会议室预约入口
"智能计算与应用"同济大学数学中心
English
学术报告
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A Penrose Type Inequality for Graphs Over Reissner-Nordstrom-Anti-Desitter ManifoldWe will talk about Minkowski type inquality, weighted Alexandrov-Fenchel inequality for the mean convex star-shaped hypersurfaces in Reissner-Nordstrom-anti-deSitter manifold and Penrose type inequality for asymptotically locally hyperbolic manifolds in which can be realized as graphs over Reissner-Nordstrom-anti-deSitter manifold.2020年11月18日
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丢番图逼近中上极限集合的分形维数由一列球或矩形确定的上极限集是丢番图逼近中两类基本的集合, 一个源自于Dirichlet定理另一个源自于Minkowski定理. 由球确定的上极限集的度量理论已经非常丰富/完备, 然而由矩形确定的上极限集的研究却非常滞后, 甚至一些基本问题都尚未完全解决. 在此报告中, 通过引入“矩形的无处不在性/满测性”, 我们确定了由矩形生成的上极限集的Hausdorff理论的一般原理.2020年11月18日
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广义 Frobenius范畴与Semi-Derived Ringel-Hall代数2013年，T. Bridgeland利用投射模的2-周期复形的 Ringel-Hall代数的局部化实现了量子包络代数的整体。之后，M. Gorsky分别用两种方法推广 T. Bridgeland的构造来定义所谓的半导出 Hall代数，一种是用 Frobenius范畴，其构造与 T. Bridgeland的没有本质区别，另一种要求比较强的条件并且其构造不是很直接。注意到他们的构造在2-周期复形的情形下都不能包含加权射影线上凝聚层范畴这类重要的遗传范畴，与卢明合作我们对任意遗传范畴的2-周期复形范畴定义了 modified Ringel-Hall代数。在本报告中，我们定义广义 Frobenius范畴与 semi-derived Ringel-Hall代数，将上述所有的构造统一在一个框架之下。这是与林记合作的工作。2020年11月17日
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The Constant Rank TheoremIn this talk, we will introduce the constant rank theorem, a technique to study the convexity of solutions to PDEs. In particular, the constant rank theorem of spacetime level sets of heat equation, a joint work with Xinan Ma and Paolo Salani, will be particularly discussed.2020年11月17日
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Free Boundary Constant P-Mean Curvature Surfaces Intersecting the Pansu SphereWe will introduce the notion of free boundary constant p-mean curvature (CPMC) surface in a 3-dimensional pseudohermitian manifold with boundary. For the domain bounded by the Pansu sphere in the 3-dimensional Heisenberg group, we will talk on examples of free boundary CPMC surfaces which are rotationally symmetric about the t-axis. This is a joint work with Shujing Pan and Yongbing Zhang.2020年11月17日
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Translation Invariant Quadratic Forms and Dense Sets of PrimesWe consider the translation invariant quadratic forms over dense sets of prime numbers. Let f be a translation invariant quadratic form in ten variables. Subject to a suitable rank condition, we prove that $f$ has a nontrivial zero over dense subset of primes. The proof involves the Hardy-Littlewood method, the sieve method, Roth's method of density increment and Green's W-trick.2020年11月17日
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Curvature Flows for Hypersurfaces in Hyperbolic Space and their Geometric ApplicationsIn this talk, we discuss the contracting curvature flow, expanding curvature flow, globally constrained curvature ow and locally constrained curvature ow for hypersurfaces in hyperbolic space and their applications to geometric inequalities.2020年11月13日
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Geometric Integral Formulas and InequalitiesIn this talk I will give a short survey on some interesting geometric integral formulas and inequalities, such as Minkowski integral formula, Heintze-Karcher inequality and isoperimetric inequalities etc. We will go over the idea of proofs and then propose some questions.2020年11月10日
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SL(n) Covariant Vector Valuations on PolytopesIn this talk, we will show that some results on vector valuation. All SL(n) covariant vector valuations on convex polytopes in Rn are completely classified without any continuity assumptions. The moment vector turns out to be the only such valuation if n ≥ 3, while two new functionals show up in dimension two.2020年11月10日
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Minkowski Problems and Related FlowsFlow method is an effective tool to study variational problems. In this seminar, we discuss Minkowski type problems and their related flow arguments.2020年11月10日
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