Algebraic Geometry and Number Theory: In Honor of Vladimir Drinfeld's 50th Birthday (Progress in Mathematics Book 253)

One of the most creative mathematicians of our times, Vladimir Drinfeld received the Fields Medal in 1990 for his groundbreaking contributions to the Langlands program and to the theory of quantum groups. These ten original articles by prominent mathematicians, dedicated to Drinfeld on the occasion of his 50th birthday, broadly reflect the range of Drinfeld's own interests in algebra, algebraic geometry, and number theory. Contributors: A. Eskin, V.V. Fock, E. Frenkel, D. Gaitsgory, V. Ginzburg, A.B. Goncharov, E. Hrushovski, Y. Ihara, D. Kazhdan, M. Kisin, I. Krichever, G. Laumon, Yu.I. Manin, A. Okounkov, V. Schechtman, and M.A. Tsfasman. Preface......Page 6 A glimpse into the life and work of V. Drinfeld......Page 12 Contents......Page 15 Pillowcases and quasimodular forms......Page 18 Cluster X-varieties, amalgamation,and Poisson–Lie groups......Page 43 Local geometric Langlands correspondence and affine Kac–Moody algebras......Page 85 Integration in valued fields......Page 277 On the Euler–Kronecker constants of global fields and primes with small norms......Page 422 Asymptotic behaviour of the Euler–Kronecker constant......Page 467 Crystalline representations and F-crystals......Page 473 Integrable linear equations and the Riemann–Schottky problem......Page 511 Fibres de Springer et jacobiennes compactifiées......Page 529 Iterated integrals of modular forms and noncommutative modular symbols......Page 578 Structures membranaires......Page 611 One of the most creative mathematicians of our times, Vladimir Drinfeld received the Fields Medal in 1990 for his groundbreaking contributions to the Langlands program and to the theory of quantum groups. These ten original articles by prominent mathematicians, dedicated to Drinfeld on the occasion of his 50th birthday, broadly reflect the range of Drinfeld's own interests in algebra, algebraic geometry, and number theory. Contributors: A. Eskin, V.V. Fock, E. Frenkel, D. Gaitsgory, V. Ginzburg, A.B. Goncharov, E. Hrushovski, Y. Ihara, D. Kazhdan, M. Kisin, I. Krichever, G. Laumon, Yu. I. Manin, A. Okounkov, V. Schechtman, and M.A. Tsfasman "One of the most creative mathematicians of our times, Vladimir Drinfeld received the Fields Medal in 1990 for his groundbreaking contributions to the Langlands program and to the theory of quantum groups. These ten original articles by prominent mathematicians, dedicated to Drinfeld on the occasion of his 50th birthday, broadly reflect the range of Drinfeld's own interests in algebra, algebraic geometry, and number theory."--Publisher's website This book represents a collection of invited papers by outstanding mathematicians in algebra, algebraic geometry, and number theory dedicated to Vladimir Drinfeld.