Program
Geometry and Physics Seminar(GPS)
Student No.:50
Time:Tuesday 9:00-12:00, 2015-9-15~2015-12-22
Instructor:Si Li, Zhengyu Zong  
Place:Conference Room 3, Floor 2, Jin Chun Yuan West Building
Starting Date:2015-9-15
Ending Date:2015-12-22

 

 

Date: 2015-12-18

 

 

Time: 13:00-14:00

 

 

Location: Jingzhai 304

 

 

Speaker: Dario Rosa (Seoul National University)

 

 

Title: New supersymmetric localizations from topological gravity

 

 

Abstract: We describe a novel cohomological approach to identify supersymmetric localizing backgrounds which starts from topological gravity coupled to topological gauge theories. We apply this topological point of view to N=(2,2) supersymmetric gauge theories in two dimensions, where we found a whole new and unexplored class of localizing supersymmetric backgrounds, which are characterized by non-vanishing fluxes for both the graviphotons of the supergravity multiplet.

 

 

Date: 2015-12-10

 

 

Time: 10:30-12:00

 

 

Speaker: Dan Xie (Harvard)

 

 

Title: Four dimensional N=2 SCFT and singularity theory

 

 

 

Abstract: One can define 4d N=2 SCFT by putting type IIB string theory on a Gorentein rational isolated three-fold singularity with a C^* action. I will describe the classification of theories by using the classification of singularity. Various interesting physical quantities such as the chiral spectrum, central charges, BPS spectrum, Seiberg-Witten solution, etc are given by the property associated with the singularity. This is a joint work with S. T. Yau.

 

 

 

 

 

 

Date: 2015-12-1

 

Time: 9:00-10:30

 

Speaker: Tang xinxing (PKU)

 

Title: A brief introduction of the KP hierarchy

 

Abstract: In this talk, first I will introduce the KP hierarchy from the pointview of Lax representation and talk a little about the dispersionless case. The followings are the wave function and the tau function, and I will give the description of the KP hierarchy in terms of bilinear identity. Finally introduce the vertex operator.

 

Reference:

 

1.      L. A. Dickey, "Soliton Equations and Hamiltonian Systems" (World Scientific, Singa- pore, 1991)

 

2.      KANEHISA TAKASAKI, TAKASHI TAKEBE. Integrable Hierarchies and Dispersionless Limit[J]. Reviews in Mathematical Physics, 1994, 7(5):743-808.

 

 

 

Date: 2015-11-24

 

Time: 9:00-10:30

 

Speaker: Yue Feng

 

Title: Homological mirror symmetry in higher categories operad duality

 

Abstract: In this talk, firstly I'll introduce Sheridan's construction of homological mirror symmetry of Calabi-Yau hypersurface, the thick-thin flip and wrapped Fukaya category of local syetems as Fukaya-Seidel category of orthogonal Lagrangian disks. Then I'll discuss some higher categorical constructions and Tamarkin's operad duality. Fianlly, I'll tell you how these stories related to Gaiotto-Moore-Witten's picture.

 

Reference:

 

1.      N. Sheridan Invent. Math. (2015) 199 1-186 2. V. Dolgushev, D. Tamarkin, B. Tsygan arXiv: 0904.2753  

 

and work in progress

 

 

Time: 10:30-12:00

 

Speaker: Weiqiang He (YMSC)

 

Title: Simple singularities and integrable hierarchy

 

Abstract: A. Givental gives a construction of the total descendent potential to a general semi-simple Frobenious manifold. This reading presentation is about the work of A. Givental and T. Milanov. They apply Givental's general theory to a special case: K. Saito's Frobenious structure on the miniversal deformation of ADE type singularities. They find that the total descendent potentials satisfy some interesting hierarchies: nKdV and Kac-Wakimoto hierarchies.

 

Reference:

A. Givental: A_{n-1} singularities and nKdV hierarchies

 

A. Givental, T. Milanov: Simple singularities and integrable hierarchies

 

 

Date: 2015-11-11

 

Time: 16:00-17:00

 

Place: Jing Zhai 304

 

Speaker: Hu Shan, (ITP)

 

Title: Group manifold approach to higher spin theory

 

Abstract: We consider the group manifold approach to higher spin theory. The deformed local higher spin transformation is realized as the diffeomorphism transformation on group manifold. With the suitable rheonomy condition and the torsion constraint imposed, unfolded equation can be obtained from the Bianchi identity, by solving which, fields on group manifold are determined by the 0-forms at one point, or equivalently, by higher spin fields in a AdS4 submanifold. 4d equations of motion are obtained by plugging the rheonomy condition into the Bianchi identity. The proper rheonomy condition allowing for the maximum on-shell degrees of freedom is given by Vasiliev equation. We also discuss the theory with the global higher spin symmetry, which is in parallel with the WZ model in supersymmetry.

 

(This week is joint with Ads seminar)

 

 

Date: 2015-11-3

 

Time: 9:00-10:30

 

Speaker: Yifan Li (YMSC)

 

Title: Landau-Ginzburg theory and tt^* geometry.

 

Abstract: This is a series of reading presentation. I will start with the LG side of the LG/CY correspondence and talk about the deformation theory of the Schrodinger operator, the Hodge theory in the noncompact case and some contents in tt^* geometry.

 

References: (1) H. Fan: Schrodinger equations, deformation theory and tt^*-geometry.

 

(2) Chiodo, Ruan: LG/CY correspondence: the sate space isomorphism

 

 

Time: 10:30-12:00 

 

(This week is joint with AG seminar. This is the first of the talk series. The second talk is on Nov 4, 15:30-17:00 at AG seminar. See http://msc.tsinghua.edu.cn/sjcontent.asp?id=738)

 

Speaker: Zhe Sun (YMSC)

 

Title: Introduction to Higher Teichmüller theory

 

Abstract:

 

Higher Teichmüller theory is the study of a specific component of the space of representations of the fundamental group of a surface of genus g in PSL(n,R). Teichmüller theory corresponds to n=2. In this talk, I willpresent some nice properties and conjectures of higher Teichmüller theory arising from different aspects---differential geometry, dynamic system, cluster algebra, algebraic geometry after N. Hitchin, F. Labourie, V. Fock, A. Goncharov etc. After that, I will talk about what I am reading now---how canonical base conjecture related to homological mirror symmetry after A. Goncharov and Linhui Shen.

 

References:

 

N. Hitchin, Lie groups and Teichmüller space

 

R. Wentworth, Higgs bundles and local systems on Riemann surfaces

 

F. Labourie, Anosov Flows, Surface Groups and Curves in Projective Space

 

F. Labourie, Cross Ratios, Surface Groups, SL (n,R) and Diffeomorphisms of the Circle

 

V. Fock, A. Goncharov, Moduli spaces of local systems and higher Teichmuller theory

 

A. Goncharov and Linhui Shen, Geometry of canonical bases and mirror symmetry.

  

 

Date: 2015-10-27

 

Time: 9:00-12:00

 

Speaker: Daniele Valeri (YMSC)

 

Title: Classical W-algebras and generalized Drinfeld-Sokolov hierarchies

Abstract: In this talk I plan to review some results about the construction of classical W-algebras within the framework of Poisson vertex algebras and to give some applications to the study of integrability of the generalized Drinfeld-Sokolov hierarchies.

 
There will be two talks:
 

9:00-10:30 will be introductory and background for students. 10:30-12:00 will be seminar talk.

 

 

Date: 2015-10-20

 

Time: 9:00-10:30

 

Speaker: Yifan Li (YMSC)

 

Title: Landau-Ginzburg theory and tt^* geometry.

 

Abstract: This is a series of reading presentation. I will start with the LG side of the LG/CY correspondence and talk about the deformation theory of the Schrodinger operator, the Hodge theory in the noncompact case and some contents in tt^* geometry.

 

References: (1) H. Fan: Schrodinger equations, deformation theory and tt^*-geometry.

(2) Chiodo, Ruan: LG/CY correspondence: the sate space isomorphism

 

Time: 10:30-12:00

 

Speaker: Junbao Wu (IHEP)

 

Title: Recent Progress on BPS Wilson Loops in 3d Chern-Simons-Matter theories

 

Abstract: Three-dimensional super Chern-Simons theories are very interesting and important. BPS Wilson loops in such theories include Gaiotto-Yin (GY) type and Drukker-Trancanelli (DT) type. Fermionic fields appear in the second type of BPS Wilson loops. Previously people only found such loop operators in 3d N=5, 6 super Chern-Simons theories. We recently constructed the half-BPS Wilson loops in 3d N=4 theory which can be obtained from orbifolding N=6 theory. Other recent results will be reported as well.

Relation between 3d super Chern-Simons theories and topological string theories will be discussed briefly.

 

This talk is mainly based on joint work with Hao Ouyang and Jia-ju Zhang. Previous related work done with Bin Chen and Meng-Qi Zhu will also be mentioned.

 

 

Date: 2015-10-13: No seminar this week

 

Date: 2015-9-15

 

Time: 9:00-10:30

 

Speaker: Yifan Li (YMSC)

 

Title: Landau-Ginzburg theory and tt^* geometry.

 

Abstract: This is a series of reading presentation. I will start with the LG side of the LG/CY correspondence and talk about the deformation theory of the Schrodinger operator, the Hodge theory in the noncompact case and some contents in tt^* geometry.

 

References: (1) H. Fan: Schrodinger equations, deformation theory and tt^*-geometry.

(2) Chiodo, Ruan: LG/CY correspondence: the sate space isomorphism.
 

 

Time: 10:30-12:00

 

Speaker: Jingyue Chen (YMSC)

 

Title: Existence and rigidity of Calabi-Yau bundles

 

Abstract: Lian and Yau developed a global Poincare residue formula to study period integrals of families of complex manifolds, and used it to construct canonical PDE systems for period integrals. The notion of a CY bundle is a crucial ingredient in their construction. The idea is to lift line bundles from a manifold X to some larger space (a CY bundle) over X. A question was therefore raised as to whether there exists such a bundle that supports the lifting of all line bundles from X simultaneously. We give partial solutions to this problem. We also discuss the classification of CY bundles. This is a joint work with Bong H. Lian.

 

References: (1) J.Chen, B.Lian, CY Principal Bundles over Compact Kähler Manifolds.

(2) B.Lian, S.T. Yau, Period integrals of CY and general type complete intersections.
 

 

Date: 2015-9-22

 

Time: 9:00-10:30

 

Speaker: Weiqiang He (YMSC)

 

Title: Simple singularities and integrable hierarchy

 

Abstract: A. Givental gives a construction of the total descendent potential to a general semi-simple Frobenious manifold. This reading presentation is about the work of A. Givental and T. Milanov. They apply Givental's general theory to a special case: K. Saito's Frobenious structure on the miniversal deformation of ADE type singularities. They find that the total descendent potentials satisfy some interesting hierarchies: nKdV and Kac-Wakimoto hierarchies.

 

Reference: A. Givental: A_{n-1} singularities and nKdV hierarchies

                    A. Givental, T. Milanov: Simple singularities and integrable hierarchies 
 

 

Time: 10:30-12:00

 

Speaker: Video Club (Online lecture by N. Nekrasov)

 

Title: Introduction to quiver gauge theory. 

 

Abstract: This is a video watching and discussion based on online lecture. We discuss how quiver arises in physics from D-brane geometry and supersymmetric Yang-Mills theory. 

 

 

Date: 2015-9-29

 

Time: 9:00-10:30

 

Speaker: Weiqiang He (YMSC)

 

Title: Simple singularities and integrable hierarchy

 

Abstract: A. Givental gives a construction of the total descendent potential to a general semi-simple Frobenious manifold. This reading presentation is about the work of A. Givental and T. Milanov. They apply Givental's general theory to a special case: K. Saito's Frobenious structure on the miniversal deformation of ADE type singularities. They find that the total descendent potentials satisfy some interesting hierarchies: nKdV and Kac-Wakimoto hierarchies.

 

Reference: A. Givental: A_{n-1} singularities and nKdV hierarchies A. Givental, T. Milanov: Simple singularities and integrable hierarchies

 

Time: 10:30-12:00

 

Speaker: Yifan Li (YMSC)

 

Title: Landau-Ginzburg theory and tt^* geometry.

Abstract: This is a series of reading presentation. I will start with the LG side of the LG/CY correspondence and talk about the deformation theory of the Schrodinger operator, the Hodge theory in the noncompact case and some contents in tt^* geometry.

 

References: (1) H. Fan: Schrodinger equations, deformation theory and tt^*-geometry.

(2) Chiodo, Ruan: LG/CY correspondence: the sate space isomorphism