Curriculum Vitae

IVAN B. PENKOV

Personal:

US citizen, born May 19, 1957, in Sofia, Bulgaria, wife Irina Sousokolova, son Boyan and daughter Anna

University Education:
• June 1982, Master Degree in Mathematics, Moscow State University. Thesis: The inverse Penrose transform
• Oct. 1987, Candidate of Physical and Mathematical Sciences (Ph.D.), Steklov Mathematical Institute. Thesis: Typical modules over  classical Lie superalgebras and their geometric realizations

Research and Teaching Positions:
 1982-1983 Research Assistant, Institute of Mathematics Bulgarian Academy of Sciences, Sofia May-June 1986 Visiting Professor at Institute Fourier, Grenoble, France 1987-1989 Research Fellow, Section of Algebra, Institute of Mathematics, Bulgarian Academy of Sciences, Sofia, Bulgaria Oct. 1989 Visiting Professor at the University of Paris VII, France Jan.-Dec. 1990 Visiting Assistant Professor, Department of Mathematics, University of California at Berkeley June-July 1990 Visiting Scholar at the University of Göttingen, Germany Jan.-June 1991 Visiting Assistant Professor, Department of Mathematics, University of California at Davis 1991-June 93 Assistant Professor, Department of Mathematics, University of California at Riverside Sept.- Oct. 1993 Visiting Scholar at the Erwin Schrödinger Institute, Vienna, Austria July 1993-June 00 Associate Professor (tenured appointment), Department of Mathematics, University of California at Riverside Apr.–May 1996 Visiting Scholar and Program Organizer at The Erwin Schrödinger Institute, Vienna, Austria June 1996 Visiting Scholar at the Max-Planck Institute of Mathematics, Bonn, Germany June 1997 Visiting Professor at the University of Burgundy Dijon, France Sept. 1997 Visiting Professor at the University Louis Pasteur, Strasbourg, France Aug.-Sept. 1998 Visiting Scholar at the Max-Planck Institute of Mathematics, Bonn, Germany Nov. 1999 Visiting Professor at the University of Hamburg, Germany April-June 2000 Visiting Scholar at the Max-Planck Institute of Mathematics, Bonn, Germany July 2000 - Oct 04 Professor (tenured appointment), Department of Mathematics, University of California at Riverside Aug.-Sept. 2001 Visiting Scholar at the Max-Planck Institute of Mathematics, Bonn, Germany Jan.-March 2002 Program organizer and MSRI scholar, MSRI, Berkeley Aug.-Sept. 2002 Visiting Scholar at the Max-Planck Institute of Mathematics, Bonn, Germany Fall 2003 Visiting Professor at Yale University Spring 2004 Visiting Scholar at the Max-Planck Institute of Mathematics, Bonn, Germany Fall 2007 Visiting Professor at University of California at Berkeley Spring 2012 Visiting Professor at Yale University Fall 2012 Visiting Scholar at the Max-Planck Institute of Mathematics, Bonn, Germany Since 2004 Professor, Jacobs University Bremen, Germany

Main Research Interests:
Representations of finite and infinite dimensional Lie algebras, generalized Harish-Chandra modules, representations of Lie superalgebras and Lie supergroups, geometry of supermanifolds, homogeneous superspaces, super D-modules, homogeneous ind-spaces and geometry of ind-varieties.

Grants and Awards:
 1991--1995 NSF research grant jointly with R.E.Block and V.Chari. 1995 NSF grant for organizing the conference in honor of R.E.Block (jointly with V.Chari). 1995 Grant from the Erwin Schr\"odinger Institute for the program Representation Theory with Applications to Mathematical Physics'' (jointly with Joseph A. Wolf). 1996 NSF grant for support of US graduate students at the Erwin Schr\"odinger Institute. 1995--1997 NSF research grant. 1997--2002 NSF Group Infrastructure Grant Lie Groups, Lie Algebras and Their Representations'' (jointly with Joseph A. Wolf and Geoffrey Mason). Jan--May, 2002 Coorganizer of the one-semester MSRI Program Representations of Infinite Dimensional Algebras and Mathematical Physics'' (jointly with Edward Frenkel, Victor Kac, Vera Serganova and Gregg Zuckerman). April 2002 Coorganizer of the MSRI Workshop Quantum field theory and supersymmetry''. Sept. 2003 Coorganizer of the workshop Locally finite Lie algebras'' at the Banff Research Institute, Canada. 2003--2006 NSF Grant Lie Groups, Lie Algebras and Their Representations'' (jointly with Joseph A. Wolf and Geoffrey Mason). 2009--2012 DFG grant (one postdoc position). 2009 Volkswagen Foundation grant for organizing the summer school "Structures in Lie Representation Theory" (jointly with A. Joseph and A. Melnikov). 2009--2015 DFG grant within the Schwerpunktprogramm 1388 "Darstellungstheorie" 2012--2013 DFG grant for German-Israeli cooperation 2012--2015 DFG grant within the priority program "SPP 1388 Darstellungstheorie" 2015--2016 AIM SQuaRE grant 2015--2018 DFG grant (3/4 postdoc position). 2018--2020 DFG grant (one postdoc position).

Other Professional Activities:

1991--2006: Founding coorganizer of the California Lie Theory Program, a cooperation program in Lie Theory between the campuses of the University of California.

2004-- : Coorganizer of the Program ”Darstellungstheorie, Transformationsgruppen und Mathematische  Physik Eof the consortium of six universities: Jacobs University Bremen, University of Bochum, University of Erlangen, University of Hamburg, University of Koeln, and University of Paderborn.

2005: Coorganizer of the conference in honor of Yu. I. Manin at the Max Planck Institute for Mathematics, February 2005.

2005: Coorganizer of the International Conference in Honor of R.O. Wells, Jr., Jacobs University Bremen (formerly IUB), December 1-2, 2005.

2010: Coorganizer of the International Conference in "Infinite-dimensional Lie Algebras" in Newfoundland, Canada

2011: Coorganizer of the conference "Lie Groups" in honor of J.A. Wolf, Bochum, Germany

2012: Coorganizer of the German-Israeli workshop "Symplectic Geometry with applications to Representation Theory" at Jacobs University, Bremen, Germany

2012: Organizer of the meeting "7 1/2" in honor of Yu. I. Manin at IHES, Bures sur Yvette, France

2013: Organizer of a conference in honor of V. Tsanov, Sofia, Bulgaria.

2014: Coorganizer of the annual meeting in Soltau of the priority program SPP 1388 Darstellungstheorie''.

2014: Coorganizer of the meeting Hodge theory and unitary representations of reductive Lie groups'', Jacobs University Bremen.

2015: Coorganizer of the meeting Groups and Rings Theory and Applications'', July 15-22, Sofia, Bulgaria.

2019: Coorganizer of the meeting  Perspectives on representations of semisimple Lie algebras: A workshop in honor of Gregg Zuckerman on the occasion of his 70th birthday'', May 22-24, Bochum, Germany.

1.The Penrose transform on general grassmannians, C.R. Acad. Sci. Bulg. 33 (1980), 1439-1442.

2.Null-geodesics of complex Einstein spaces, Funk. Anal. i Priloz. 16, No.1 (1982), 78-79 (Russian), (with Yu.I.Manin).

3.Linear differential operators and cohomology of analytic spaces, Uspekhi Mat. Nauk 37, No 4 (1982), 171-172 (Russian).

4.D-modules on supermanifolds, Invent. Math. 71 (1983), 501-512.

5.The formalism of left and right connections on supermanifolds, (1982). In: Lect. on supermanifolds, geom. methods and conf. groups, editors Döbner et al, World Scientific, Singapore, 1989, 3-13 (with Yu.  I. Manin).

6.An introduction to geometric representation theory for complex simple Lie superalgebras. In: Proc. Conf. Diff. Geom. Math. in Physics, Shumen 1984, World Scientific 1986, 89-106.

7.Serre duality for projective supermanifolds, Funk. Anal. i Priloz. 18,No.1 (1984), 78-79, (Russian) (with O. Ogievetsky).

8.Projectivity and D-affinity of flag supermanifolds, Uspekhi Math. Nauk 40 No.1 (1985), 211-212, (Russian) (with I. Skornyakov).

9.A geometric approach to the linear Penrose transform, Transactions AMS 290 (1985), 555-575.

10.Cohomologie des D-modules typiques sur les supervariétés de drapeaux, C. R. Acad. Sci. Paris 199 (1984), 1005-1008 (with I. Skornyakov).

11.Characters of typical irreducible finite dimensional -modules, Funk. Anal. i Priloz. 20 (1986), No. 1, 37-45 (Russian).

12.Localisation des representations typiques d'une superalgèbre de Lie complexe classique, C. R. Acad. Sci. Paris 304 (1987), 163-166.

13.Borel-Weil-Bott theory for classical Lie supergroups. In: Curr. Probl. Math., Moscow, vol. 32 (1988), 71-124 (Russian).

14.Elements of supergeometry. In: Curr. Probl. Math., Moscow, vol. 32 (1988), 3-25, (Russian), (with Yu. I. Manin and A. Voronov).

15.Character formulas for some classes of atypical -and -modules, Lett. Math. Phys. 16 (1988), 251-261 (with V. Serganova).

16.Cohomology of for classical complex Lie supergroups and characters of some atypical G-modules, Annales Fourier 39 (1989), 845-873, (with V. Serganova).

17.Generic irreducible representations of classical Lie superalgebras. In: Lecture Notes in Physics, vol. 375 (1991), Springer Verlag, Berlin, 311-319 (with V. Serganova).

18.Representations of classical Lie superalgebras of type 1, Indag. Math., N.S. 3(2), (1992), 419-466 (with V. Serganova).

19.Generic representations of classical Lie superalgebras and their localisation, Monatsh. Math. 118 (1994), 267-313.

20.Generic irreducible representations of finite-dimensional Lie superalgebras, Intern. Journ. Math. 5 (1994), 389-419 (with V. Serganova).

21.Partially and fully integrable modules over Lie superalgebras. In: Studies in Advanced Mathematics (series editor S.-T. Yau), vol. 4, AMS and Internatl. Press 1997, 49-67 (with I. Dimitrov).

22.Characters of irreducible -modules and cohomology of for the Lie supergroup , Journ. of Math. Sci. 84 (1997), 1382-1412 (with V. Serganova).

23.Characters of finite-dimensional irreducible -modules, Lett. Math. Phys. 40 (1997), 147-158 (with V. Serganova).

24.Characters of strongly generic irreducible Lie superalgebra representations, Intern. Journ. Math. 9 (1998), 331-366.

25.Partially integrable highest weight modules, Transformation Groups 3 (1998), 241-253 (with I. Dimitrov).

26.The support of an irreducible Lie algebra representation, Journ. of Algebra 209 (1998), 129-142 (with V. Serganova).

27.Weight modules of direct limit Lie algebras, IMRN 1999, no. 5, 223-249 (with I. Dimitrov).

28.Weight representations of the Cartan type Lie algebras and , Math. Research Lett. 6 (1999), 397-416 (with V. Serganova).

29.On the structure of weight modules, Transactions AMS 352 (2000), 2857-2869 (with I. Dimitrov and O. Mathieu).

30. Generalized Harish-Chandra modules, Moscow Math. Journal 2 (2002), 753-767 (with V. Serganova).

34. Finite rank vector bundles on inductive limits of grassmannians, IMRN 2003, no. 34, 1871-1887 (with J. Donin).

35. Classically semisimple locally finite Lie superalgebras, Forum Math. 16 (2004), 431-446.

36.On the existence of (g,k)-modules of finite type, Duke Math. Journal 125 (2004), 329-349 (with V. Serganova and G. Zuckerman).

37.A Reduction Theorem for Highest Weight Modules over Toroidal Lie Algebras, Comm. Math. Physics 250(2004), no. 1, 47-53 (with I. Dimitrov and V. Futorny).

38.Generalized Harish-Chandra modules: a new direction of the structure theory of representations, Acta Applicandae Mathematicae, 81(2004), 311-326(with G. Zuckerman).

39. Ind-varieties of generalized flags as homogeneous spaces for classical ind-groups, IMRN 2004, no. 55, 2935-2953 (with I. Dimitrov).

40. Borel subalgebras of , Resenhas IME-USP 6 (2004),111-119 (with I. Dimitrov).

41. Generalized Harish-Chandra modules with generic minimal k-type, Asian Journal of Mathematics 8(2004), 795-812 (with G. Zuckerman)

42. A construction of generalized Harish-Chandra modules with arbitrary minimal k-type, Canad. Math. Bull. 50 (2007), 603-609 (with G. Zuckerman).

43. Cartan subalgebras of root-reductive Lie algebras, Journ. of Algebra, 308(2007), 583-611 (with E. Dan-Cohen and N. Snyder).

44. A construction of generalized Harish-Chandra modules for locally reductive Lie algebras, Transformation Groups 13 (2008), 799-817 (with G. Zuckerman).

45. Locally semisimple and maximal subalgebras of the finitary Lie algebras $$\mathfrak{gl}(\infty), \mathfrak{sl}(\infty), \mathfrak{so}(\infty)$$, and $$\mathfrak{sp}(\infty)$$, Journal of Algebra 322 (2009), 2069-2081 (with I. Dimitrov)

46. Parabolic and Levi subalgebras of finitary Lie algebras, IMRN, International Mathematics Research Notices, Article ID rnp169, doi:10.1093/imrn/rnp169 (with E. Dan-Cohen)

47. Parabolic Subgroups of Real Direct Limit Lie Groups. In: Contemporary Mathematics, vol. 499, AMS 2009 (with E. Dan-Cohen and J. A. Wolf)

48. Rank 2 vector bundles on ind-grassmannians.In, Manin Festschrift, Progress in Mathematics 270, Birkhaeuser Boston, 2009, 555-572 (with A. S. Tikhomirov).

49. Bounded simple (g; sl(2))-modules for rkg = 2, Journal of Lie Theory 20 (2010), 581-615 (with V. Serganova).

50. Tensor representations of infinite-dimensional root-reductive Lie algebras. In: Developments and Trends in Infinite-Dimensional Lie Theory, Progress in Mathematics 288, Birkh\"auser, 2011, 127-150 (with K. Styrkas).

51. On bounded generalized Harish-Chandra modules, Annales de l'Institut Fourier, 62(2012), 477-496 (with V. Serganova).

52. Triviality of vector bundles on twisted ind-Grassmannians, Mat. Sbornik 202:1 (2011), 1-39 (with A. S. Tikhomirov).

53. A Bott-Borel-Weil theorem for diagonal ind-groups, Canadian Journal of Mathematics, doi:10.4153/CJM-2011-032-6 (with I. Dimitrov).

54. Categories of integrable $sl(\infty)$-, $o(\infty)$-, $sp(\infty)$-modules. In: Representation Theory and Mathematical Physics, Contemporary Mathematics 557, AMS 2011, 335-357 (with V. Serganova).

55. Levi components of parabolic subalgebras of finitary Lie algebras, arXiv:1008.0311v1, in Representation Theory and Mathematical Physics, Contemporary Mathematics, vol. 557, AMS 2011, 129-149 (with E. Dan-Cohen).

56. A Koszul category of representations of finitary Lie algebras, Advances of Mathematics 289 (2016), 250-278 (with E. Dan-Cohen and V. Serganova).

57. On the structure of the fundamental series of generalized Harish-Chandra modules, Asian Journal of Mathematics 16 (2012), 489-514 (with G. Zuckerman).

58. On Ideals in the enveloping algebra of a locally simple Lie algebra, Int Math Res Notices 2015 (2015), 5196-5228 (with A. Petukhov).

59. Linear ind-Grassmannians, Pure and Applied Math. Quarterly 10 (2014), 289-323 (with A. Tikhomirov).

60. Algebraic methods in the theory of generalized Harish-Chandra modules. In: Developments and Retrospectives in Lie Theory: Algebraic Methods, Developments in Mathematics, vol. 38, Springer Verlag, 2014, 331-350 (with G. Zuckerman).

61. Tensor representations of Mackey Lie algebras and their dense subalgebras. In: Developments and Retrospectives in Lie Theory: Algebraic Methods, Developments in Mathematics, vol. 38, Springer Verlag, 291-330 (with V. Serganova).

62. On the Barth-Van de Ven-Tyurin-Sato Theorem, Sbornik: Mathematics, 206:6 (2015), 814-848 (with A. Tikhomirov).

63. A categorification of the boson-fermion correspondence via representation theory of $sl(\infty)$, Comm. Math. Phys., 341:3 (2016), 911-931 (with I. Frenkel and V. Serganova).

64. Annihilators of highest weight $sl(\infty)$-modules, Transformation Groups 21 (2016), 821-849 (with A. Petukhov).

65. Infinite Konstant cascades and centrally generated primitive ideals of U(n) in types A_∞, C_∞, Journal of Algebra 447(2016), 109-134 (with M. Ignatyev).

66. Schubert decompositions for ind-varieties of generalized flags, Asian Journal of Mathematics 21 (2017), 599-630 (with L. Fresse).

67. On ideals in U(sl(∞)), U(o(∞)), U(sp(∞)). In: Representation theory - current trends and perspectives, EMS Series of Congress Reports, European Mathematical Society (EMS), 2016, 565-602 (with A. Petukhov).

68. Ordered tensor categories and representations of the Mackey Lie algebra of infinite matrices, Algebra and Representation Theory (2018), DOI:10.1007/s10468-018-9765-9, arXiv:1512.08157 (with A. Chirvasitu).

69. Real group orbits on flag ind-varieties of SL(∞,ℂ). In: Lie Theory and Its Applications in Physics, Springer Proceedings in Mathematics and Statistics, vol. 191 (2016), 111-135 (with M. V. Ignatyev and J. A. Wolf), corrected version.

70. On categories of admissible $$\big(\mathfrak{g},\mathrm{sl}(2)\big)$$-modules, Transformation Groups 23(2) (2018), 463-489(with V. Serganova and G. Zuckerman).

71. Primitive ideals of $$\mathrm{U}\big(\mathfrak{sl}(\infty)\big)$$, Bulletin LMS 50 (2018), 443-448 (with A. Petukhov).

72. Ind-varieties of generalized flags: a survey of results, arXiv:1701.08478, preprint 2016 (with M. Ignatyev).

72'. Ind-varieties of generalized flags: a survey of results. In:'' Itogi nauki i techniki, series Modern mathematics and its applications'', Russian Academy of Sciences 2018, Topic Surveys 147, 3-50, (with M. Ignatyev), Russian version.

73. Decomposition of cohomology of vector bundles on homogeneous ind-spaces, C. R. Acad. Sci. Bulg. 70:7 (2017), 907-916 (with E. Hristova).

74. Orbit duality in ind-varieties of maximal generalized flags, Transactions of the Moscow Mathematical Society, 2017, 131-160 (with L. Fresse).

74'. Orbit duality in ind-varieties of maximal generalized flags, Transactions of the Moscow Mathematical Society 78 (2017), no 1(with L. Fresse), Russian version, arXiv:1704.03671.

75. Representation categories of Mackey Lie algebras as universal monoidal categories, Pure and Applied Mathematics Quarterly 13 (2017), 77-121 (with A. Chirvasitu).

76. Primitive ideals of $$\mathrm{U}\big(\mathfrak{sl}(\infty)\big)$$ and the Robinson-Schensted algorithm at infinity, arXiv:1801.06692, to appear in Representation of Lie Algebraic Systems and Nilpotent orbits, Progress in Mathematics, Birkhauser (with A. Petukhov).

77. Integrable $$\mathfrak{sl}(\infty)$$-modules and category $$\mathcal{O}$$ for $$\mathfrak{gl}(m|n)$$, Journal LMS, DOI: 10.1112/jlms.12176, arXiv:1712.00664 (with C. Hoyt and V. Serganova).

78. On an infinite limit of BGG categories $$\mathcal{O}$$, Moscow Mathematical Journal, to appear; arXiv:1802.06343 (with K. Coulembier).

79. On the existence of infinite-dimensional generalized Harish-Chandra modules, Sao-Paulo Jour. Math. 12(2018), 290-294(with G. Zuckerman).

80. Simple bounded weight modules of $$\mathfrak{sl}_{\infty}$$, $$\mathfrak{o}_{\infty}$$, $$\mathfrak{sp}_{\infty}$$, arXiv:1807.01899, preprint 2018 (with D. Grantcharov).

81. Large annihilator category $$\mathcal{O}$$ for $$\mathfrak{sl}_{\infty}$$, $$\mathfrak{o}_{\infty}$$, $$\mathfrak{sp}_{\infty}$$, Journal of Algebra, to appear; arXiv:1809.09394 (with V. Serganova).

82. Examples of automorhism groups of ind-varieties of generalized flags, Journal of Geometry and Symmetry in Physics 50(2018), 71-77(doi:10.7546/jgsp-50-2018-71-77)

Books edited:

1. V. Chari, I. B. Penkov - editors. Modular Interfaces: Modular Lie Algebras, Quantum Groups, and Lie Superalgebras. Studies in Advanced Mathematics, vol. 4, 1997, AMS.

2. A. Joseph, A. Melnikov, I. Penkov - editors. Highlights in Lie Algebraic Methods. Progress in Mathematics, vol. 295, 2011, Birkhauser.

3. A. Huckleberry, I. Penkov, G. Zuckerman - editors. Lie Groups: Structure, Actions, and Representations. Progress in Mathematics, vol. 306, 2013, Birkhauser.

4. G. Mason, I. Penkov, J.A. Wolf - editors. Developments and Retrospectives in Lie Theory: Geometric and Analytic Methods, Developments in Mathematics, vol.37, 2014, Springer Verlag.

5. G. Mason, I. Penkov, J.A. Wolf - editors. Develpoments and Retrospectives in Lie Theory: Algebraic Methods, Developments in Mathematics, vol. 38, 2014, Springer Verlag.

Special journal issues edited:

Sao Paulo Journal of Mathematical Sciences, vol. 12(2018), issue 2 (jointly with A.Huckleberry).