This book is a tribute to the memory of Yuri Ivanovich Manin, who passed away on January 7, 2023. Manin was one of the giants of modern mathematics. His work covered a wide range of fields, including logic, number theory, geometry, mathematical physics, theoretical computer science, and linguistics. The contributions collected here are on topics close to his life-long passion: arithmetic and algebraic geometry.
Preface.- Projecting lattice polytopes according to the Minimal Model
Program.- Zeta-polynomials, superpolynomials, DAHA and plane curve
singularities.- Rational points over C1 fields.- On isomorphisms of
ind-varieties of generalized flags.- Spectral description of non-commutative
local systems on surfaces and non-commutative cluster varieties.- Semi-stable
reduction of foliations.- The Hasse principle for 9-nodal cubic 3-folds.-
Manin's work in birational geometry.- Endomorphism Algebras and Automorphism
Groups of certain Complex Tori.
Yuri Tschinkels research is at the interface of algebraic geometry and number theory. He studies higher-dimensional algebraic varieties, their hidden symmetries and rational points. He is the author of 160 papers and editor of 20 books. He is a Fellow of the American Mathematical Society and of the American Association for the Advancement of Science. He is a member of Leopoldina, the German National Academy of Sciences, and a Foreign Member of Academia Europaea.
