Integrability, Quantization, and Geometry

Sergey Novikov, University of Maryland, College Park, MD, and Steklov Institute of Mathematics, Moscow, RussiaIgor Krichever, Columbia University, New York, NY, and Skoltech, Moscow, RussiaOleg Ogievetsky, Center of Theoretical Physics, Marseille, France, and Lebedev Physical Institute, Moscow, RussiaSenya Shlosman, Center of Theoretical Physics, Marseille, France, and Skoltech, Moscow, Russia

• Part I. Integrable Systems: K. Aleshkin and K. Saito, Primitive forms without higher residue structure and integrable hierarchies (I)M. Alkadhem, G. Antoniou, and M, Feigin, Solutions of $BC_n$ type of WDVV equationsP. P. Boalch, Topology of the Stokes phenomenonG. Cotti and A. Varchenko, Equivariant quantum differential equation and qKZ equations for a projective space: Stokes bases as exceptional collections, Stokes matrices as Gram matrices, and $\mathcyr{B}$-theoremL. David and C. Hertling, Meromorphic connections over F-manifoldsG. Jorjadze and S. Theisen, Canonical maps and integrability in $T\bar{T}$ deformed 2d CFTsI. Krichever and A. Varchenko, Incarnations of XXX $\widehat{\mathfrak{sl}_N}$ Bethe ansatz equations and integrable hierarchiesF. Magri, The Kowalewski separability conditionsO. Mokhov and N. A. Strizhova, On the Liouville integrable reduction of the associativity equations in the case of three primary fieldsS. M. Natanzon and A. Yu. Orlov, Hurwitz numbers from matrix integrals over Guassian measureN. Reshetikhin, Spin Calogero-Moser models on symmetric spacesM. Semenov-Tian-Shansky, Quantum toda lattice: A challenge for representation theoryA. O. Smirnov, M. V. Pavlov, V. B. Matveev, and V. S. Gerdjikov, Finite-gap solutions of the Mikhalev equationI. A. B. Strachan, Flat coordinates on orbit spaces: From Novikov algebras to cyclic quotient singularitiesK. Takasaki, Cubic Hodge integrals and integrable hierarchies of Volterra typeG. Tian and G. Xu, Gauged Witten equation and adiabatic limitPart II. Quantum Theories and Algebraic Geometry: T. Bridgeland, Geometry from Donaldson-Thomas invariantsV. M. Buchstaber and A. P. Veselov, Fricke identities, Frobenius $K$-characters and Markov equationI. Cherednik, On Harish-Chandra theory of global nonsymmetric functionsN. C. Combe and Y. I. Manin, Symmetries of genus zero modular operadR. Coquereaux and J.-B. Zuber, On Schur problem and Kostka numbersP. Etingof, E. Frenkel, and D. Kazhdan, An analytic version of the Langlands correspondence for complex curvesD. Gaiotto, T. Johnson-Freyd, and E. Witten, A note on some minimally supersymmetric models in two dimensionsO. Garcia-Prada and D. Salamon, A moment map interpretation of the Ricci form, Kahler-Einstein structures, and Teichmuller spacesE. Getzler and S. W. Pohorence, Global gauge conditions in the Batalin-Vilkovisky formalismV. Golyshev and D. Zagier, Interpolated Apery numbers, quasiperiods of modular forms, and motivic gamma functionsY.-P. Lee, H.-W. Lin, and C.-L. Wang, Quantum flips I: Local modelM. Marcolli, Aspects of $p$-adic geometry related to entanglement entropyS. Merkulov, Grothendieck-Teichmuller group, operads and graph complexes: A surveyO. Ogievetsky and S. Shlosman, Platonic compounds of cylinders.