Curriculum Vitae
IVAN B. PENKOV
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
Grants and Awards:
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),
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)
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). |

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