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Seiberg-Witten theory and random partitions

- N. Nekrasov, A. Okounkov
- Physics, Mathematics
- 1 June 2003

We study \( \mathcal{N} = 2 \) supersymmetric four-dimensional gauge theories, in a certain 525-02 = 2 supergravity background, called theΩ-background. The partition function of the theory in the… Expand

Dimers and amoebae

- R. Kenyon, A. Okounkov, S. Sheffield
- Mathematics, Physics
- 5 November 2003

We study random surfaces which arise as height functions of random perfect matchings (a.k.a. dimer configurations) on a weighted, bipartite, doubly periodic graph G embedded in the plane. We derive… Expand

Quantum Groups and Quantum Cohomology

- D. Maulik, A. Okounkov
- Mathematics, Physics
- 6 November 2012

In this paper, we study the classical and quantum equivariant cohomology of Nakajima quiver varieties for a general quiver Q. Using a geometric R-matrix formalism, we construct a Hopf algebra Y_Q,… Expand

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

- A. Okounkov, N. Reshetikhin
- Mathematics, Physics
- 6 July 2001

Schur process is a time-dependent analog of the Schur measure on partitions studied in math.RT/9907127. Our first result is that the correlation functions of the Schur process are determinants with a… Expand

Gromov–Witten theory and Donaldson–Thomas theory, I

- D. Maulik, N. Nekrasov, A. Okounkov, R. Pandharipande
- Mathematics
- Compositio Mathematica
- 2 December 2003

We conjecture an equivalence between the Gromov–Witten theory of 3-folds and the holomorphic Chern–Simons theory of Donaldson and Thomas. For Calabi–Yau 3-folds, the equivalence is defined by the… Expand

Quantum Calabi-Yau and Classical Crystals

- A. Okounkov, N. Reshetikhin, C. Vafa
- Physics, Mathematics
- 22 September 2003

We propose a new duality involving topological strings in the limit of the large string coupling constant. The dual is described in terms of a classical statistical mechanical model of crystal… Expand

Asymptotics of Plancherel measures for symmetric groups

- A. Borodin, A. Okounkov, G. Olshanski
- Mathematics
- 5 May 1999

1.1. Plancherel measures. Given a finite group G, by the corresponding Plancherel measure we mean the probability measure on the set G∧ of irreducible representations of G which assigns to a… Expand

Toda equations for Hurwitz numbers

- A. Okounkov
- Mathematics, Physics
- 19 April 2000

We consider ramified coverings of P^1 with arbitrary ramification type over 0 and infinity and simple ramifications elsewhere and prove that the generating function for the numbers of such coverings… Expand

Shifted Schur Functions

- A. Okounkov, G. Olshanski
- Mathematics
- 28 May 1996

The classical algebra $\Lambda$ of symmetric functions has a remarkable deformation $\Lambda^*$, which we call the algebra of shifted symmetric functions. In the latter algebra, there is a… Expand

Gromov-Witten theory, Hurwitz theory, and completed cycles

- A. Okounkov, R. Pandharipande
- Mathematics
- 24 April 2002

We establish an explicit equivalence between the stationary sector of the Gromov-Witten theory of a target curve X and the enumeration of Hurwitz coverings of X in the basis of completed cycles. The… Expand

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