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Book DetailsContemporary MathematicsVolume: 823; 2025; 270 ppMSC: Primary 14; 32; 33; 35; 60; 81
This volume contains the proceedings of IDPEIS-22: Isomonodromic Deformations, Painlevé Equations, and Integrable Systems, held virtually June 27–July 1, 2022, hosted by Columbia University, and AGMPS-22: Algebraic Geometry, Mathematical Physics, and Solitons, held October 7–9, 2022, at Columbia University, New York, NY. This volume is dedicated to the legacy of Igor Krichever, and the papers in it are closely connected to the main themes of Igor's research interests.
The range of topics in this volume is very broad. The paper by Bobenko, Bobenko, and Suris generalizes Krichever's approach to algebro-geometric integrability to the dimer models. The paper by Röhrle and Zakharov considers a tropical version of classical algebro-geometric objects such as the Prym variety. The papers by Grekov and Nekrasov and by Felder, Smirnov, Tarasov, and Varchenko study quantum integrable systems from the point of view of 3D mirror symmetry and gauge theories. The paper by Etingof and Varchenko studies properties of certain families of flat connections, and the paper by Yamada describes a Lax form of a quantum \(q\)-Painlevé equation. The paper by Cherednik belongs to the area of combinatorial probability and the paper by Braverman and Kazhdan to the geometric Langlands program. The two remaining papers are in the area of applied mathematics. The paper by de Leon, Frauendiener, and Klein considers the computational approach to the Schotky problem. The paper by Blackstone, Gassot, and Miller studies soliton ensembles for the Benjamin-Ono equation.
ReadershipGraduate students and research mathematicians interested in classical and quantum integrable systems.
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Table of Contents
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Articles
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Alexander I. Bobenko, Nikolai Bobenko and Yuri B. Suris — Dimers and M-curves
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Felix Röhrle and Dmitry Zakharov — A matroidal perspective on the tropical Prym variety
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Yasuhiko Yamada — A Lax form for quantum $q$-$P_{\mathrm {VI}}$ equation
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Andrei Grekov and Nikita Nekrasov — Elliptic Calogero-Moser system, crossed and folded instantons, and bilinear identities
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G. Felder, A. Smirnov, V. Tarasov and A. Varchenko — Hypergeometric integrals, hook formulas and Whittaker vectors
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Pavel Etingof and Alexander Varchenko — Periodic and quasi-motivic pencils of flat connections
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Alexander Braverman and David Kazhdan — Hecke algebras for the 1st congruence subgroup and bundles on $\mathbb {P}^1$ I: the case of finite field
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Ivan Cherednik — Discrete Poisson hardcore 1D model and applications
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Eddy B. de Leon, Jörg Frauendiener and Christian Klein — Computational approach to the Schottky problem
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Elliot Blackstone, Louise Gassot and Peter D. Miller — On strong zero-dispersion asymptotics for Benjamin-Ono soliton ensembles
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This volume contains the proceedings of IDPEIS-22: Isomonodromic Deformations, Painlevé Equations, and Integrable Systems, held virtually June 27–July 1, 2022, hosted by Columbia University, and AGMPS-22: Algebraic Geometry, Mathematical Physics, and Solitons, held October 7–9, 2022, at Columbia University, New York, NY. This volume is dedicated to the legacy of Igor Krichever, and the papers in it are closely connected to the main themes of Igor's research interests.
The range of topics in this volume is very broad. The paper by Bobenko, Bobenko, and Suris generalizes Krichever's approach to algebro-geometric integrability to the dimer models. The paper by Röhrle and Zakharov considers a tropical version of classical algebro-geometric objects such as the Prym variety. The papers by Grekov and Nekrasov and by Felder, Smirnov, Tarasov, and Varchenko study quantum integrable systems from the point of view of 3D mirror symmetry and gauge theories. The paper by Etingof and Varchenko studies properties of certain families of flat connections, and the paper by Yamada describes a Lax form of a quantum \(q\)-Painlevé equation. The paper by Cherednik belongs to the area of combinatorial probability and the paper by Braverman and Kazhdan to the geometric Langlands program. The two remaining papers are in the area of applied mathematics. The paper by de Leon, Frauendiener, and Klein considers the computational approach to the Schotky problem. The paper by Blackstone, Gassot, and Miller studies soliton ensembles for the Benjamin-Ono equation.
Graduate students and research mathematicians interested in classical and quantum integrable systems.
-
Articles
-
Alexander I. Bobenko, Nikolai Bobenko and Yuri B. Suris — Dimers and M-curves
-
Felix Röhrle and Dmitry Zakharov — A matroidal perspective on the tropical Prym variety
-
Yasuhiko Yamada — A Lax form for quantum $q$-$P_{\mathrm {VI}}$ equation
-
Andrei Grekov and Nikita Nekrasov — Elliptic Calogero-Moser system, crossed and folded instantons, and bilinear identities
-
G. Felder, A. Smirnov, V. Tarasov and A. Varchenko — Hypergeometric integrals, hook formulas and Whittaker vectors
-
Pavel Etingof and Alexander Varchenko — Periodic and quasi-motivic pencils of flat connections
-
Alexander Braverman and David Kazhdan — Hecke algebras for the 1st congruence subgroup and bundles on $\mathbb {P}^1$ I: the case of finite field
-
Ivan Cherednik — Discrete Poisson hardcore 1D model and applications
-
Eddy B. de Leon, Jörg Frauendiener and Christian Klein — Computational approach to the Schottky problem
-
Elliot Blackstone, Louise Gassot and Peter D. Miller — On strong zero-dispersion asymptotics for Benjamin-Ono soliton ensembles
