Based on complex analysis, we prove a general (local, semi-global) existence of nonlinear partial differential systems with principle part of mixed higher order Cauchy-Riemann operators in dimension two, and then we apply the same framework set forth in dimension two and Newtonian potentials to proved a general (local, semi-global) existence of nonlinear partial differential systems with principle part of higher order Laplace operators in any dimensions

演讲人：楼元教授(Ohio State University, USA）题目： PDE Models from Population Genetics时间：2012年6月21日(星期四)下午2：00—5：00地点：数学系致远楼10

Witten genus is the loop space analogue of the Hirzebruch A-hat genus. On a string manifold, the Witten genus is a modular form and is the equivariant index of the Dirac operator on the free loop space. Hohn and Stolz conjectured that existence of a positive Ricci curvature metric on a string manifold implies the vanishing of the Witten genus. In this talk, we will present vanishing results for generalized Witten genus on complete intersections and describe a possible mod 2 extension of the Hohn-Stolz conjecture. The talk is based on the joint work with Qingtao Chen and Weiping Zhang

我将从Jacobian 簇(秩1向量丛模空间)的诞生和它上面的theta函数谈起，建立高秩的广义theta函数理论由A. Weil (1938)在一篇著名文章中提出。建立该理论的第一步是构造高秩向量丛的模空间，我将按历史的次序介绍 Narasimhan-Seshadri，Mumford 的工作。最后是由共形场论（Conformal Field Theory) 激发的模空间退化和广义theta函数分解定理

We introduce a commutative associative algebra structure on the direct sum Z of the centers of the Hecke algebras associated to the symmetric groups in n letters for all n. As a natural deformation of the classical construction of Frobenius, we establish an algebra isomorphism from Z to the ring of symmetric functions. This isomorphism gives rise to a characteristic map for Hecke algebras. This is joint work with Jinkui Wan (Beijing).

题目：BGG type resolutions for Lie superalgebras of classical type报告人：程舜仁 (台湾中央研究院研究员, 数学所副所长）时间：2012年6月21日（周四）16:30-17:30地点：数学系（致远楼）10

报告人：陈新富教授（University of Pittsburgh, USA）题目： Effects of white noise in multistable dynamics时间：2012年6月7日(星期四)下午3：30—4：30地点：数学系致远楼10

Test procedures for serial correlation of unknown form with wavelet methods are investigated in this paper. The new wavelet-based consistent tests are motivated using Fan's (1996) canonical multivariate normal hypothesis testing model. In our framework, the test statistics rely on empirical wavelet coefficients of a wavelet-based spectral density estimator. We advocate the choice of the simple Haar wavelet function, since evidence demonstrates that the choice of the wavelet function is not critical. Under the null hypothesis of no serial correlation, the asymptotic distribution of a vector of empirical wavelet coefficients is derived, which is the multivariate normal distribution in the limit. It is also shown that the wavelet coefficients are asymptotically uncorrelated. The proposed test statistics present the serious advantage to be completely data-driven or adaptive, avoiding the need to select any smoothing parameters.