Leonid Positselski received his Ph.D. in Mathematics from Harvard University in 1998.  He did his postdocs at the Institute for Advanced Study (Princeton), Institut des Hautes Etudes Scientifiques (Bures-sur-Yvette), Max-Planck-Institut fuer Mathematik (Bonn), the University of Stockholm, and the Independent University of Moscow in 1998-2003. He taught as an Associate Professor at the Mathematics Faculty of the National Research University Higher School of Economics in Moscow in 2011-2014.  In Spring 2014 he moved from Russia to Israel, and since 2018 he work as a Researcher at the Institute of Mathematics of the Czech Academy of Sciences in Prague.He is an algebraist specializing in homological algebra.  His research papers span a wide area including algebraic geometry, representation theory, commutative algebra, algebraic K-theory, and algebraic number theory.He is the author of four books and memoirs, including "Quadratic Algebras" (joint with A.Polishchuk, AMS University Lecture Series, 2005), "Homological algebra of semimodules and semicontramodules: Semi-infinite homological algebra of associative algebraic structures" (Monografie Matematyczne IMPAN, Birkhauser Basel, 2010), "Two kinds of derived categories, Koszul duality, and comodule-contramodule correspondence" (AMS Memoir, 2011), and "Weakly curved A-infinity algebras over a topological local ring" (Memoir of the French Math. Society, 2018-19).

Select Guide Rating

• Preface.- Prologue.- Introduction.- Homogeneous Quadratic Duality over a Base Ring.- Flat and Finitely Projective Koszulity.- Relative Nonhomogeneous Quadratic Duality.- The Poincare-Birkhoff-Witt Theorem.- Comodules and Contramodules over Graded Rings.- Relative Nonhomogeneous Derived Koszul Duality: the Comodule Side.- Relative Nonhomogeneous Derived Koszul Duality: the Contramodule Side.- The Co-Contra Correspondence.- Koszul Duality and Conversion Functor.- Examples.- References.

Leonid Positselski received his Ph.D. in Mathematics from Harvard University in 1998.  He did his postdocs at the Institute for Advanced Study (Princeton), Institut des Hautes Etudes Scientifiques (Bures-sur-Yvette), Max-Planck-Institut fuer Mathematik (Bonn), the University of Stockholm, and the Independent University of Moscow in 1998-2003. He taught as an Associate Professor at the Mathematics Faculty of the National Research University Higher School of Economics in Moscow in 2011-2014.  In Spring 2014 he moved from Russia to Israel, and since 2018 he work as a Researcher at the Institute of Mathematics of the Czech Academy of Sciences in Prague.He is an algebraist specializing in homological algebra.  His research papers span a wide area including algebraic geometry, representation theory, commutative algebra, algebraic K-theory, and algebraic number theory.He is the author of four books and memoirs, including "Quadratic Algebras" (joint with A.Polishchuk, AMS University Lecture Series, 2005), "Homological algebra of semimodules and semicontramodules: Semi-infinite homological algebra of associative algebraic structures" (Monografie Matematyczne IMPAN, Birkhauser Basel, 2010), "Two kinds of derived categories, Koszul duality, and comodule-contramodule correspondence" (AMS Memoir, 2011), and "Weakly curved A-infinity algebras over a topological local ring" (Memoir of the French Math. Society, 2018-19).

Select Guide Rating

• Preface.- Prologue.- Introduction.- Homogeneous Quadratic Duality over a Base Ring.- Flat and Finitely Projective Koszulity.- Relative Nonhomogeneous Quadratic Duality.- The Poincare-Birkhoff-Witt Theorem.- Comodules and Contramodules over Graded Rings.- Relative Nonhomogeneous Derived Koszul Duality: the Comodule Side.- Relative Nonhomogeneous Derived Koszul Duality: the Contramodule Side.- The Co-Contra Correspondence.- Koszul Duality and Conversion Functor.- Examples.- References.

Leonid Positselski received his Ph.D. in Mathematics from Harvard University in 1998.  He did his postdocs at the Institute for Advanced Study (Princeton), Institut des Hautes Etudes Scientifiques (Bures-sur-Yvette), Max-Planck-Institut fuer Mathematik (Bonn), the University of Stockholm, and the Independent University of Moscow in 1998-2003. He taught as an Associate Professor at the Mathematics Faculty of the National Research University Higher School of Economics in Moscow in 2011-2014.  In Spring 2014 he moved from Russia to Israel, and since 2018 he work as a Researcher at the Institute of Mathematics of the Czech Academy of Sciences in Prague.He is an algebraist specializing in homological algebra.  His research papers span a wide area including algebraic geometry, representation theory, commutative algebra, algebraic K-theory, and algebraic number theory.He is the author of four books and memoirs, including "Quadratic Algebras" (joint with A.Polishchuk, AMS University Lecture Series, 2005), "Homological algebra of semimodules and semicontramodules: Semi-infinite homological algebra of associative algebraic structures" (Monografie Matematyczne IMPAN, Birkhauser Basel, 2010), "Two kinds of derived categories, Koszul duality, and comodule-contramodule correspondence" (AMS Memoir, 2011), and "Weakly curved A-infinity algebras over a topological local ring" (Memoir of the French Math. Society, 2018-19).

Select Guide Rating

• Preface.- Prologue.- Introduction.- Homogeneous Quadratic Duality over a Base Ring.- Flat and Finitely Projective Koszulity.- Relative Nonhomogeneous Quadratic Duality.- The Poincare-Birkhoff-Witt Theorem.- Comodules and Contramodules over Graded Rings.- Relative Nonhomogeneous Derived Koszul Duality: the Comodule Side.- Relative Nonhomogeneous Derived Koszul Duality: the Contramodule Side.- The Co-Contra Correspondence.- Koszul Duality and Conversion Functor.- Examples.- References.