Morningside Center of Mathematics

Chinese Academy of Sciences

The 7th International Congress of Chinese Mathematicians

ICCM2016 will be held from Aug 6 - 11, 2016 in Beijing. It is jointly hosted by AMSS and MCM. It is expected that about 1500 participants will attend the ICCM 2016.

2016 WORKSHOP ON THE p-ADIC LANGLANDS CORRESPONDENCE

The goal of this workshop is, in the first part, to understand the recent work of Dospinescu-Le Bras and Pan Lue on the geometric realisation of the p-adic local Langlands correspondence for GL2(Qp) and, in the second part, to understand the work of Scholze on the p-adic cohomology of the Lubin-Tate tower and its application to the p-adic Langlands program.

2016 Seminar on Hamiltonian Dynamics

It is based on latest developments in dynamical instability of Hamiltonian systems, viscosity solutions of Hamilton-Jacobi equations and other related fields located at the intersection of dynamical system and calculus of variation. The seminar is hosted by Prof. Cheng Chongqing from Nanjing University and will last from January 7, 2016 to January 30, 2016.

Generalised Kato classes and applications

This lecture series will be devoted to various arithmetic applications of the eponymous cohomology classes of the title, to such questions as the equivariant Birch and Swinnerton-Dyer conjecture, Perrin-Riou's conjecture relating Beilinson elements to rational points on elliptic curves, the theory of Stark-Heegner points, and the construction of explicit Selmer classes on elliptic curves in settings where the underlying Selmer group has rank two.

Nearby cycles over general bases and Thom-Sebastiani theorems

For germs of holomorphic functions $f : \mathbf{C}^{m+1} \to \mathbf{C}$, $g : \mathbf{C}^{n+1} \to \mathbf{C}$ having an isolated critical point at 0 with value 0, the classical Thom-Sebastiani theorem describes the vanishing cycles group $\Phi^{m+n+1}(f \oplus g)$ (and its monodromy) as a tensor product $\Phi^m(f) \otimes \Phi^n(g)$, where $(f \oplus g)(x,y) = f(x) + g(y), x = (x_0,...,x_m), y = (y_0,...,y_n)$. I will discuss algebraic variants and generalizations of this result over fields of any characteristic, where the tensor product is replaced by a certain local convolution product, as suggested by Deligne. The main theorem is a Künneth formula for $R\Psi$ in the framework of Deligne's theory of nearby cycles over general bases.