Leonid Positselski`s homepage

I am a mathematician specializing in Homological Algebra.  I have written papers about Koszul duality, semi-infinite cohomology, matrix factorizations, derived categories of the second kind, Galois cohomology, and mixed motives with finite coefficients.

Since Spring 2008, I was working as a Senior Researcher, and since Fall 2013 am an Acting Leading Researcher in the Laboratory of Algebra and Number Theory (http://www.iitp.ru/ru/researchlabs/277.htm) of the Institute for Information Transmission Problems.  Between 2011-2014, I was working as an Associate Professor (http://www.hse.ru/org/persons/35825480) of the Department of Mathematics (http://math.hse.ru/) of the Higher School of Economics.  Sometimes I taught advanced courses at the Independent University of Moscow (http://www.mccme.ru/ium/english/).

My preprints in the arXiv can be accessed from the link http://arxiv.org/a/positselski_l_1.html or http://arxiv.org/a/positselski_l_1.atom 

An extended version of my Spring 2014 presentation about the comodule-contramodule correspondence is available from http://positselski.narod.ru/co-contra.pdf  My Spring 2011 lectures on Koszul duality (in Russian) are available from http://erb-files.narod.ru/  My Spring 2009 lectures on the comodule-contramodule correspondence and representations of infinite-dimensional Lie algebras (also in Russian) are available from http://club.pdmi.ras.ru/moodle/course/view.php?id=10  

My memoir "Two kinds of derived categories, Koszul duality, and comodule-contramodule correspondence" has been published by the American Mathematical Society in 2011.  See http://www.ams.org/bookstore-getitem/item=MEMO-212-996 and http://www.ams.org/journals/memo/2011-212-996/S0065-9266-2010-00631-8/home.html

My monograph "Homological algebra of semimodules and semicontramodules", containing appendices written in collaboration with Sergey Arkhipov (http://www.math.toronto.edu/cms/arkhipov-sergey/) and Dmitriy Rumynin (http://www2.warwick.ac.uk/fac/sci/maths/people/staff/dmitriy_rumynin/), was published by Birkhauser Basel in 2010.  See http://www.springer.com/birkhauser/mathematics/book/978-3-0346-0435-2

My book "Quadratic Algebras", written jointly with Alexander Polishchuk (http://www.uoregon.edu/~apolish/), was published by the American Mathematical Society in 2005.  See http://www.ams.org/bookstore?fn=20&arg1=ulectseries&item=ULECT-37

I received my Ph.D. from Harvard University in 1998.  An expanded version of my thesis is available from the K-theory preprint archives at http://www.math.uiuc.edu/K-theory/0730/  A slightly newer and improved version can be found on the arXiv at http://arxiv.org/abs/1405.0965

My very first paper was published by Functional Analysis and its Applications in 1991.  See http://mi.mathnet.ru/rus/faa/v25/i4/p74 (Russian; notice the mistake in the title) or http://dx.doi.org/10.1007/BF01080085 (English).

My other coauthors are Roman Bezrukavnikov (http://en.wikipedia.org/wiki/Roman_Bezrukavnikov), Alexander Braverman (http://research.brown.edu/myresearch/Alexander_Braverman), and Alexander Vishik (http://www.nottingham.ac.uk/mathematics/people/alexander.vishik).

I cannot undertake to mention here all my teachers, but most of the mathematics I ever knew I learned from Michael Finkelberg (http://www.hse.ru/org/persons/2806441/index.html) and Arkady Vaintrob (http://www.uoregon.edu/~vaintrob/).

To see my photograph, click on the link "Person profile" in the left frame.  To access the list of my publications with hyperlinks, click on the "Publications" link.  My extended CV with a research summary (outdated) is available from http://www.iitp.ru/upload/content/277/positselskiCV.pdf  The latest version of the CV can be found at http://positselski.narod.ru/cv.pdf

Draft versions of my unfinished works are being posted from time to time on the page http://positselski.narod.ru 

My questions and answers on mathoverflow.net can be accessed through the page http://mathoverflow.net/users/2106/

This homepage is no longer maintained properly, and some of the links and information above may be outdated.  Since Fall 2018 I am working as a Researcher at the Institute of Mathematics of the Czech Academy of Sciences in Prague.  My homepage on the site of the Institute of Mathematics is located at http://users.math.cas.cz/~positselski/