## Welcome to GAP seminar

This seminar aims at filling up the gap between graduate level math and research math, and enlarging the scope of graduate students as well as more advanced researchers. In each talk, the speaker will focus on a currently active research topic. He/she will spend one hour or so to introduce the background of the topic, including basic conceptions/examples, important known results and major problems etc. The last part of the talk will usually be more technical and is related to the speaker's own work. The subjects of future talks are mainly chosen from geometry(G), algebra, analysis(A), and mathematical physics(P) etc.

## Upcoming Talks

## Past Talks

Archive of GAP Seminar: Fall 2013 | Spring 2014 | Fall 2014 | Spring 2015 | Fall 2015

Date: 5/20, 3:30-5:00

Speaker: 陈伊凡（北京航空航天大学）

Title: On canonically polarized Gorenstein 3-folds satisfying the Noether equality

Abstract: I will talk about the Noether type inequalities for complex projective surfaces and 3-folds of general type.I will introduce the recent work of Meng Chen and Jungkai Chen on the Noether inequality for Gorenstein minimal 3-folds.Then I talk about the joint work with Yong Hu on the classification of canonically polarized Gorenstein 3-folds satisfying the Noether equality.

Date: 5/13, 4:00-5:30

Speaker: 余君（北京国际数学中心）

Title: Construction of isospectral manifolds with different topologies

Abstract: A famous question in differential geometry asked by Marc Kac: "Can one hear the shape of a drum?" It concerns the comparison of Laplace spectra on different Riemannian manifolds. By studying particular kind of manifolds like flat tori and local symmetric spaces, and with Sunada's method and torus action method, there are plenty of examples of isospectral manifolds with the same or different local geometry. I will give a brief account of some history of this subject and the first examples of isospectral manifolds which are simply connected but not homotopic, due to Jinpeng An, Jiu-Kang Yu and the speaker.

Date: 5/6, 4:00-5:30

Speaker: 张先得（中国科学技术大学）

Title: Introduction to combinatorial designs theory and its applications in coding theory

Abstract: Combinatorial design theory is one of the important branches of Combinatorics, where we study the discrete objects with high balanced properties and nice structures according to specified rules. The rapid advances in design theory can be attributed in large degree to its impetus from applications in coding theory and communications and its continued deep interactions with graph theory, geometry, algebra, and number theory. In this talk, I will introduce some basic facts about design theory,including pairwise balanced designs, t-designs, Latin squares and their applications in coding theory. Some interesting open problems will also be mentioned.

Date: 4/29, 4:00-5:30

Speaker: 谈强（武汉大学）

Title: J-anti-invariant cohomology on almost Kaehler manifolds

Abstract: In this talk, we study the J-anti-cohomology on almost Kaehler manifolds. We introduce the generalized Lejmi operator on closed almost Kaehler 2n-manifold. By studying the properties of this operator, we get some results about J's pureness and fullness. Additionally, we study the deformations of almost Kaehler structures on closed four-manifolds.

Date: 4/19, 3:00-4:30

Speaker: 王芝兰（中科院数学所）

Title: A brief introduction to moduli spaces and enumerative problems

Abstract: Various moduli spaces appear in order to solve problems in enumerative algebraic geometry. We begin with the definition and basic properties of moduli spaces. Then we will give some examples of moduli spaces, including moduli space of stable curves and Hilbert schemes, and illustrate the corresponding enumerative problems.

Date: 4/15, 4:00-5:30

Speaker: 夏利猛 （江苏大学理学院）

Title: On the center of the quantized enveloping algebra of a semisimple Lie algebra

Abstract: Let g be a complex simple finite dimensional Lie algebra and Uq(g) the quantized enveloping algebra in Jantzen's sense with q being generic. As a continuous work in [LWP, WWL], we prove that the center Z(Uq(g)) of the quantum group Uq(g) is isomorphic to a monoid algebra, and Z(Uq(g)) is a polynomial algebra if and only if g is of type A1, Bn, Cn, D2k+2, E7, E8, F4 and G2. It turns out that when g is of type Dn with n odd then Z(Uq(g)) is isomorphic to a quotient algebra of polynomial algebra with n+1 variables and one relation, and while when g is of type E6 then Z(Uq(g)) is isomorphic to a quotient algebra of polynomial algebra with 14 variables and eight relations.

Date: 4/8, 4:00-5:30

Speaker: 罗栗（华东师范大学）

Title: Schur-Weyl duality and coideals of quantum groups

Abstract: The classical Schur-Weyl duality shows a double centralizer property between general linear groups and symmetric groups. In this talk, we will give a brief survey about this duality and its generalizations. Especially, we will introduce some coideals of (affine) quantum groups, which admit Schur-Weyl duality with (affine) Hecke algebras. These coideals can be realized by a geometric approach due to Beilinson-Lusztig-MacPherson.

Date: 4/1, 4:00-5:30

Speaker: 耿俊（兰州大学）

Title: Elliptic Problems and Periodic Homogenization on Non-smooth Domains

Abstract: In this talk I will introduce some recent results for boundary value problem of elliptic equations on non-smooth domains. Also, I will discuss recent progress on uniform estimates for elliptic/parabolic homogenization.

Date: 3/25, 2:30-4:00

Speaker: 刘会（中国科学技术大学）

Title: Closed orbits in Hamiltonian dynamics via index theory for symplectic paths

Abstract: In 1984-1990, C. Conley, E. Zehnder and Y. Long introduced the index theory of symplectic paths in Sp(2), and then in 1990's, Y. Long established the index theory of symplectic paths in Sp(2n) and its iteration theory which he and his coworkers successfully used to study the problem of multiplicity and stability of closed orbits in Hamiltonian dynamics. In this talk, I will introduce this index iteration theory and its applications to the problem of periodic orbits in Hamiltonian systems, including closed characteristics on given energyhypersurfaces and closed geodesics on Finsler manifolds.

Date: 3/18, 4:00-5:30

Speaker: 朱绪鼎（浙江师范大学）

Title: Online list colouring of graphs

Abstract: List colouring of graphs is a resource distribution problem: The colours are resources, and vertices of a graph represent consumer of these resources, and the lists gives the information which colours (resources) are available to each vertex (consumer). The edges of the graph represents conflicts between consumers sharing a same resource. List colouring of graphs deals with the problem of how to assign colours to vertices that avoids the conflicts. Online list colouring of graphs deals with the problem when the availability of the colours to the vertices is revealed online and the distribution needs to be given online. In this talk, I shall survey some results, open problems in this area and explain some methods used in the study of online list colouring of graphs.

Date: 3/11, 4:00-5:30

Speaker: 生云鹤（吉林大学）

Title: Introduction to nonlinear Lie theory and higher structures

Abstract: Lie algebroids are generalizations of Lie algebras and tangent bundles. They are infinitesimal objects of Lie groupoids. We call corresponding theory nonlinear Lie theory. Higher structures are mainly about Lie 2-algebras and Lie 2-groups. They are categorification of Lie algebras and Lie groups. In this talk, I will introduce some basic facts about Lie algebroids. In particular, I will talk about a Lie bialgebroid, whose double is not a Lie algebroid anymore (this is different from the case of Lie algebras), but a so called Courant algebroid. Then higher structures show up naturally. On the other hand, from graded geometry point of view, a Courant algebroid corresponds to a degree 2 symplectic NQ manifolds. Finally, I will talk about recent work on degree 3 symplectic NQ manifolds. A degree 2 symplectic NQ manifold gives rise to an LWX 2-algebroid (named after Liu-Weinstein-Xu), which is a categorified Courant algebroid.

Date: 3/4, 4:00-5:30

Speaker: LIN Yi（Georgia Southern University）

Title: Symplectic Harmonic theory and the Federer-Fleming deformation theorem

Abstract: Symplectic Harmonic theory was initiated by Ehresmann and Libermann in 1940's, and was rediscoverd by Brylinski in late 1980's. More recently, Bahramgiri showed in his MIT thesis that symplectic Harmonic representatives of Thom classes exhibited some interesting global feature of symplectic geometry. In this talk, we will discuss a new approach to symplectic Harmonic theory via geometric measure theory, and explain how the measure theoretic method leads to a complete solution to an open question asked by V. Guillemin concerning the symplectic Harmonic representatives of Thom classes. This talk is based on a recent work of the speaker.