* Did you know: In one's
afterlife, one is condemned to finding counter-examples to all false
statements made in life? Hence the advice: Start early! *

From W. H. Aumer:

*
Two millenniums back / Euclid founded the science of Data.
Two Wikipedia lines / are all it merits to date. *

Department of Mathematics

University of California Berkeley

Berkeley, California, 94720

Vladimir Arnold (my teacher)

June 12, 1937 -- June 3, 2010

As a Matter of Thought
(English)
(Russian)

Links (at MCCME)
Photos (courtesy of S. Tretyakova)

A duck with ducklings

A book for grownups about children's mathematics

Aharoni played a major role in a successful fight against "fuzzy math" in his country, and in the implementation of a competent, no-frills curriculum (based on Primary Math from Singapore).

In this book, he shares with the reader -- a parent, or a teacher -- the insights he gained concerning elementary mathematics and mathematical education.

Available from Sumizdat , Amazon.com and SingaporeMath.com.

Selected Russian Poetry Rendered in English

A book by Natasha Rozhkovskaya (KSU)

based on her teaching in 2009

at the Berkeley Math Circle

Available in Russian at Amazon.com

and in English translation

at the AMS bookstore

Virasoro constraints for toric bundles (with Tom Coates and Hsian-Hua Tseng)

Kepler's laws and conic sections. Irina Boyadzhiev from Ohio State U provided the following visualization for this paper.

Explicit reconstruction in quantum cohomology and K-theory

The Hirzebruch-Riemann-Roch theorem in true genus-0 quantum K-theory (with Valentin Tonita)

Soliton equations, vertex operators, and simple singularities (with Edward Frenkel and Todor Milanov)

Quantum cobordisms and formal group laws (with Tom Coates)

Symplectic geometry of Frobenius structures

Simple singularities and integrable hierarchies (with Todor Milanov)

A_{n-1}-singularities and nKdV hierarchies

Quantum Riemann-Roch, Lefschetz and Serre (with Tom Coates)

Gromov-Witten invariants and quantization of quadratic hamiltonians

Semisimple Frobenius structures at higher genus

Introduction to symplectic field theory (with Yakov Eliashberg and Helmut Hofer)

Quantum K-theory on flag manifolds, finite-difference Toda lattices and quantum groups (with Yuan-Pin Lee)

On the WDVV-equation in quantum K-theory

Singularity theory and symplectic topology

A tutorial on quantum cohomology

Stationary phase integrals, quantum Toda lattices, flag manifolds and the mirror conjecture

The mirror formula for quintic threefolds

Elliptic Gromov-Witten invariants and the generalized mirror conjecture

A mirror theorem for toric complete intersections

Equivariant Gromov-Witten invariants

Homological geometry and mirror symmetry

Homological geometry I. Projective hypersurfaces

Quantum cohomology of flag manifolds and Toda lattices (with Bumsig Kim)

A symplectic fixed point theorem for toric manifolds

Whitney singularities of solutions of partial differential equations

Singular Lagrangian varieties and their Lagrangian mappings (based on my PhD thesis)