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Victor G. Kac

Victor G. Kac

Award Badge
Mathematics
USA
2026

D-Index & Metrics

Mathematics

D-Index
84
Citations
35559
World Ranking
112
National Ranking
63

Research.com Recognitions

  • 2026 - Research.com Mathematics in United States Leader Award
  • 2025 - Research.com Mathematics in United States Leader Award
  • 2015 - Steele Prize for Lifetime Achievement
  • 2013 - Fellow of the American Mathematical Society
  • 2013 - Member of the National Academy of Sciences
  • 2007 - Fellow of the American Academy of Arts and Sciences
  • 1986 - Fellow of John Simon Guggenheim Memorial Foundation
  • 1981 - Fellow of Alfred P. Sloan Foundation

Overview

Victor G. Kac is affiliated with MIT in the United States and has made extensive contributions to the field of mathematics, with a primary focus on algebraic structures and mathematical physics. Their work spans several subfields, including Geometry and Topology, Algebra and Number Theory, Statistical and Nonlinear Physics, Mathematical Physics, and Computational Theory and Mathematics.

Key topics explored in their research include:

  • Algebraic structures and combinatorial models
  • Advanced Topics in Algebra
  • Nonlinear Waves and Solitons
  • Advanced Algebra and Geometry
  • Homotopy and Cohomology in Algebraic Topology
  • Molecular spectroscopy and chirality
  • Advanced Algebra and Logic

Victor G. Kac has published numerous papers, with recent notable works including:

  • Polynomial tau-functions of the KP, BKP, and the s-component KP hierarchies, 2021, Journal of Mathematical Physics
  • Multicomponent KP type hierarchies and their reductions, associated to conjugacy classes of Weyl groups of classical Lie algebras, 2023, Journal of Mathematical Physics
  • Polynomial Tau-Functions for the Multicomponent KP Hierarchy, 2022, Publications of the Research Institute for Mathematical Sciences
  • $$\underline{p}$$-reduced Multicomponent KP Hierarchy and Classical $$\mathcal {W}$$-algebras $$\mathcal {W}(\mathfrak {gl}_N,\underline{p})$$, 2020, Communications in Mathematical Physics (co-authored)
  • Lie conformal superalgebras and duality of modules over linearly compact Lie superalgebras, 2020, Advances in Mathematics (co-authored)

Frequent publication venues for their work include:

  • arXiv (Cornell University)
  • Communications in Mathematical Physics
  • Japanese journal of mathematics
  • Advances in Mathematics
  • Transformation Groups

Frequently collaborating co-authors are:

  • Alberto De Sole
  • Pierluigi Möseneder Frajria
  • Paolo Papi
  • Daniele Valeri
  • Bojko Bakalov

Victor G. Kac has been recognized with several awards throughout their career. These include the Steele Prize for Lifetime Achievement (2015), membership in the National Academy of Sciences (2013), Fellow of the American Mathematical Society (2013), Fellow of the American Academy of Arts and Sciences (2007), Fellow of John Simon Guggenheim Memorial Foundation (1986), and Fellow of Alfred P. Sloan Foundation (1981).

Best Publications

  • Infinite Dimensional Lie Algebras

    Victor G. Kac

  • Vertex algebras for beginners

    Victor G. Kac

  • Basic representations of affine Lie algebras and dual resonance models

    I.B. Frenkel;V.G. Kac

  • Bombay Lectures on Highest Weight Representations of Infinite Dimensional Lie Algebras

    Victor G. Kac;A. K. Raina

  • Infinite-dimensional Lie algebras, theta functions and modular forms

    Victor G Kač;Dale H Peterson

  • Representations of classical lie superalgebras

    V. Kac

  • A sketch of Lie superalgebra theory

    V. G. Kac

  • SIMPLE IRREDUCIBLE GRADED LIE ALGEBRAS OF FINITE GROWTH

    V G Kac

  • Infinite root systems, representations of graphs and invariant theory

    V. G. Kac

  • Structure of representations with highest weight of infinite-dimensional Lie algebras☆

    V.G Kac;D.A Kazhdan

  • Contravariant form for infinite-dimensional Lie algebras and superalgebras

    V. G. Kac

  • Modular invariant representations of infinite-dimensional Lie algebras and superalgebras

    Victor G. Kac;Minoru Wakimoto

  • Some remarks on nilpotent orbits

    V.G. Kac

  • Infinite-dimensional algebras, Dedekind's η-function, classical möbius function and the very strange formula

    V.G Kac

  • Characters and fusion rules for W-algebras via quantized Drinfeld-Sokolov reduction

    Edward Frenkel;Victor Kac;Minoru Wakimoto

  • Spin and wedge representations of infinite-dimensional Lie algebras and groups

    Victor G. Kac;Dale H. Peterson

  • Quantum reduction for affine superalgebras

    Victor Kac;Shi-Shyr Roan;Minoru Wakimoto

  • Structure theory of finite conformal algebras

    Alessandro D'Andrea;Victor G. Kac

  • Moduli Spaces of Curves and Representation Theory

    E. Arbarello;C. De Concini;V. G. Kac;C. Procesi

  • Infinite flag varieties and conjugacy theorems

    Dale H. Peterson;Victor G. Kac

  • Modular and conformal invariance constraints in representation theory of affine algebras

    Victor G Kac;Minoru Wakimoto

  • Representations of quantum groups at roots of 1: Reduction to the exceptional case

    Corrado De Concini;Victor G. Kac

Frequent Co-Authors

Weiqiang Wang
Weiqiang Wang University of Virginia
Edward Frenkel
Edward Frenkel University of California, Berkeley
Claudio Procesi
Claudio Procesi Sapienza University of Rome
Chongying Dong
Chongying Dong University of California, Santa Cruz
David Kazhdan
David Kazhdan Hebrew University of Jerusalem
Yuri I. Manin
Yuri I. Manin Max Planck Institute for Mathematics
Igor Moiseevich Krichever
Igor Moiseevich Krichever Columbia University
Igor B. Frenkel
Igor B. Frenkel Yale University
S. P. Novikov
S. P. Novikov Russian Academy of Sciences

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