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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 ...
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...
In the first lecture I will give an introduction to toric algebras. A toric algebra can be seen as a monomial subalgebra, or as a quotient of a polynomial ring by a binomial prime ideal. We will discu...
Mapping class groups and homeomorphism groups are symmetry groups of surfaces and all manifolds. They are usually very rigid, in the sense that their automorphism groups only consist of conjugation. I...
Since the discovery of Camassa-Holm equation, because of the special properties that peakon gets, it has received considerable attention in modern Mathematics and Physics. Many new integrable dynamic ...
Bjorner and Ekedahl (Ann. of math., 2008) proved that lower Bruhat intervals of crystallographic Coxeter groups are top-heavy using Hodge theory. Using Soergel bimodules and their Hodge theory establi...
The unimodality of lower Bruhat intervals for the “upper half” remains as an open problem. For affine Weyl group W with corresponding finite Weyl group W_f, we prove that lower W_f-parabolic Bruhat in...
We define a higher-dimensional analogue of symplectic Khovanov homology. Consider the standard Lefschetz fibration of a 2n-dimensional Milnor fiber of the A_{k-1} singularity. We represent a link by a...
In this talk, we present recent progress on holomorphic Morse inequalities. We first review the history and motivation. Then we introduce recent results on CR manifolds. Finally we give a uniform proo...
In this talk, we define a new class of differential fields called separably differentially closed fields and show their several characterizations by comparing them with differentially closed fields of...
Grothendieck predicted that the cohomological Brauer group of a regular scheme X is insensitive to removing a closed subscheme Z of X of codimension>=2. By Gabber's several results, the conjecture was...
The stable reduction theorem was proved by Grothendieck for Abelian varieties and subsequently by Deligne and Mumford for projective curves.
The Morse boundary of a proper geodesic metric space is a generalization of the Gromov boundary of a hyperbolic space. It is a quasi-isometry invariant to study "hyperbolic directions" in the space. T...
因子设计可分为正规设计和非正规设计,其中正规设计结构简单,试验次数被限制在2的幂次上。非正规设计结构复杂,但具有较为灵活的试验次数,并可用于估计更多的因子效应。作为一类特殊的非正规设计,平行平面设计受到了越来越多的关注。正规设计也被称为单平面设计,由来自同一家族的几个单平面行并置得到的设计被称为平行平面设计。由三个平行平面构成的平行平面设计是最常用的非正规设计。将其推广到具有f个平面的平行平面设计...
In this talk, I will give some of the context and a sketch of the proof of the following result which I proved a while ago: It is consistent (relative to a Mahlo catrdinal) that there is a projective ...

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