Prof. Dr. Ivan B. Penkov

Adjunct Professor of Mathematics

School of Computer Science & Engineering

Constructor University Bremen gGmbH, Campus Ring 1 28759 Bremen Germany

Phone number

+49 421 200-3219

Fax number

+49 421 200-3103

Email Address

ipenkov@constructor.university

Office

Research I, Room 126

Website

http://math.jacobs-university.de/penkov/

Algebra, Lie Theory and Geometry

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.

In our group, we research three interconnected core areas in pure mathematics. For the last three decades, Prof. Ivan Penkov has had a broad research programme in Lie theory, algebra, and geometry. He and his research group are working in close collaboration with research groups in the United States at Yale University; the University of California, Berkeley; the University of Texas in Arlington; and the University of Buffalo. Penkov’s research group maintains close working contacts with the Max Planck Institute of Mathematics in Bonn, as well as with the University of Hamburg, the University of Cologne, and the Ruhr University in Bochum. His research has been funded continuously by multiple DFG projects for the last 15 years.

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 realization

Fellowships 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).
2020--2023	DFG grant (one postdoc position).
2023	Batsheva de Rothschild Fellow, Israel.
2023--2025	DFG grant (3/4 postdoc position).

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
Nov.-Dec. 2018	Visiting Scholar at the Weizmann Institute of Science, Rehovot, Israel
Nov. 2019	Visiting Professor at the University of Padua, Italy
Fall 2004 -- Spring 2023	Professor, Jacobs University Bremen, Germany (named International University Bremen before 2007)
Spring 2023 -- present	Adjunct Professor, Constructor University Bremen, Germany (named Jacobs University Bremen before 2023)

Selected Publications

Bounded weight modules for basic classical Lie superalgebras at infinity

Topological semiinfinite tensor (super)modules

On homogeneous spaces for diagonal ind-groups

Topological tensor representations of gl(V) for a space V of countable dimension

Automorphism Groups of ind-Varieties of Generalized Flags

An algebraic–geometric construction of ind-varieties of generalized flags

Finite-Dimensional Lie Algebras

Splitting Borel Subalgebras of $$\mathfrak {sl} (\infty )$$ , $$\mathfrak {o}(\infty )$$ , $$\mathfrak {sp}(\infty )$$ and Generalized Flags

Weight Modules

Two Generalizations

Classical Lie Algebras at Infinity

General Cartan, Borel and Parabolic Subalgebras of $$\mathfrak {gl} (\infty )$$ and $$\mathfrak {sl}(\infty )

Tensor Modules of $$\mathfrak {sl}(\infty )$$ , $$\mathfrak {o}(\infty )$$ , $$\mathfrak {sp}(\infty )

Root-Reductive Lie Algebras

The Bott–Borel–Weil Theorem

Generalized Harish-Chandra Modules

Universal Tensor Categories Generated by Dual Pairs

Integrable bounded weight modules of classical Lie superalgebras at infinity

Automorphism groups of ind-varieties of generalized flags

Ind-varieties of generalized flags: a survey of results

Publications on Scopus

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.