学术报告
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On A Conjecture of Toponogov on Complete Convex SurfacesIn 1995, Victor Andreevich Toponogov authored the following conjecture: “Every smooth strictly convex and complete classical surface of the type of a plane has an umbilic point, possibly at infinity“. In our talk, we will outline a proof, in collaboration with Brendan Guilfoyle. Namely we prove that (a) the Fredholm index of an associated Riemann Hilbert boundary problem for holomorphic discs is negative, which is an outcome of the regularity of the Cauchy-Riemann operator in presence of a symmetry group. Thereby, (b) no such solutions may exist for a generic perturbation of the boundary condition (these form a Banach manifold under the assumption that the Conjecture is incorrect).Wilhelm Klingenberg (Durham University)致远楼101室2019年3月25日 星期一 15:00-16:00
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τ-Tilting Finiteness of Two-Point Algebrasτ-tilting theory was introduced by Adachi, Iyama and Reiten, which completes the classical tilting theory from the viewpoint of mutation. They constructed a class of Λ modules named (support) τ-tilting modules, where Λ is a finite dimensional basic algebra over an algebraically closed field. We call Λ a τ-tilting finite algebra if there are finitely many isomorphism classes of basic τ-tilting Λ-modules. In this talk, we explain τ-tilting theory by discussing the τ-tilting finiteness of two-point algebras. More precisely ,we will show the poset structure on the set of support τ-tilting modules, the bijection between support τ-tilting modules and two-term silting complexes, etc,.Qi Wang (Osaka University)致远楼108室2019年3月19日 4:00pm —5:00pm
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九维流形上的切触结构在本报告中,我将给出九维流形上存在切触结构的充分必要条件。该结果是与墨尔本大学Diarmuid Crowley合作完成的。杨会军(河南大学)致远楼101室2019年3月15日16:15-17:15
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Scalar Curvature along the Ricci FlowHamilton's conjecture in the Ricci flow says that the scalar curvature of the finite-time Ricci flow blows up. In this talk under a curvature condition we give a proof of this conjecture.李逸(东南大学)致远楼101室2019年3月15日15:00-16:00
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Kahler Tensor Calculus and Invariant Differential Operators on Bounded Symmet...Kahler tensor calculus could be formulated in terms of directed graphs. We use to it explore the algebraic relations of invariant differential operators on bounded symmetric domains. I will also talk about the Feynman diagram formulas for the coefficients in the asymptotic expansion of Bergman and heat kernels.徐浩(浙江大学)致远楼101室2019年3月15日10:00-11:00
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Fundamental Classes in Motivic Homotopy TheoryWe develop a Fulton-style intersection theory in motivic homotopy categories, which is expressed in terms of the fundamental class in twisted bivariant groups. By introducing a general notion of Euler classes of vector bundles, we prove a formula of excess intersection in this framework; as an application, we deduce a motivic Gauss-Bonnet formula computing the Euler characteristic. This is a joint work with F. Déglise and A. Khan.金方舟 博士(Uiniversity Duisburg-Essen Department of Mathematics)致远楼101室2019年2月28日 16:00-17:00
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Robust Tensor Completion and Its ApplicationsIn this talk, we report the results of robust tensor completion using tubal singular value decomposition, and its applications. Several applications and theoretical results are discussed. Numerical examples are also presented for demonstration.吴国宝 教授(香港浸会大学)致远楼101室2019年1月22日15:30-16 : 30
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xVA: Definition, Evaluation and Risk ManagementxVA is a collection of valuation adjustments made to the classical risk-neutral valuation of a derivative or derivatives portfolio for pricing or for accounting purposes, and it has been a matter of debate and controversy. This presentation is intended to clarify the notion of xVA as well as the usage of the xVA items in pricing, accounting or risk management. Based on replication pricing using shares and credit default swaps, we attribute the P/&L of a derivatives trade into the compensation for counterparty default risks and the costs of funding. The expected present values of the compensation and the funding costs under the risk-neutral measure are defined to be the bilateral CVA and FVA, respectively. The latter further breaks down into FCA, MVA, ColVA and KVA. We show that the market funding liquidity risk, but not any idiosyncratic funding risks,can be bilaterally priced into a derivative trade, without causing price asymmetry between the counterparties.Lixin Wu (香港科技大学)致远楼101室2019年1月16日10:00-11:00