主讲教师：王诗宬 人气：1178 更新时间: 2016年12月02日
11-30吴文俊讲座【王诗宬 院士】 摘要: I will give a survey talk on the recent results (joint with Derbez, Liu and Sun) around the title
主讲教师：Mark J.Ablowitz 人气：1064 更新时间: 2016年07月01日
The study of nonlinear waves is filled with many remarkable discoveries, one of them being `solitons’, found 50 years ago. Solitons motivated the development of the Inverse Scattering Transform (IST) method that leads to the solution of a class of nonlinear evolution equations. Some new equations solvable by IST and also dispersive shock waves in 2+1 dimensions will also be discussed.
主讲教师：郁星星 人气：999 更新时间: 2016年05月25日
A subdivision of a graph G is denoted T G. Mader conjectured that every C4-free graph with average degree d contains TK_l with l = ?(d). Koml′os and Szemer′edi reduced this problem to expanders and proved Mader’s conjecture for n-vertex expanders with average degree d < exp(log1/8 n). We show that Mader's conjecture is true for n-vertex expanders with average degree d < n3/10, which improves Koml′os and Szemer′edi’s bound to a polynomial bound. As a consequence, we show that every C4-free graph with average degree d contains a TK_l with l = ?(d/(log d) c ) for any c > 3/2. This is joint work with H. Huang and Y. Wang
主讲教师：彭岳建 人气：884 更新时间: 2016年05月25日
摘要：A number α ∈ [0,1) is jump for r-uniform graphs if there exists a constant c > 0 such that for any family F of r-uniform graphs, if the Turán density of F is greater than α, then the Tur´ an density of F is at least α + c. A fundamental result in extremal graph theory due to Erd¨ os and Stone implies that every number in [0,1) is a jump for r = 2. Erd¨ os also showed that every number in [0,r!r r ) is a jump for r ≥ 3. Furthermore, Frankl and R¨ odl showed the existence of non-jumps for r ≥ 3. But there are still a lot of unknowns regarding jumps or non-jumps for hypergraphs. We give a survey on the known result.
主讲教师：张继平 人气：1125 更新时间: 2016年05月25日
摘要：Adequacy of subgroups is very important in generalizations of Taylor-Wiles method for proving the automorphy of Galois representations. I will talk about some new progress on linear groups and the application related to adequacy of subgroups.
主讲教师：张晓东 人气：1055 更新时间: 2016年05月10日
Let G be a simple graph and L(G) = D(G)?A(G) be its Laplacian matrix,where A(G) and D(G) are the adjacency matrix and degree diagonal matrix.Then ?(G) = (L(G)+I n ) ?1 is called the doubly stochastic matrix of G. Merris in 1998 proposed two conjectures and two problems of the doubly stochastic matrix, which are revealed some relations among, algebraic connectivity, the entry of ?(G) and graph structure. In this talk, we survey some progress and results on these conjectures and problems of Merris. In addition, some new problems are included
主讲教师：许宝刚 人气：1222 更新时间: 2015年10月20日
吴文俊数学重点实验室组合图论系列讲座之六十一【许宝刚】 摘要： We show that if a graph $G$ has neither triangles nor quadrilaterals, and has no odd holes of lengthat least 7, then $chi(G)le 4$ and $chi(G)le 3$ if $G$ has radius at most $3$, and for each vertex$u$ of $G$, the set of vertices of the same distance to $u$ induces a bipartite subgraph. This answers some questions of Plummer and Zha. Joint work with Gexin Yu and Xiaoya Zha.
主讲教师：A.Losev等 人气：13130 更新时间: 2015年08月27日
［吴文俊数学重点实验室系列报告会］量子场论和弦论 吴文俊数学重点实验室系列报告会 Workshop on mathematics of quantum field theory and strings 地点：管研楼1611 时间：8月10日，8月11日，8月13日，8月14日 Day 1, August 10 (Theme: BV language for mathematicians and physicists) Morning: 9am – 12 am (3 hours) A. Losev: Introduction to BV Language ( 3 morning hours) Afternoon: 1pm – 6 pm (5 hours) A. Milekhin: Introduction to Wen’s work on topological order Xuexing Lu: Combinatorics approach of graph calculus Jue Le: On tensor category of Hochschildcohomology (17-00) Day 2, August 11 (Theme: Different languages for QFT, divergences (therefore configuration spaces), regular geometries) Morning: 9am – 12 am A. Losev: General picture of QFT (2 hours) Zhi Chen: Cohomology of configuration spaces and knot invariants (11-00) Afternoon: 1pm – 6 pm Bailin Song: Quantization of sigma models of generalized Calabi-Yaumanifold( 13-00) A. Milekhin: On Wen’s theory of topological order Losev-Kononov - higher knot space cohomology (optional) Informal discussions on noncommutativity approach - informally Day 4, August 13 (Theme: Interesting solutions to BV and different geometrical applications) Morning: 9am – 12 pm Qin Li: B-model from BV Minxin Huang: Topological strings (optional) Afternoon: 1pm – 6 pm Zhi Hu: Variation of Hodge structures of generalized Kahler manifold S. Hu: On Noncommutativity I Day 5, August 14 Morning: 9am – 12 pm Peng Liu: Knot invariants from the Yang-Yang functional Rosly-Polyubin: On conformal anomaly in SD Yang-Mills Afternoon: 1pm – 6 pm A. Losev: Higher Morse theory vs GMW P. Mnev: TBA S. Hu: On Noncommutativity II
主讲教师：Nefton Pali 人气：1938 更新时间: 2015年06月21日
TITLE 1： The Soliton-Ricci Flow with fixed volume form Abstract: We introduce a flow of Riemannian metrics over compact manifolds with formal limit at infinite time a shrinking Ricci soliton. We call this flow the Soliton-Ricci flow. It correspond to a Perelman's modified backward Ricci type flow with some special restriction conditions. The restriction conditions are motivated by convexity results for Perelman's W-functional over convex subsets inside adequate subspaces of Riemannian metrics. We show indeed that the Soliton-Ricci flow is generated by the gradient flow of the restriction of Perelman's W-functional over such subspaces. Assuming long time existence of the Soliton-Ricci flow we show exponentially fast convergence to a shrinking Ricci soliton provided that the Bakry-Emery-Ricci tensor is uniformly strictly positive with respect to the evolving metric TITLE 2：The Soliton-Ricci Flow with variable volume form Abstract: We introduce a flow of Riemannian metrics and positive volume forms over compact oriented manifolds whose formal limit is a shrinking Ricci soliton. The case of a fixed volume form has been considered in our previous work. We still call this new flow the Soliton-Ricci flow. It corresponds to a forward Ricci type flow up to a gauge transformation generated by the gradient of the density of the volumes. The new Soliton-Ricci flow exist for all times and represents the gradient flow of Perelman's W functional with respect to a pseudo-Riemannian structure over the space of metrics and normalized positive volume forms. We obtain an expression of the Hessian of the W functional with respect to such structure. Our expression shows the elliptic nature of this operator in directions orthogonal to the orbits obtained by the action of the group of diffeomorphism. In the case the initial data is K"ahler then the Soliton-Ricci flow preserves the K"ahler condition and the symplectic form. The space of tamed complex structures embeds naturally to the space of metrics and normalized positive volume forms via the Chern-Ricci map. Over such space the pseudo-Riemannian structure restricts to a Riemannian one. We perform a study of the sign of the restriction of the Hessian of the W functional over such space. This allows us to obtain a finite dimensional reduction, and thus the solution, of the well known problem of the stability of K"ahler-Ricci solitons.
主讲教师：刘公祥 人气：1825 更新时间: 2015年05月29日
吴文俊数学重点实验室代数学系列讲座之七十三 【刘公祥】报告题目：Quasi-Frobenius-Lusztig kernels 报告人：刘公祥 （南京大学）报告时间：2015年5月27日（星期三） 下午2:40--3:40 报告地点：东区管理科研楼1518