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I will give an introduction to Sobolev extensions, including the use of variants of the Whitney extension technique. I will concentrate on the basics of the theory.
In this talk, we give a proof of the conjecture of Hofer-Wysocki-Zehnder published in 2003 asserting that a smooth and autonomous Hamiltonian flow on R4 has either two or infinitely many simple period...
It is now known that the complement of any polynomially convex compact set K in C^n is an Oka manifold. In particular this holds if K is convex. I will discuss a recent result, joint with Forstneri?, ...
The Brauer-Manin obstruction is an old topic in local-global principle of varieties. I will talk about Brauer-Manin obstruction on algebraic stacks and extend some classical results such as the exact ...
The Grobner basis for a zero-dimensional polynomial ideal comprises a univariate polynomial in the least variable. The elimination process in Buchberger's algorithm unnecessarily involves the least va...
For any θ<1/3 , we show that very weak solutions to the two-dimensional Monge–Ampère equation with regularity C1,θ are dense in the space of continuous functions. This result is shown by a convex inte...
The Bogomolv theorem holds great importance in algebraic geometry, particularly in the field of birational geometry. During this presentation, we will introduce our recent work on a variant of the Bog...
I will present a dimension jump result of limit sets on RP^2 for representations of surface groups in SL(3,R). For Anosov representations, we prove the equality between the Hausdorff dimension and the...
In this talk, we will discuss some of our recent work on the master equation involving the fully fractional heat operator. Specifically, we will present two main results. The first one pertains to a g...
Even though the research style of algebra and analysis are quite different, many algebraic structures naturally arose from analysis, differential equations and integral equations, inspiring further ap...
2023年11月8日,由中国人民大学高瓴人工智能学院主办的第二届计算经济学研究与应用研讨会顺利召开。北京大学前沿计算研究中心讲席教授邓小铁,中科院计算所前瞻研究实验室、处理器芯片重点实验室研究员孙晓明,中国科学院数学与系统科学研究院研究员陈旭瑾,清华大学计算机科学与技术系教授陈婧,中国科学院计算技术研究所研究员张家琳,北京交通大学经济管理学院教授曹志刚,谷歌研究科学家左淞,中国科学院数学与系统科学...
High-order interaction occurs in various complex network, such as social network, bionetwork and network medicine. Comparing with that there are a lot of well-developed math tools (from graph theory) ...
I will present a dimension jump result of limit sets on RP^2 for representations of surface groups in SL(3,R). For Anosov representations, we prove the equality between the Hausdorff dimension and the...
This talk mainly concerns the projective, Moishezon and Kahler loci of a family. We first introduce four conjectures on this topic and then the works of the deformation limit of projective manifolds a...
In this talk, we first recall some classical Hopf algebras on rooted trees, including Connes-Kreimer Hopf algebra and Loday-Ronco Hopf algebra. Then we give a combinatorial description of the coproduc...

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