World's Best Scientists 2026 revealed!

D-Index & Metrics

Mathematics

D-Index
35
Citations
5728
World Ranking
2757
National Ranking
1129

Research.com Recognitions

  • 2013 - Fellow of the American Mathematical Society
  • 1995 - Fellow of Alfred P. Sloan Foundation

Overview

Alexander Barvinok is affiliated with the University of Michigan-Ann Arbor in the United States. Their research spans multiple fields including Mathematics and Computer Science, with particular focus on Statistics and Probability, Computational Theory and Mathematics, Mathematical Physics, Applied Mathematics, and Numerical Analysis.

The scientist's research covers the following main topics:

  • Markov Chains and Monte Carlo Methods
  • Random Matrices and Applications
  • Stochastic processes and statistical mechanics
  • Mathematical functions and polynomials
  • Matrix Theory and Algorithms
  • Mathematics and Applications
  • Computational Geometry and Mesh Generation

Alexander Barvinok has published extensively, with a notable presence in venues such as arXiv (Cornell University), Forum of Mathematics Sigma, Advances in Mathematics, SIAM Journal on Discrete Mathematics, and Linear Algebra and its Applications.

Recent significant papers include:

  • More on zeros and approximation of the Ising partition function, 2021, Forum of Mathematics Sigma
  • When a system of real quadratic equations has a solution, 2022, Advances in Mathematics
  • Testing for Dense Subsets in a Graph via the Partition Function, 2020, SIAM Journal on Discrete Mathematics
  • A remark on approximating permanents of positive definite matrices, 2020, Linear Algebra and its Applications
  • Integrating Products of Quadratic Forms, 2023, Discrete & Computational Geometry

Frequent co-authors include Mark Rudelson, Nicholas Barvinok, and Anthony Della Pella. Collaboration with these researchers has contributed to a subset of the published works.

Alexander Barvinok has been recognized by several awards including being named a Fellow of the American Mathematical Society in 2013 and a Fellow of the Alfred P. Sloan Foundation in 1995.

Best Publications

  • A Course in Convexity

    Alexander Barvinok

  • A polynomial time algorithm for counting integral points in polyhedra when the dimension is fixed

    Alexander I. Barvinok

  • An Algorithmic Theory of Lattice Points in Polyhedra

    Alexander Barvinok;James Pommersheim

  • Problems of distance geometry and convex properties of quadratic maps

    A. I. Barvinok

  • Integer Points in Polyhedra

    Alexander Barvinok

  • Combinatorics and Complexity of Partition Functions

    Alexander Barvinok

  • Short rational generating functions for lattice point problems

    Alexander Barvinok;Kevin Woods

  • Two algorithmic results for the traveling salesman problem

    Alexander I. Barvinok

  • Polynomial time algorithms to approximate permanents and mixed discriminants within a simply exponential factor

    Alexander Barvinok

  • On the number of matrices and a random matrix with prescribed row and column sums and 0–1 entries☆

    Alexander Barvinok

  • Computing the volume, counting integral points, and exponential sums

    Alexander I. Barvinok

  • Feasibility testing for systems of real quadratic equations

    Alexander I. Barvinok

  • The number of graphs and a random graph with a given degree sequence

    Alexander I. Barvinok;J. A. Hartigan

  • Computing the Ehrhart quasi-polynomial of a rational simplex

    Alexander I. Barvinok

  • Computing the Permanent of (Some) Complex Matrices

    Alexander Barvinok

  • Computing the Ehrhart polynomial of a convex lattice polytope

    A. I. Barvinok

  • A Remark on the Rank of Positive Semidefinite Matrices Subject to Affine Constraints

    A. Barvinok

  • New algorithms for linear k -matroid intersection and matroid k -parity problems

    Alexander I. Barvinok

  • Thrifty approximations of convex bodies by polytopes

    Alexander Barvinok

  • Maximum entropy Gaussian approximations for the number of integer points and volumes of polytopes

    Alexander Barvinok;J. A. Hartigan

Frequent Co-Authors

Gerhard J. Woeginger
Gerhard J. Woeginger RWTH Aachen University
David S. Johnson
David S. Johnson AT&T (United States)
Arie Tamir
Arie Tamir Tel Aviv University
Bernd Sturmfels
Bernd Sturmfels Max Planck Institute for Mathematics in the Sciences
Sergey Fomin
Sergey Fomin University of Michigan–Ann Arbor

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