With the development of the hardware, the numerical study on the all-electron Kohn-Sham equation has been attracting more and more attention, which potentially would play an important role in studying a variety of physical phenomena such as high harmonic generation. In this talk, towards the efficient numerical solver for the all-electron Kohn-Sham equation, an adaptive finite element framework

We address the following rainbow Ramsey problem: For posets P, Q what is the smallest number n such that any coloring of the elements of the Boolean lattice Bn either admits a monochromatic copy of PP or a rainbow copy of QQ. We consider both weak and strong (non-induced and induced) versions of this problem.

Vizing’s planar graph conjecture says that every class two planar has maximum degree at most 5. The conjecture is still open. We consider the problem for graphs embeddable on a surface Sigma and attempt to find the best possible upper bound for the maximum degree of class two graphs embeddable on Sigma. In this talk I will give a survey on this topic and present some new results.

The talk will describe various generalizations of the Hadamard jump condition, and how they can lead to information about polycrystal microstructure arising from martensitic phase transformations. (Joint work with Carsten Carstensen (Humboldt University, Berlin)

We propose a new and short proof for the Macdonald identities using only some easy facts from the theory of Jacobi forms of lattice index and classical root systems. (The needed basic features of these theories will be explained in the talk). We discuss applications and open questions related to the new proof, and we end the talk by deducing from the Macdonald identities, for 42 elliptic curves over the rationals and of rank 1 product identities for the (classical) Jacobi forms attached to elliptic curves by the theory of modular forms.

Let $g$ be a metric over $B$ which is conformal to $g_0$.We assume $/|R(g_k)/|_{L^p} <C$, where $R$ is the scalar curvature and $p/geq /frac{n}{2}$.We will use the John-Nirenberg inequality to prove that if $vol(B,g_k) /rightarrow 0$, then there exists $c_k /rightarrow+/infty$, such that $c_ku_k$ converges to a positive function weakly in $W^{2,p}_{loc}(B)$. As an application, we will study the bubble tree convergence of a conformal metric sequence with integral-bounded scalar curvature.

n the theory of tensor categories, especially the theory of fusion categories, the near group categories are an important class of fusion categories.The $/mathbb{Z}_+$-representations over near group fusion rings are closely related to the module categories over near group categories. In this talk we shall introduce a general theory of irreducible $/mathbb{Z_+}$-representations over near group fusion rings. We give the minimum upper the bound of rank of irreducible$/mathbb{Z_+}$-representation over a near group fusion ring, and the general classification methods of irreducible $/mathbb{Z_+}$-representations over near group fusion rings. We give explicitly the classifications of irreducible $/mathbb{Z_+}$-representations over some near group fusion rings, such as $K(/mathbb{Z}_2, n)$, $K(/mathbb{Z}_3, n)$, $K(/mathbb{K}_4, n)$ and $K(/mathbb{S}_3, n)$.

In this talk, we first introduce the quasitriangular Hopf algebras, the Drinfeld doubles of finite dimensional Hopf algebras, and their representation theory. Then we introduce the cocycle deformation theory of Hopf algebras. Finally, we introduce Taft algebras, their Drinfeld doubles and their representation theory and Green rings.