学术报告
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Sparse Grid Meets Random Hashing: Learning High Dimensional Functions of Few ...We investigate the optimal sample complexity of recovering a general high dimensional smooth and sparse function based on point queries. Our result provides a precise characterization of the potential loss in information when restricting to point queries as opposed to the more general linear queries., as well as the benefit of adaption. In addition, we also developed a general framework for function approximation to mitigate the curse of dimensionality that can also be easily adapted to incorporate further structure such as lower order interactions, leading to sample complexities better than those obtained earlier in the literature.Professor Ming YUAN(美国哥伦比亚大学)致远楼101室2019年1月14日(周一)下午16:00开始
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Asymptotic Analysis for Yamabe EquationsThe Yamabe equation is an important class of equations in the geometric analysis and nonlinear elliptic equations. It arises from the conformal geometry and describes the scalar curvatures of the conformal metrics. In this talk, we study asymptotic behaviors of solutions of the Yamabe equation with isolated singularities and discuss some important results by Caffarelli, Schoen, Spruck, Korevaar, Mazzeo and Pacard. We will also present some recent results that solutions near isolated singularities are well approximated by series that decay at discreet orders.韩青 教授 (美国Notre Dame大学、北京大学)致远楼101室2019年1月11日16:00-17:00
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Picard Group of the Moduli Space of SheavesIn this talk, I will review a few existing results about Picard groups of moduli spaces of sheaves over curves, as well as the rank 2 case over surfaces. Based on the related methods, I will discuss how to obtain similar results for high rank cases over surfaces. This is work in progress, conducted jointly with Jun Li, Howard Nuer, Xiaolei Zhao and Yi Xie.林胤榜 博士 (清华大学)致远楼101室2019年1月9日 10:00-11:00
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Subsets Counting and Borwein ConjectureIn this talk, I will first review a subsets- counting technique, and then present some applications in number theory and coding theory, with a focus on a partial result on the Borwein conjecture. This is based on joint work with Daqing Wan.李吉有 教授致远楼103室2018年12月28日16:50-17:35
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密码货币体系的数学理论我们将给出密码货币体系中数字权益歧视性的定义,并分析歧视性与安全性、歧视性与效率之间的关系,并尽可能详细介绍相关的数学理论。刘春雷 教授致远楼103室2018年12月28日15:55-16:40
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P-Adic Theory of Exponential SumsExponential sums over finite fields play a fundamental role in number theory, arithmetic geometry and their applica- tions. This talk presents an expository introduction to the p-adic aspects of this subject. Various classical examp- les will be given to illustrate the general theory.万大庆 教授致远楼103室2018年12月28日15:00-15:45
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The Landau-Siegel Zero Problem with Application in Number Theory致远楼108室
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Slim Cyclotomic Q-Schur AlgebrasSlim cyclotomic q-Schur algebras were first introduced by Z. Lin and H. Rui, as centralizer subalgebras of Dipper-James-Mathas’ cyclotomic q-Schur algebras. Recent developments allow us to take the investigation to a new level. First, by using the matrix labelling of C. Mak for certain double cosets, we may construct an integral basis, simpler than the cellular basis, for these algebras. Second, the introduction of the Lusztig type form for quantum affine gl_n by Q. Fu and myself allows us to establish the cyclotomic Schur-Weyl duality at the integral level. Finally, when q is not a root of unity, we obtain a classification of irreducible representations. I will also mention some problems and conjectures. This is joint work with B. Deng and G. Yang.杜杰 教授致远楼108室2018年12月27日 16:00-17:00