Y. Manin

Publications187
h-index42
Citations6,702
Highly Influential Citations450
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Frobenius manifolds, quantum cohomology, and moduli spaces
Introduction: What is quantum cohomology? Introduction to Frobenius manifolds Frobenius manifolds and isomonodromic deformations Frobenius manifolds and moduli spaces of curves Operads, graphs, and…
Gauge Field Theory and Complex Geometry
Geometrical Structures in Field Theory.- 1. Grassmannians, Connections, and Integrability.- 2. The Radon-Penrose Transform.- 3. Introduction to Superalgebra.- 4. Introduction to Supergeometry.- 5.…
Rational points of bounded height on Fano varieties
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,,…
Arrangements of Hyperplanes, Higher Braid Groups and Higher Bruhat Orders
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)…
Real Multiplication and noncommutative geometry
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…
Stacks of Stable Maps and Gromov-Witten Invariants
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
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…
THE THEORY OF COMMUTATIVE FORMAL GROUPS OVER FIELDS OF FINITE CHARACTERISTIC
CONTENTSIntroductionChapter I. Formal groups and Dieudonne modules; basic concepts1. Groups in categories2. Algebraic and formal groups. Bialgebras3. The structure of commutative artinian groups4.…
Some remarks on Koszul algebras and quantum groups
La categorie des algebres quadratiques est munie d'une structure tensorielle. Ceci permet de construire des algebres de Hopf du type «(semi)-groupes quantiques»
Algebraic aspects of nonlinear differential equations
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