Peter Koroteev

Peter Koroteev


Department of Mathematics

Office: Evans 833
University of California, Berkeley

Last updated:

Research Interests
Representation theory, integrable systems, algebraic geometry, mathematical aspects of string theory and quantum field theory.

My current research is focused on the interaction between enumerative algebraic geometry, geometric representation theory and integrable systems. In general I work on physical mathematics which nowadays represents a large part of modern math. A significant amount of problems that are studied by mathematicians comes from string/gauge theory.

In 2020 I was awarded AMS-Simons grant

I am currently on the job market for tenure track faculty positions

Teaching [List of my courses]
In Summer 2020 I teach MATH 53 Multivariable Calculus

Selected Publications [Complete list]
[Arxiv] [MathSciNet] [Inspire HEP] [RG]
Below I list selected publications on several topics in math and physics

Algebraic Geometry and Representation Theory
Toroidal q-Opers [2007.11786] Submitted to Annales Henri Poincare
q-Opers, QQ-Systems, and Bethe Ansatz [2002.07344] Submitted to JEMS
(SL(N),q) -opers, the q-Langlands correspondence, and quantum/classical duality [1811.09937] Submitted to Comm.Math.Phys.
A-type Quiver Varieties and ADHM Moduli Spaces [1805.00986] Submitted to Comm.Math.Phys.
qKZ/tRS Duality via Quantum K-Theoretic Counts [1802.04463] Accepted in Math. Res. Lett.
Quantum K-theory of Quiver Varieties and Many-Body Systems [1705.10419] Submitted to Selecta Math.

Integrable Systems and Supersymmetry
The Quantum DELL System [1906.10354] Lett. Math. Phys. 110, 969–999 (2020)
On Elliptic Algebras and Large-n Supersymmetric Gauge Theories [1601.08238] J. Math. Phys. 57, no. 11, 112302 (2016)
On Quantum Hydrodynamics from Large-n Supersymmetric Gauge Theories [1510.00972 ] Lett. Math. Phys. 108, no. 1, 45 (2018)
Defects and Quantum Seiberg-Witten Geometry [1412.6081] JHEP 1505, 095 (2015)
On Three Dimensional Quiver Gauge Theories and Integrability [1304.0779] JHEP 1305, 126 (2013)
BPS States in Omega Background and Integrability [1207.0460] JHEP 1210, 116 (2012)
Quantum Deformations of the One-Dimensional Hubbard Model [0802.0777] J. Phys. A 41, 255204 (2008)

Three-Dimensional Mirror Symmetry
Good IR Duals of Bad Quiver Theories [1712.06068] JHEP 1805, 114 (2018)
On Three-Dimensional Quiver Gauge Theories of Type B [1612.00810] JHEP 1709, 067 (2017)
Mirror Symmetry in Three Dimensions via Gauged Linear Quivers [1402.0016] JHEP 1406, 059 (2014)

Resurgence and Holomorphy: From Weak to Strong Coupling [1410.0388] J. Math.Phys. 56, no. 5, 053505 (2015)
Statistical mechanics of Coulomb gases as quantum theory on Riemann surfaces [1303.6386] J. Exp. Theor. Phys. 117, 517 (2013)

Nonperturbative Dynamics of QFTs
Studying Critical String Emerging from Non-Abelian Vortex in Four Dimensions [1605.01472] Phys. Lett. B 759, 154 (2016)
Quantum Dynamics of Low-Energy Theory on Semilocal Non-Abelian Strings [1107.377 9] Phys. Rev. D 84, 065018 (2011)
Large-N Solution of the Heterotic Weighted Non-Linear Sigma-Model [1009.6207] Phys. Rev. D 82, 125023 (2010)

Holographic Applications
On the Null Energy Condition and Causality in Lifshitz Holography [1007.1428] Phys. Rev. D 82, 084002 (2010)
Spectra of Field Fluctuations in Braneworld Models with Broken Bulk Lorentz Invariance [0901.4347] Phys. Rev. D 79, 045023 (2009)
On Existence of Self-Tuning Solutions in Static Braneworlds without Singularities [0712.1136] JHEP 0802, 104 (2008)

Recent and Upcoming Conferences and Seminars
See [Complete list] for slides, notes and videos

Nordita String Seminar, Stockholm, Sweden (over zoom) [notes]
Joint Mathematics Meeting, Denver, CO [slides]
Algebra and Geometry Seminar, California Institute of Technology, Pasadena, CA
Algebra seminar, Virginia Polytechnic, Blacksburg, VA [slides]
AMS Fall 2019 Sectional Meeting, University of California, Riverside [slides]
Geometric Representation Theory and Quantum Field Theories, Tsinghua Sanya International Mathematics Forum, Sanya, China
Representation Theory and Mathematical Physics seminar, UC Berkeley [slides]
Geometry, Physics, and Representation Theory Seminar, Northeastern University, Boston, MA [link] [slides]
Quantum Field Theory seminar, CMSA, Harvard, Cambrdige, MA [link] [slides][video]
Program on Holomorphic Differentials in Mathematics and Physics, MSRI, Berkeley, CA [link]
Program on Quiver varieties and representation theory, Centre de Recherches Mathematiques, Montreal, QC, Canada [link]
Workshop `BPS/CFT Correspondence', Centre International de Rencontres Mathematiques, Marseille, France [link][notes]
Conference on Verlinde Algebra and Grassmannian, Sun Yatsen University, Guangzhou, China [link][slides]
Conference on Higher Symmetries, Aspnen, CO [link][slides]
Geometry seminar, Korean Institute for Advanced Study, Seoul, Korea [slides]

Lecture courses
Duluth Winter School 2014 on Supersymmetry and String Theory

Previous Employment
University of California, Davis, Department of Mathematics (2016-2018)
Perimeter Institute for Theoretical Physics, Waterloo, ON, Canada (2012-2016)

PhD: University of Minnesota (2012) [My PhD Thesis]
During my Minnesota years I mostly worked on physics of gauge theories with extended supersymmetry in various dimensions.
I was a Graduate Fellow at Kavli Institute for Theoretical Physics in Spring 2012.

MS: Moscow Institute of Physics and Technology (2008) [Paper 0901.4347 is based on my master thesis]
BS: Moscow Institute of Physics and Technology (2006) [Paper 0712.1136 is based on my bachelor diploma]

Other Teaching Activities
I teach math to school kids at the Berkeley Math Circle
I serve as a mentor at Hermiona Education which helps grade school students with choosing their higher eduation in the US
In Summer 2019 I teach at Sichuan Univeristy, Chengdu, China as a part of Lion education program. Slides of my public lecture on black holes and entanglement.

I enjoy doing endurance sports: biking, running (my last marathon), cross country skiing.
My Strava profile

My wife is also a scientist, at the moment she is a graduate student at Physics Department of University of Minnesota. Together we have daughter Anna.

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