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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.
Causal inference is a permanent challenge topic in statistics, data science, and many other applied fields. Existing machine learning methods often focus on the correlations in the data and ignore the...
This course will give an introduction to inverse problems for elliptic partial differential equations. The most famous example of such problems is the Calderón problem, which arises in seismic and med...
We study a class of ultra-parabolic equations, it is a high order degenerate parabolic operators of Hormander type, so it is strongly degenerate, but we prove that this class operators possesses the a...
In the past two decades, starting with the pioneering work of Bourgain, Brezis, and Mironescu, there has been widespread interest in characterizing Sobolev and BV (bounded variation) functions by mean...
中国科学院金属研究所研究员张志东在计算机领域计算复杂性理论研究方面取得重要进展,确定了布尔可满足性问题的计算复杂度下限。相关研究成果发表在《数学》(Mathematics)上。 
A Hénon map is a map of the form H(z, w) = (f(z) + aw, z). A main focus of interest are the Fatou sets and the Julia sets. In this lecture I will show that it is possible that the Fatou set and the Ju...
In this talk, we will introduce some applications of Nevanlinna theory to “arithmetic properties” of exponential polynomials and some special cases of Green-Griffiths-Lang conjecture with moving targe...
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...
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.
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 ...
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?, ...
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 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...
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...

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