms, Mathematische Annalen 324 (2002), 431--449.

45. (with J. Brundan) Modular representations of the supergroup Q(n), Journal of Algebra 260 (2003), 64--98.

46. (with J. Brundan) Representation theory of symmetric groups and their double covers, in Groups, combinatorics & geometry (Durham, 2001), pp. 31--53, World Sci. Publishing, River Edge, NJ, 2003.

47. (with Pham-Huu Tiep) On restrictions of modular spin representations of symmetric and alternating groups, Transactions of the American Mathematical Society 356 (2004), 1971-1999.

48. (with A.E. Zalesskii) Minimal polynomials of elements of order $p$ in $p$-modular representations of alternating groups, Proceedings of the American Mathematical Society, 132 (2004), 1605-1612.

49. (with J. Brundan) Parabolic presentation of the Yangian Y(gl_n), Communications in Mathematical Physics, 254 (2005), 191-220.

50. Linear and Projective Representations of Symmetric Groups, Cambridge University Press, 2005. (Series: Cambridge Tracts in Mathematics No. 163, Hardback (ISBN-10: 0521837030 | ISBN-13: 9780521837033), 292 pages).

51. (with J. Brundan) Shifted Yangians and finite W-algebras, Advances in Mathematics, 200 (2006), 136-195.

52. (with J. Brundan) James' regularization theorem for double covers of symmetric groups, J. Algebra 306 (2006), 128-137.

Accepted for publication

53. (with J. Brundan) Cyclotomic Schur-Weyl duality, Selecta Mathematica, 52 pages.

54. (with J. Brundan and S. Goodwin) Highest weight theory for finite $W$-algebras, International Mathematical Research Notices, 38 pages.

55. (with J. Brundan) Representations of finite W-algebras and shifted Yangians, Memoirs of the American Mathematical Society, 99 pages.

Submitted for publication

56. (with P.-H. Tiep) representations of the general linear groups which are irreducible over subgroups, 35 pages.

57. (with P.-H. Tiep) Representations of finite special linear groups in non-defining characteristic, 22 pages.

In preparation