Leonid Positselski's Homepage

I am a mathematician. My field is homological algebra.

I've done some work on quadratic and Koszul algebras, nonhomogeneous quadratic duality and curved DG-algebras, absolute Galois groups and Galois cohomology, mixed motives and motivic sheaves with finite coefficients, semi-infinite homological algebra, derived nonhomogeneous Koszul duality, derived categories and functors of the second kind, quasi-coherent matrix factorizations and relative singularity categories, contramodules and the comodule-contramodule correspondence, contraherent cosheaves, MGM duality, locally presentable abelian categories, infinitely generated tilting theory, very flat and strongly flat modules, etc.

Since September 10, 2018, I am working as a researcher at the Department of Algebra, Geometry and Mathematical Physics of the Institute of Mathematics of the Czech Academy of Sciences in Prague.

My official web page with a photograph, the contact information, CV and publication data is here.

My ORCID page is here, my arXiv preprint feed is here, my Google Scholar profile is here, and my MathSciNet profile is here. My questions and answers on MathOverflow are accessible from here.

The slides of my Beamer presentations (2014-18) are available below.

Contramodules: their history, and applications in commutative and noncommutative algebra. A mostly historical overview on contramodules, including the prehistory and history of my studies of contramodules. Presented as a 50 min. talk at the external meeting of the Institute of Mathematics in Zvánovice in October 2018. Big pdf file (compiled with the \pause commands in force); small pdf file (compiled with the \pause commands ignored).

Covers, direct limits, and pro-perfect topological rings. The slides of a 25 min. talk at the ECI workshop in Třešť, October 2018, about an application of contramodules to the Enochs conjecture on covers and direct limits. Based on my joint work with Silvana Bazzoni. Big pdf file (compiled with the \pause commands in force); small pdf file (compiled with the \pause commands ignored).

∞-tilting theory. The slides of a 25 min. talk at the 18th ICRA conference in Prague, August 2018, about infinitely generated, infinite projective/injective dimension tilting-cotilting theory for abelian categories. Based on my joint work with Jan Šťovíček. Big pdf file (compiled with the \pause commands in force); small pdf file (compiled with the \pause commands ignored).

The very flat conjecture. A discussion of the formulation, a detailed technical overview of the proof, and formulations of some analogous results at the end. Presented as a 50 min. talk at the ECI workshop in Telč in October 2017. Based on my joint work with Alexander Slávik. Big pdf file (compiled with the \pause commands in force); small pdf file (compiled with the \pause commands ignored).

Semi-infinite algebraic geometry. A lengthy technical overview of the (at present rather nonexistent or hypothetical) subject; with lots of details, definitions, examples, and particular cases. Presented as a 50 min. talk at the conference "Some Trends in Algebra" in Prague in September 2015. Big pdf file (compiled with the \pause commands in force); small pdf file (compiled with the \pause commands ignored).

Comodule-contramodule correspondence. A technical overview of the subject, with a considerable amount of detail. A slightly expanded version of the slides of 50 min. talk at the ECI workshop in Třešť, April 2014 (my first ever projector talk). Big pdf file (compiled with the \pause commands in force); small pdf file (compiled with the \pause commands ignored).