nLab Andrei Okounkov

• webpage

• Yen Duong, A Profile of Andrei Okounkov, Simons Foundation News, June 06, 2021

Selected writings

On dimers in quantum many-body physics:

• Richard Kenyon, Andrei Okounkov, What is… a dimer?, Notices of the AMS, Vol. 52 No 3 (2005) (pdf)

On pillowcase orbifolds:

• Alex Eskin, Andrei Okounkov, Pillowcases and quasimodular forms, In: Ginzburg V. (ed.) Algebraic Geometry and Number Theory, Progress in Mathematics, vol 253. Birkhäuser 2006

  (arXiv:math/0505545, doi:10.1007/978-0-8176-4532-8_1)

On the Gromov-Witten/Donaldson-Thomas correspondence:

• Davesh Maulik, Nikita Nekrasov, Andrei Okounkov, Rahul Pandharipande, Gromov–Witten theory and Donaldson–Thomas theory, I. Compositio Mathematica. 142 (5): 1263–1285. (2003) (arXiv:math/0312059. doi:10.1112/S0010437X06002302)

• Davesh Maulik, Alexei Oblomkov, Andrei Okounkov, Rahul Pandharipande, Gromov-Witten/Donaldson-Thomas correspondence for toric 3-folds (arXiv:0809.3976)

On the representation theory of the symmetric group via the Gelfand-Tsetlin basis/seminormal representation:

On the representation theory of the symmetric group via the seminormal representation:

• Anatoly Vershik, Andrei Okounkov, A New Approach to the Representation Theory of the Symmetric Groups,

  Part I: Selecta Mathematica, New Series 2, 581-605 (arXiv:math/0503040, doi:10.1007/BF02433451); Part II (incorporates Part I in revised and improved form): Russian version: Записки научных семинаров ПОМИ 307 (2004), 57–98 (Zapiski nauchnyh seminarov POMI 307 (2004), 57–98); English version: Journal of Mathematical Sciences 131 (2005), 5471–5494 (doi:10.1007/s10958-005-0421-7).

Discussion of Witten indices and K-theoretic enumerative geometry (with Hilbert schemes):

• Andrei Okounkov, Lectures on K-theoretic computations in enumerative geometry (arXiv:1512.07363)

On Lie theory:

• Andrei Okounkov, New worlds for Lie theory, talk at ICM 2018 (pdf)

On equivariant elliptic cohomology of quiver varieties in relation to the AGT correspondence:

• Mina Aganagic, Andrei Okounkov, Elliptic stable envelopes (arXiv:1604.00423)

• Andrei Okounkov, Inductive construction of stable envelopes and applications, I. Actions of tori. Elliptic cohomology and K-theory (arXiv:2007.09094)

following the analogous non-elliptic discussion in:

• Davesh Maulik, Andrei Okounkov, Quantum Groups and Quantum Cohomology, Asterisque 408(2019) (arXiv:1211.1287, ISBN: 978-2-85629-900-5)

Review in:

• Andrey Smirnov, Stable envelopes for $A_n$, $\widehat A_n$-quiver varieties, 2019 (pdf)

Related $n$Lab entries

• geometric Langlands correspondence

• Lie theory

category: people