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Beijing-Novosibirsk seminar on geometry and mathematical physics (online seminar)

TIME:Every second Thursday, 17:00 Beijing time, 16:00 Novosibirsk time
REGISTRATION DEADLINE:No Need to Register
LOCATION:online
    Description

    The lecture announcements will be continually updated. The arrangement of the upcoming lectures is as follows:

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    Lecture XXXII - December 16th, 2021

    Dispersive shock waves: theory and observations

    Speaker: Anatoly M. Kamchatnov (Institute of Spectroscopy, Russian Academy of Sciences)

    Time: 2021-12-16 17:00 Beijing time, 16:00 Novosibirsk time

    Abstract: In this talk, I give a brief introduction to physics of dispersive shock waves (DSWs) and to basic principles of Gurevich-Pitaevskii theory of such waves. I show that many important characteristics of DSW, such as speeds of its edges and the amplitude of the leading soliton, can be calculated by an elementary method based on the asymptotic theory of propagation of high-frequency wave packets along a smooth background evolved from an intensive nonlinear pulse. In particular, this method allows one to find the number of solitons produced from an initial pulse for a wide class of evolution equations and initial conditions.

    To Join Zoom Meeting: https://us02web.zoom.us/j/82573458140?pwd=dE9lTGhVdmljanIvU2djNFg0WFRhdz09
    Meeting ID: 825 7345 8140
    Password: 626379


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    Previous Lectures

    Lecture XXXI - December 2nd, 2021

    A new construction of the moduli space of pointed stable curves of genus 0 

    Speaker: Young-Hoon Kiem (Seoul National University)

    Time: 2021-12-02 17:00 Beijing time, 16:00 Novosibirsk time

    Abstract: The moduli space of n points on a projective line up to projective equivalence has been a topic of research since the 19th century. A natural moduli theoretic compactification was constructed by Deligne and Mumford as an algebraic stack. Later, Knudsen, Keel, Kapranov and others provided explicit constructions by sequences of blowups. The known inductive constructions however are rather inconvenient when one wants to compute the cohomology of the compactified moduli space as a representation space of its automorphism group because the blowup sequences are not equivariant. I will talk about a new inductive construction of the much studied moduli space from the perspective of the Landau-Ginzburg/Calabi-Yau correspondence. In fact, we consider the moduli space of quasimaps of degree 1 to a point over the moduli stack of n pointed prestable curves of genus 0. By studing the wall crossing, we obtain an equivariant sequence of blowups which ends up with the moduli space of n+1 pointed stable curves of genus 0. As an application, we provide a closed formula of the character of the cohomology of the moduli space. We also provide a partial answer to a question which asks whether the cohomology of the moduli space is a permutation representation or not. Based on a joint work with J. Choi and D.-K. Lee. 

    Join Zoom Meeting:
    https://zoom.us/j/86570181622?pwd=TzIyMnZUL2JZb2RjdjI4amVTWWx1UT09 

    Meeting ID: 865 7018 1622
    Password: 600908 


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    Lecture XXX - November 18th, 2021

    Towards a mirror theorem for GLSMs
    Speaker:  Mark Shoemaker (Colorado State University)
    Time: 2021-11-18 10:00 Beijing time, 09:00 Novosibirsk time
    Abstract: A gauged linear sigma model (GLSM) consists roughly of a complex vector space V, a group G acting on V, a character \theta of G, and a G-invariant function w on V.  This data defines a GIT quotient Y = [V //_\theta G] and a function on that quotient.  GLSMs arise naturally in a number of contexts, for instance as the mirrors to Fano manifolds and as examples of noncommutative crepant resolutions. GLSMs provide a broad setting in which it is possible to define an enumerative curve counting theory, simultaneously generalizing FJRW theory and the Gromov-Witten theory of hypersurfaces. Despite a significant effort to rigorously define the enumerative invariants of a GLSM, very few computations of these invariants have been carried out.  In this talk I will describe a new method for computing generating functions of GLSM invariants.  I will explain how these generating functions arise as derivatives of generating functions of Gromov-Witten invariants of Y.

     


    Lecture XXIX - November 4th, 2021
    Poisson manifolds with semi-simple modular symmetry
    Speaker: Prof. Xiaojun Chen (Sichuan University)
    Time: 2021-11-04 17:00 Beijing time, 16:00 Novosibirsk time
    Abstract: In this talk, we study the “twisted” Poincare duality of smooth Poisson manifolds, and show that, if the modular symmetry is semisimple, that is, the modular vector is diagonalizable, there is a mixed complex associated to the Poisson complex which, combining with the twisted Poincare duality, gives a Batalin-Vilkovisky algebra structure on the Poisson cohomology, and a gravity algebra structure on the negative cyclic Poisson homology. This generalizes the previous results obtained by Xu et al for unimodular Poisson algebras. We also show that these two algebraic structures are preserved under Kontsevich's deformation quantization, and in the case of polynomial algebras they are also preserved by Koszul duality. This talk is based on a joint work with Liu, Yu and Zeng.


    Lecture XXVIII - October 21st, 2021
    Non-diagonalisable Hydrodynamic Type Systems, Integrable by Tsarev's Generalised Hodograph Method
    Speaker: Maxim Pavlov
    Time:2021-10-21 17:00 Beijing time, 16:00 Novosibirsk time
    Abstract:
    We present a wide class of non-diagonalisable hydrodynamic type systems, which can be integrated by Tsarev' s generalised hodograph method. This class of hydrodynamic type systems contains Jordan blocks 2x2 only. The Haantjes tensor has vanished. This means such 2N component hydrodynamic type systems possess N Riemann invariants and N double eigenvalues only.
    First multi-component example was extracted from El's nonlocal kinetic equation, describing dense soliton gas. All conservation laws and commuting flows were found. A general solution is constructed.

    Download Slides:

    /upload/editor/file/20211022/22085533159.pdf


    Lecture XXVII - October 7th, 2021

    On the Saito-Givental theory of elliptic singularities
    Speaker:Dr. Wang Xin (Shandong University)
    Time:2021-10-07 17:00
    Abstract:
    In this talk, we will first discuss genus zero Givental I function for Saito’s singularity theory of any invertible singularities. Then we show how to use Givental formalism to do explicit computation about higher genus invariants of Saito-Givental theory. As an example, we compute the genus-1 and genus-2 G function for the associated semisimple Frobenius manifold of elliptic singularities. At the end, we discuss the higher genus structures about the generating function of  Saito-Givental  invariants for Fermat elliptic singularities.


    Lecture XXVI - September 16th, 2021

    Integration of algebraic functions, polynomial approximation, nonclassical boundary problems and Poncelet-type theorems.
    Speaker: Prof. Sergey Tsarev (Siberian Federal University, Krasnoyarsk)
    Time: 2021-09-16 17:00-18:00 Beijing time, 16:00-17:00 Novosibirsk time, 12:00-13:00 Moscow time

    Abstract: In this review talk we expose remarkably tight relations between the four topics mentioned in the title. Starting from the paper by H.Abel published in 1826 and subsequent results of Chebyshev and Zolotarev we finish at the recent results by Burskii, Zhedanov, Malyshev (et al.)  devoted to algorithmic decidability of some identities for the values of the Weierstrass P-function, unexpected elementary geometric applications and many, many more hidden equivalences in seemingly unrelated areas of analysis, modern computer algebra and geometry.

     

    Slides: https://disk.pku.edu.cn:443/link/F1CA39F7D183F668A242DEFBDEC43AE4

    Video:https://disk.pku.edu.cn:443/link/EC62753E3F712DC7EA925DA9CB7BB11B
    Valid Until: 2026-10-01 23:59

     

    Lecture XXV - June 10th2021

    Mirror symmetry for a cusp polynomial Landau-Ginzburg orbifold
    Speaker: Basalaev Alexey Andreevich (HSE)
    Time: 2021-06-10 17:00 Beijing time, 16:00 Novosibirsk time, 12:00 Moscow time

    Abstract:  

    We will establish mirror symmetry between  the cusp polynomials considered with a nontrivial symmetry group and Geigle-Lenzing orbifold projective lines. In particular, we will introduce Dubrovin-Frobenius manifold of equivariant Saito theory of any cusp polynomial and show that it is isomorphic to Dubrovin-Frobenius manifold of the respective Geigle-Lenzing orbifold.
    We will also show that in the case of simple-elliptic singularities this mirror isomorphism is equivalent the certain relations in the ring of modular forms.
    This is a joint work with A.Takahashi (Osaka).

     

    Video: https://disk.pku.edu.cn:443/link/038A4056A5DFA2E111A615470EFAA6B5

    Expiration Time:2026-06-01 23:59

     

    Lecture XXIV - May 20th2021

    Virasoro conjecture for FJRW theory
    Speaker: Dr. He Weiqiang (Sun Yat-sen University)
    Time: 2021-05-20 17:00 Beijing time, 16:00 Novosibirsk time, 12:00 Moscow time

    Abstract:  

    Virasoro conjecture is one of the most fascinating conjecture in Gromov-Witten theory, which is introduced by Eguchi-Hori-Xiong. It state that the Gromov-Witten potential Z is a solution of a sequence of nonlinear differential equation: L_k(Z)=0, k>=-1. And L_k satisfies the following Virasoro relation [L_m, L_n]=(m-n)L_{m+n}

    In this talk, I will give a survey on Virasoro conjecture. I will also talk about the explicit  form of Virasoro constraints on FJRW theory and prove it in some simple case, base on the joint work with Yefeng Shen.

     

    Lecture XXIII - April 29th2021

    Spinorial description of G_2 and SU(3)-manifolds
    Speaker: I. Agricola (Marburg, Germany)
    Time: 2021-04-29 17:00 Beijing time, 16:00 Novosibirsk time, 12:00 Moscow time

    Video: 

    https://cloud.mail.ru/stock/3XmMgG8dduEKd55qxfS2fCDy

    or

    https://disk.pku.edu.cn:443/link/69A1A095EFD2E28809739E9664B9B6B9
    Valid Until: 2025-01-01

     

    Lecture XXII - April 15th2021

    Homological mirror symmetry for chain type polynomials
    Speaker: Umut Varolgunes
    Time: 2021-04-15 12:00 Beijing time, 11:00 Novosibirsk time

    Abstract: I will start by explaining Takahashi's homological mirror symmetry (HMS) conjecture regarding invertible polynomials, which is an open string interpretation of Berglund-Hubsch-Henningson mirror symmetry. In joint work with A. Polishchuk, we resolve this HMS conjecture in the chain type case up to rigorous proofs of general statements about Fukaya-Seidel categories. Our proof goes by showing that the categories in both sides are obtained from the category Vect(k) by applying a recursion. I will explain this recursion categorically and sketch the argument for why it is satisfied on the A-side assuming the aforementioned foundational results. If time permits, I will also mention what goes into the proof in the B-side.

     

    Lecture XXI - March 18th2021

    Virasoro constraints for Drinfeld-Sokolov hierarchies and equations of Painlevé type

    Speaker: Prof. Wu Chaozhong(Sun Yat-Sen University)

    Time: 2021-03-18 17:00 Beijing time, 16:00 Novosibirsk time

    Abstract: By imposing Virasoro constraints to Drinfeld-Sokolov hierarchies, we obtain their solutions of Witten-Kontsevich and of Brezin-Gross-Witten types, and those characterized by certain ordinary differential equations of Painlevé type. We also show the existence of affine Weyl group actions on solutions of such Painlevé-type equations, which generalizes the theory of Noumi and Yamada on affine Weyl group symmetries of the Painlevé-type equations. This work is joint with Si-Qi Liu and Youjin Zhang. 

     

    Lecture XX - February 18th2021

    Fukaya category for Landau-Ginzburg orbifolds and Berglund-H\"ubsch homological mirror symmetry for curve singularities.

    Speaker: Prof. Cheol-Hyun Cho(Seoul National University)

    Time: 2021-02-18 17:00 Beijing time, 16:00 Novosibirsk time

    Abstract: For a weighted homogeneous polynomial and a choice of a diagonal symmetry group, we define a new Fukaya category based on wrapped Fukaya category of its Milnor fiber together with monodromy information. It is analogous to the variation operator in singularity theory.  As an application, we formulate a complete version of Berglund-H\"ubsch homological mirror symmetry and prove it for two variable cases.  This is a joint work with Dongwook Choa and Wonbo Jung.

     

    Lecture XIX

    Real-valued semiclassical approximation for the asymptotics with complex-valued phases of the  Hermitian type orthogonal polynomials

    S. Yu. Dobrokhotov,  A.V. Tsvetkova (Ishlinsky Institute for Problems in Mechanics RAS)

    based on joint work with A.I. Aptekarev, D. N. Tulyakov (Keldysh Institute of Applied Mathematics RAS)

    Time: 2021-02-04 17:00 Beijing time, 16:00 Novosibirsk time

     

    Lecture XVIII

    Multiple Orthogonal Polynomials with respect to Hermite weights: applications and asymptotics
    Speaker: A.I. Aptekarev, (Keldysh Institute of Applied Mathematics RAS),
    Joint work with S. Yu. Dobrokhotov, A.V. Tsvetkova (Ishlinsky Institute for Problems in Mechanics RAS) and D. N. Tulyakov (Keldysh Institute of Applied Mathematics RAS)
    Time: 2021-01-21 17:00

    Abstract: We start with the definition of the Hermite multiple orthogonal polynomials by means of orthogonality relations. Then we present several recent applications, such as eigenvalues distribution of random matrices ensembles with external field and Brownian bridges. The main goal of the talk will be the asymptotics of this polynomial sequence when the degree of the polynomial is growing in the scale corresponding to its variable (so called Plancherel – Rotach type asymptotics). The starting point for our asymptotical analysis is the recurrence relations for multiple orthogonal polynomials. We will present an approach based on the construction of decompositions of bases of homogeneous difference equations. Another approach, based on the  semiclassical  asymptotics in the case of complex-valued phases will be presented in S. Yu. Dobrokhotov’s talk.

     

    Lecture XVII

    Video:https://disk.pku.edu.cn:443/link/79BFC86B8E4BF6B39A0F7342732A65F9

    Video Until:2025-01-01

    A discretization of complex analysis for triangulated surfaces.
    SpeakerIvan Dynnikov ( Steklov Mathematical Institute, Russia)

    Time:2020-12-10 17:00 Beijing time (12:00 Moscow time, 16:00 Novosibirsk time) 

    Abstract: 

    I will overview results on a particularly simple discrete version of the notion of a holomorphic function. It was suggested by S.P.Novikov and myself in 2002 and stemmed from the idea that the discrete analogue of the Cauchy--Riemann operator must be a first order difference operator. This is most naturally defined on a triangular lattice or a triangulated surface admitting a checkerboard coloring.

     

    Lecture XVI

    Video:https://disk.pku.edu.cn:443/link/3E5C254A4C00FAE8BAB460A757F08C66

    Video Until:2025-01-01 

     

    Exponential Networks and enumerative invariants of local CY

    Speaker:Mauricio Romo (Tsinghua University)
    Time:2020-11-26 17:00
    Abstract: Exponential networks (EN) are a variant of the spectral networks of Gaiotto-Moore-Neitzke, for the case of logarithmic differentials and they naturally lead to Donaldson-Thomas type invariants of local CY 3-folds. I will define ENs and subsequently describe how to get the invariants, illustrated by some examples. If time permits I will show some recent development for cases with compact 4-cycles. 

     

    Lecture XV

    Video:https://disk.pku.edu.cn:443/link/74EB24823ABACB010B4349C229404068

    Video Until:2025-01-01

    Higher, Super, and Quantum
    Speaker:Vincent Bouchard (University of Alberta, Саnada)
    Time:2020-11-12 17:00
    Abstract: Kontsevich and Soibelman recently introduced the concept of quantum Airy structures, which may be understood as generalizations of Virasoro constraints in enumerative geometry. In this talk I will present two broad generalizations, namely higher and super quantum Airy structures. I will explain how many examples of these structures can be constructed as modules of vertex operator algebras, in particular W-algebras. I will comment (and speculate) on the enumerative interpretation of these new constructions in terms of intersection numbers on various moduli spaces. If time permits, I may also briefly explain how these higher and super quantum Airy structures further expand the definition of the Eynard-Orantin topological recursion.

     

    I will overview results on a particularly simple discrete version of the notion of a holomorphic function. It was suggested by S.P.Novikov and myself in 2002 and stemmed from the idea that the discrete analogue of the Cauchy--Riemann operator must be a first order difference operator. This is most naturally defined on a triangular lattice or a triangulated surface admitting a checkerboard coloring.

     

    Lecture XIV

    Video:https://disk.pku.edu.cn:443/link/DE42FB3F2DD64F94C7A966B6B8AC193B

    Video Until: 2025-01-01

    Title: Logarithmic GLSM and its applications
    Speaker: Prof.Ruan Yongbin,IAS,Zhejiang University,Hangzhou.
    Time: 2020-10-29 17:00-18:00
    Abstract: In early 2010, a mathematical theory of GLSM was proposed by Fan-Jarvis-Ruan to generalize both Gromov-Witten theory and FJRW-theory. The mathematical GLSM theory produced an open moduli space, in contrast to the traditional moduli theory where the compactness is required. Then, a cosection (constructed out of superpotential) localized the theory to the critical locus. The above theory is theoretically beautiful, but not so useful in computation. Recently, a delicate compactification of GLSM (logarithmic GLSM) was constructed to remedy the above defect. Its localization formula is proved to be extremely effective to solve many outstanding problems in the subject of Gromov-Witten theory, including BCOV axioms of higher genus Gromov-Witten theory of quintic 3-fold, r-spin conjecture relating r-spin virtual cycle and locus of holomorphic differential, modularity of Gromov-Witten theory of elliptic fibration and so on. In the talk, we will survey the above developments.
    These are joint works with Shuai Guo, Felix Janda and Qile Chen.

     

    Lecture XIII

    Video:https://disk.pku.edu.cn:443/link/DE42FB3F2DD64F94C7A966B6B8AC193B

    Video Until:2025-01-01 

    Transposed Poisson algebras

    Time: 2020-10-15 17:00 Beijing time (16:00 Novosibirsk time)
    Speaker: Prof. Bai Chengming (Nankai Institute)
    Abstract:
    We introduce a notion of transposed Poisson algebra which is a dual notion of the Poisson algebra by exchanging the roles of the two binary operations in the Leibniz rule defining the Poisson algebra. We interpret the close relationships between it and some structures such as Novikov-Poisson and pre-Lie Poisson algebras including the example given by a commutative associative algebra with a derivation, and 3-Lie algebras.

     

     

    Lecture XII
    The Landau-Ginzburg/Calabi-Yau correspondence for the quintic threefold
    Time: 2020-07-10 17:00 Beijing time (12:00 Moscow time, 16:00 Novosibirsk time)
    Speaker: Prof. Guo Shuai, Department of Mathematics, School of Mathematical Sciences, Peking University
    Abstract: In this talk, we will first introduce the physical and mathematical versions of the Landau-Ginzburg/Calabi-Yau correspondence conjecture for the Calabi-Yau threefolds. Then we will explain our approach to prove this conjecture for the most simple Calabi-Yau threefold - the quintic threefold. This is a work in progress joint with Felix Janda and Yongbin Ruan. 

     

    Video:

    https://disk.pku.edu.cn:443/link/F54316E400E92E93AEA5D31C6DE880B2
    Valid Until: 2025-08-31 23:59

     

    Lecture XI

    Kostant, Steinberg, and the Stokes matrices of thett*-Toda equations

    Time: 2020-07-03 17:00 Beijing time (12:00 Moscow time, 16:00 Novosibirsk time)

    Speaker: Ho Nan-Kuo (Department of Mathematics, NTHU)

    Abstract: 

    We propose a Lie-theoretic definition of the tt*-Toda equations for anycomplex simple Lie algebra, based on the concept of topological-antitopological fusion which was introduced by Cecotti and Vafa. Our main result concerns the Stokes dataof a certain meromorphic connection, whose isomonodromic deformations are controlled by these equations. First, by exploiting a framework introduced by Boalch,we show that this data has a remarkable structure. It can be described using Kostant’stheory of Cartan subalgebras in apposition and Steinberg’s theory of conjugacy classesof regular elements, and it can be visualized on the Coxeter Plane. Second, we compute canonical Stokes data for a certain family of solutions of the tt*-Toda equationsin terms of their asymptotics.This is joint work with Martin Guest.

     

    Video: https://disk.pku.edu.cn:443/link/F3047C92A5299C446000061029BB1915

    Valid Until: 2025-08-31 23:59

     

    Lecture X

    Derived categories and Chow theory of Quot-schemes of Grassmannian type.

    Time: 2020-06-26 17:00 Beijing time (12:00 Moscow time, 16:00 Novosibirsk time)

    Speaker: Jiang Qingyuan (University of Edinburgh)

    Abstract: 

    Quot-schemes of Grassmannian type naturally arise as resolutions of degeneracy loci of maps between vector bundles over a scheme. In this talk we will discuss the relationships of the derived categories and Chow groups among these Quot-Schemes. This provides a unified way to understand many known formulae such as blowup formula, Cayley's trick, projectivization formula, Grassmannian bundles formula and formula for Grassmannain type flops and flips, as well as provide new phenomena such as virtual flips. We will also discuss applications to the study of moduli of linear series on curves, blowup of determinantal ideals, generalized nested Hilbert schemes of points on surfaces, and Brill--Noether problem for moduli of stable objects in K3 categories.

     

    Download Slides: https://disk.pku.edu.cn:443/link/E89CA08FEABF9D84D2569EE6B5529037
    Valid Until: 2025-07-31 23:59

     

    Lecture IX

    Mirror Symmetry for quasi-smooth Calabi-Yau hypersurfaces in weighted projective spaces 

    Time: 2020-06-19 17:00 Beijing time (12:00 Moscow time, 16:00 Novosibirsk time)

    Speaker: Victor Batyrev (University of Tubingen)

    Abstract: 

    In the talk based on my joint work with K.Schaller I will explain a general combinatorial framework for constructing mirrors of d-dimensional Calabi-Yau orbifolds defined by arbitrary non-degenerate weighted homogeneous polynomials W. Our mirror construction generalizes the one of Berglund-Huebsch-Krawitz in the case of invertible polynomials W. 

     

    Lecture VIII
    Gamma conjecture I for del Pezzo surfaces 
    Time: 2020-06-12 17:00 Beijing time (12:00 Moscow time, 16:00 Novosibirsk time)
    Speaker: Li Changzheng (Sun Yat-Sen University)
    Abstract: 
    Gamma conjectures were proposed to relate the quantum cohomology of a Fano manifold and the Gamma class interms of differential equations. Gamma conjectures consist of the underlying conjecture O and Gamma conjecture I and II. In this talk, I will first introduce the conjecture O for del Pezzo surfaces, then I will talk about the Gamma conjecture I for del Pezzo surfaces. This talk is based on a joint work with Jianxun Hu, Hua-Zhong Ke and Tuo Yang.

     

    Lecture VII

    Open r-spin intersection theory and the open analog of Witten’s r-spin conjecture.

    Speaker: Ran Tessler (Weizmann Institute of Science)

    Time:2020-06-05 17:00 Beijing time (12:00 Moscow time, 16:00 Novosibirsk time)

    Abstract:

    We will describe the moduli of r-spin disks and its associated vector bundles. We will then define intersection theory on the moduli of r-spin disks, and relate its potential to the r-KdV hierarchy. We will also make a high genus conjecture, generalizing Witten’s r-spin conjecture to the open setting. Based on joint works with A. Buryak and E. Clader.

    Video: https://disk.pku.edu.cn:443/link/28299E6CBADB355CE99D8E869E298CA7 

    Valid Until: 2026-10-01 23:59

     

    Lecture VI

    Quantum integrable systems and Symplectic Field Theory

    Speaker: Paolo Rossi (University of Padua, Italy)

    Time:2020-05-29 17:00 Beijing time (12:00 Moscow time, 16:00 Novosibirsk time)

    Abstract:

    Eliashberg, Givental and Hofer's Symplectic Field Theory is a large project aiming to subsume under a unified topological field theoretical approach several techniques from symplectic topology (Floer homology, contact homology and more). Similarly to what happens in Gromov-Witten theory, at its core we find holomorphic curve counting. The general target manifold considered in SFT is a symplectic cobordism between contact manifolds (or more generally between stable Hamiltonian structures). When the cobordism is just a cylinder from a contact manifold to itself, the corresponding operator in SFT is, in particular, a collection of mutually commuting quantum Hamiltonians in a Weyl algebra. 

    These ideas were behind the introduction, by Buryak and myself, of the quantum double ramification hierarchy, which can be seen as a transposition of the SFT  approach to the algebraic category together with several enhancements. I will introduce the double ramification hierarchy with an eye to its origins in Symplectic FIeld Theory and showcase some examples that we were able to fully compute.

    Video: https://disk.pku.edu.cn:443/link/A2FC001A09694D73B18E709AD0CB2BA5 

    Valid Until: 2026-10-01 23:59

     

    Lecture V

    Geometrization, integrability and knots.

    Speaker: A.P. Veselov  (Loughborough, UK and Moscow, Russia)

    Time:2020-05-22 17:30 Beijing time (16:30 Novosibirsk time)

    Abstract:

    I will discuss the coexistence of the chaos and Liouville integrability in relation with Thurston’s geometrization programme, using as the main example the geodesic flows on the 3-folds with SL(2,R)-geometry. 

    A particular case of such manifold SL(2,R)/SL(2,Z) is known after Milnor and Quillen to be topologically equivalent to the complement of the trefoil knot in 3-sphere. I will explain that the remarkable results of Ghys about modular and Lorenz knots can be naturally extended to the integrable region, where these knots are replaced by the cable knots of trefoil.

    The talk is based on a joint work with Alexey Bolsinov and Yiru Ye. 

     

    Video: https://cloud.mail.ru/stock/kv7Re1gF8pM3Jk2us6F9CNS8 

    or https://disk.pku.edu.cn:443/link/9E7818092043A5BE2BBC442433970C73 

    Valid Until: 2026-10-01 23:59

     

    Lecture IV

    Spaces with indefinite metrics and the spectral theory of singular Schrodinger operators

    Time: 2020-05-15 17:30

    Speaker: P.G. Grinevich (Steklov Mathematical Institute)

    Abstract: The famous Korteweg- de Vries (KdV) equation admits important singular solutions, but only very special singularities are compatible  with the KdV dynamics. We show, that for the Schrodinger operators from the KdV Lax pair with such special singularities the spectral theory can be naturally formulated in terms of pseudo-Hilbert spaces with indefinite metrics. IN particular, the number of negative squares in this metric  provides a new conservation law for such solutions. The talk is based on joint works with S.P. Novikov.

     

    Video: https://disk.pku.edu.cn:443/link/349ADE069333C744171CA06241D030A1 

    Valid Until: 2026-10-01 23:59

     

    Lecture III

    Topological recursion and KP tau-functions

    Time: 2020-05-08 17:00

    Speaker:  Sergey Shadrin (University of Amsterdam, Netherlands)

    Abstract:

    We would like to recall some basic definitions of the so-called Chekhov-Eynard-Orantin theory of topological recursion. Originally it was developed to compute the cumulants for a class of matrix model, but since then it has evolved to one of the key tools on the edge between combinatorics and algebraic geometry that helped to resolve some famous open conjectures. In particular, it has appeared that the topological recursion can be proved for a large class of KP tau-functions from the Orlov-Scherbin family. We'll explain what extra properties of these tau-functions can be derived this way.An example of a direct application of this circle of ideas is a recent proof (our joint work with Dunin-Barkowski, Kramer, and Popolitov) of the so-called r-ELSV formula conjectured by Zvonkine in mid 2000's. We'll try to explain that formula, and, if time permits, sketch the main steps of the proof.


    Video: https://disk.pku.edu.cn:443/link/AA7F132E5B69726DED4743D0B57368C2 

    Valid Until: 2026-10-01 23:59


    Lecture II

    Stokes phenomenon, reflection equations and Frobenius manifolds

    Time: 2020-05-01 17:00

    Speaker:  Xu Xiaomeng (Peking university)

    Abstract: Reflection equations, arsing from quantum integrable systems with boundary conditions, are the analog of Yang-Baxter equations on a half line. Geometrically, they encode the cylinder braid groups. Algebraically they are closely related to quantum homogenous spaces. In this talk, we first give an introduction to the Stokes phenomenon of an ODE with irregular singularities. We then prove that the Stokes matrices of cyclotomic Knizhnik–Zamolodchikov (KZ) equations give universal solutions to reflection equations. As an application, we show that the isomonodromy deformation of the KZ equations is a quantization of the Dubrovin connections of Frobenius manifolds from various aspects.

     

    Slides Download: https://disk.pku.edu.cn:443/link/4AF416B93C5C1656C693CAA784A33B0C 

    Valid Until: 2026-10-01 23:59

     

    Lecture I

    Flat F-manifolds in higher genus and integrable hierarchies

    Time: 2020-04-24 17:00

    Speaker: Alexandr Buryak (National Research University Higher School of Economics)

    Abstract: By Dubrovin--Zhang theory, there is a deep relation between dispersive deformations of the hierarchies of hydrodynamic type corresponding to Frobenius manifolds and the geometry of the moduli spaces of stable algebraic curves. I will talk about a generalization of some of the results of the Dubrovin--Zhang theory for flat F-manifolds, which we obtained in joint works with A. Arsie, P. Lorenzoni and P. Rossi.



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    Organization Committee 

    ◆ Huijun FAN 

    ◆ A.E. MIRONOV

    ◆ I.A. TAIMANOV

    ◆ Youjin ZHANG

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