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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...
In recent work with Will Johnson, we have shown that given a curve C over the rational number field Q with genus at least 2 and C(Q) is empty, the class of fields K of characteristic 0 such that C(K) ...
In this talk, I shall explain the work of G. Faltings on a p-adic Simpson correspondence, using exponential twisting. This reinterpretation of the correspondence makes clearer analogy between the p-ad...
Consider a finite set of segments on a plane with endpoints in the general position. In [1] Sylvester posted a problem of finding the measure of the set of lines intersecting all of this segments. In ...
We continue to discuss the proof of the Allard regularity theorem. In the second presentation, we will focus on the harmonic approximation and the iteration argument for getting the decay of the tilt-...
In this short seminar, we will discuss the proof of the Allard regularity theorem, which is an $\epsilon$-regularity theorem for the mean curvature equation in the Geometric Measure Theory(GMT) settin...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Multiple solutions for semilinear subelliptic Dirichlet problem。
In 2007, Andrews introduced the odd rank of odd Durfee symbols. Let N^0 (m,n) denote the number of odd Durfee symbols of n with odd rank m, and N^0 (r,m;n) be the number of odd Durfee symbols of n wit...
In this talk, we investigate congruence properties for Motzkin numbers and central trinomial coefficients. Let M_n and T_n denote the nth Motzkin number and the nth central trinomial coefficient respe...
The framework of derived algebraic geometry (DAG), developed by Toen-Vezzosi, Lurie and many others, allows us to extend Grothendieck’s theory of flag schemes of sheaves to the cases of complexes. In ...
In this talk, we will talk about a local method to find compositional inverses of all PPs, some new PPs and their compositional inverses are given.
The Zariski dense orbit conjecture of the arithmetic dynamic is to study the existence of a rational point P with a Zariski dense orbit of a dominant rational self-map f of a projective variety X. Whe...
Higher dimensional Heegaard Floer homology (HDHF) is a higher dimensional analogue of Heegaard Floer homology in dimension three. It's partly used to study contact topology in higher dimensions. In a ...
Let x be an algebraic number. Lehmer's problem predicts that the product of the degree of x and the Weil height of x is bounded by an absolute constant. The basic idea to tackle this problem is to stu...
Discuss [Bha, §2.3-2.4]. See [Dri20, §1.3] for the notion of cones and quasi-ideals. Note that some of the remarks (e.g. Remark 2.2.15) [Bha, §2.2] may not have been covered in Lecture 1. Explain them...

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