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Nicolai Reshetikhin

Professor, Yau Mathematical Sciences Center, Tsinghua University

Research Areas

Quantum field theory, representation theory, low-dimensional topology, quantum groups, and integrable systems.

Education

  • 1979, A.B., Leningrad Polytechnical Institute.
  • 1982, B.S., Leningrad University.
  • 1982, M.A., Leningrad University.
  • 1984, Ph.D., Leningrad Branch, Steklov Mathematical Institute (LOMI).

Employment

  • 2021-present, Professor, Yau Mathematical Sciences Center, Tsinghua University.
  • 1989-1991, Assistant Professor, Harvard University.

Research Summary

Nicolai Reshetikhin's research links quantum groups, integrable systems, representation theory, and low-dimensional topology. His recent papers revisit this circle of ideas through irregular KZ equations, Kac-Moody representations, Rozansky-Witten foams, quantum integrable systems on classical integrable backgrounds, Calogero-Moser-Sutherland systems, and two-dimensional Yang-Mills theory with corners. The common thread is the construction of algebraic and geometric mechanisms that turn topological or representation-theoretic data into exactly solvable quantum systems, and conversely use integrability to illuminate topology.

Representative Publications

  • N. Reshetikhin, V. G. Turaev, “Invariants of 3-manifolds via link polynomials and quantum groups,” Invent. Math. 103 (1991) 547-597.
  • N. Reshetikhin, J. Stokman, B. Vlaar, “Boundary quantum Knizhnik-Zamolodchikov equations and Bethe vectors,” Comm. Math. Phys. 336 (2015) 953-986, arXiv:1404.5492.
  • N. Reshetikhin, J. Stokman, B. Vlaar, “Boundary quantum Knizhnik-Zamolodchikov equations and fusion,” Ann. Henri Poincare 17 (2016) 137-177, arXiv:1404.5492.
  • N. Reshetikhin, A. Sridhar, “Integrability of limit shapes of the six vertex model,” Comm. Math. Phys. 356 (2017) 535-565, arXiv:1510.01053.
  • N. Reshetikhin, J. Stokman, B. Vlaar, “Integral solutions to boundary quantum Knizhnik-Zamolodchikov equations,” Adv. Math. 323 (2018) 486-528, arXiv:1602.08457.
  • N. Reshetikhin, “Semiclassical geometry of integrable systems,” J. Phys. A 51 (2018) 164001, arXiv:1802.00416.
  • A. S. Cattaneo, P. Mnev, N. Reshetikhin, “Perturbative quantum gauge theories on manifolds with boundary,” Comm. Math. Phys. 357 (2018) 631-730, arXiv:1507.01221.
  • A. S. Cattaneo, P. Mnev, N. Reshetikhin, “A cellular topological field theory,” Comm. Math. Phys. 374 (2020) 1229-1320.

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