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Frobenius manifolds, quantum cohomology, and moduli spaces

- Y. Manin
- Mathematics
- 6 July 1999

Introduction: What is quantum cohomology? Introduction to Frobenius manifolds Frobenius manifolds and isomonodromic deformations Frobenius manifolds and moduli spaces of curves Operads, graphs, and… Expand

Gauge Field Theory and Complex Geometry

- Y. Manin
- Mathematics
- 1988

Geometrical Structures in Field Theory.- 1. Grassmannians, Connections, and Integrability.- 2. The Radon-Penrose Transform.- 3. Introduction to Superalgebra.- 4. Introduction to Supergeometry.- 5.… Expand

Rational points of bounded height on Fano varieties

- J. Franke, Y. Manin, Y. Tschinkel
- Mathematics
- 1 June 1989

a prime pe7Z. Let V be an algebraic variety defined over F and lI~ a metrized line bundle on V, i.e., a system (L, ]'],) consisting of a line bundle L and a family of Banach v-adic metrics on L | F,,… Expand

Arrangements of Hyperplanes, Higher Braid Groups and Higher Bruhat Orders

- Y. Manin, V. Schechtman
- Mathematics
- 1989

Let zi be coordinate functions on en. Consider the arrangement of hyperplanes Di 1 : zi -z 1 = 0 in en and let U = en -U Di 1 be its complement. The fundamental group of U is called the (colored)… Expand

Real Multiplication and noncommutative geometry

- Y. Manin
- Mathematics
- 12 February 2002

Classical theory of Complex Multiplication (CM) shows that all abelian extensions of a complex quadratic field $K$ are generated by the values of appropriate modular functions at the points of finite… Expand

Stacks of Stable Maps and Gromov-Witten Invariants

- K. Behrend, Y. Manin
- Mathematics
- 27 June 1995

We correct some errors in the earlier version of this paper. Most importantly, the definition of isogeny of marked stable graphs has changed.

Iterated integrals of modular forms and noncommutative modular symbols

- Y. Manin
- Mathematics
- 28 February 2005

The main goal of this paper is to study properties of the iterated integrals of modular forms in the upper half-plane, possibly multiplied by z s−1, along geodesics connecting two cusps. This setting… Expand

THE THEORY OF COMMUTATIVE FORMAL GROUPS OVER FIELDS OF FINITE CHARACTERISTIC

- Y. Manin
- Mathematics
- 31 December 1963

CONTENTSIntroductionChapter I. Formal groups and Dieudonne modules; basic concepts1. Groups in categories2. Algebraic and formal groups. Bialgebras3. The structure of commutative artinian groups4.… Expand

Some remarks on Koszul algebras and quantum groups

- Y. Manin
- Mathematics
- 1987

La categorie des algebres quadratiques est munie d'une structure tensorielle. Ceci permet de construire des algebres de Hopf du type «(semi)-groupes quantiques»

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