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Mathematics

D-Index
58
Citations
14790
World Ranking
627
National Ranking
316

Research.com Recognitions

  • 2016 - Fellow of the American Academy of Arts and Sciences
  • 2012 - Member of the National Academy of Sciences
  • 2006 - Fields Medal of International Mathematical Union (IMU) For his contributions bridging probability, representation theory and algebraic geometry.
  • 2000 - Fellow of Alfred P. Sloan Foundation

Overview

Andrei Okounkov is a mathematician affiliated with Columbia University in the United States. Their work is primarily situated within the field of Mathematics, with a particular focus on several subfields including Geometry and Topology, Mathematical Physics, Discrete Mathematics and Combinatorics, Algebra and Number Theory, and Applied Mathematics.

The main areas of research for Andrei Okounkov include algebraic structures and combinatorial models, advanced algebra and geometry, algebraic geometry and number theory, advanced combinatorial mathematics, nonlinear waves and solitons, mathematics and applications, and advanced topics in algebra.

The scientist has authored numerous papers, with recent notable publications including:

  • Quantum difference equation for Nakajima varieties, 2022, Inventiones mathematicae
  • Elliptic stable envelopes, 2020, Journal of the American Mathematical Society
  • Inductive construction of stable envelopes, 2021, Letters in Mathematical Physics
  • Nonabelian stable envelopes, vertex functions with descendents, and integral solutions of q-difference equations, 2020, arXiv (Cornell University)
  • Virasoro constraints for stable pairs on toric threefolds, 2022, Forum of Mathematics Pi

Frequent collaborators include Alexei Oblomkov, Rahul Pandharipande, David Kazhdan, Miguel Moreira, and Ya. Kononov. These co-authorships reflect a collaborative engagement across various research problems in the mathematical sciences.

Andrei Okounkov's work has been published frequently in venues such as arXiv (Cornell University), Communications in Mathematical Physics, Functional Analysis and Its Applications, Notices of the American Mathematical Society, and Inventiones mathematicae.

The scientist has received multiple recognitions, including membership in the National Academy of Sciences in 2012 and fellowship in the American Academy of Arts and Sciences since 2016. They were awarded the Fields Medal by the International Mathematical Union in 2006 for contributions that bridge probability, representation theory, and algebraic geometry. Earlier in their career, they were a Fellow of the Alfred P. Sloan Foundation since 2000.

Best Publications

  • Seiberg-Witten theory and random partitions

    Nikita A. Nekrasov;Andrei Okounkov

  • Gromov-Witten theory and Donaldson-Thomas theory, I

    D. Maulik;N. Nekrasov;A. Okounkov;R. Pandharipande

  • Dimers and amoebae

    Richard Kenyon;Andrei Okounkov;Scott Sheffield

  • Asymptotics of Plancherel measures for symmetric groups

    Alexei Borodin;Andrei Okounkov;Andrei Okounkov;Grigori Olshanski

  • Correlation function of Schur process with application to local geometry of a random 3-dimensional Young diagram

    Andrei Okounkov;Nikolai Reshetikhin

  • Quantum Calabi-Yau and Classical Crystals

    Andrei Okounkov;Nikolai Reshetikhin;Cumrun Vafa

  • Gromov-Witten theory, Hurwitz theory, and completed cycles

    Andrei Okounkov;Rahul Pandharipande

  • Toda equations for Hurwitz numbers

    Andrei Okounkov

  • Infinite wedge and random partitions

    Andrei Okounkov

  • A new approach to representation theory of symmetric groups

    Andrei Okounkov;Anatoly Vershik

  • Quantum Groups and Quantum Cohomology

    Davesh Maulik;Andrei Okounkov

  • Shifted Schur Functions

    Andrei Okounkov;Grigori Olshanski

  • Quantum foam and topological strings

    Amer Iqbal;Cumrun Vafa;Nikita Nekrasov;Andrei Okounkov

  • Gromov-Witten theory, Hurwitz numbers, and Matrix models, I

    Andrei Okounkov;Rahul Pandharipande

  • Asymptotics of numbers of branched coverings of a torus and volumes of moduli spaces of holomorphic differentials

    Alex Eskin;Andrei Okounkov

  • Limit shapes and the complex Burgers equation

    Richard W. Kenyon;Andrei Okounkov

  • The boundary of Young graph with Jack edge multiplicities

    Sergei Kerov;Andrei Okounkov;Grigori Olshanski

  • Random Matrices and Random Permutations

    Andrei Okounkov

  • A Fredholm determinant formula for Toeplitz determinants

    Alexei Borodin;Andrei Okounkov

  • Brunn–Minkowski inequality for multiplicities

    Andrei Okounkov

  • Quantum Foam and Topological Strings

    A. Iqbal;N. Nekrasov;A. Okounkov;C. Vafa

Frequent Co-Authors

Grigori Olshanski
Grigori Olshanski Institute for Information Transmission Problems
Richard Kenyon
Richard Kenyon Yale University
Mina Aganagic
Mina Aganagic University of California, Berkeley
Alex Eskin
Alex Eskin University of Chicago
Cumrun Vafa
Cumrun Vafa Harvard University
Spencer Bloch
Spencer Bloch University of Chicago
Edward Frenkel
Edward Frenkel University of California, Berkeley
Eric M. Rains
Eric M. Rains California Institute of Technology

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