2016“图论和数学物理研讨会”由9728太阳集团数学系主办。我们邀请了4位专家学者在人大做报告，研讨会将于2016年12月9日在人大信息楼召开，欢迎广大师生参加。

组委会成员：林勇， Alexei Zhedanov

会议日程表:

时间：2016年12月9日

地点：人大信息楼三层343研讨室

09:00-10:00 Paul Horn（University of Denver）

Multicolored trees in graphs

10:00-11:00 Huabin Ge（北京交通大学）

p-th Kazdan-Warner equation on graph

15:30-16:30 Luc Vinet（University of Montreal）

Quantum state transport, entanglement generation and orthogonal polynomials

16:30-17:30 Satoshi Tsujimoto（Kyoto University）

Soliton Box-Ball Systems in Automata

Abstract:

p-th Kazdan-Warner equation on graph

Huabin Ge

In this talk, we will focus on the solvabiity of the p-th

Kazdan-Warner equation on a finite graph

Multicolored trees in graphs

Paul Horn

A old conjecture of Brualdi and Hollingsworth states that if the edges of the complete graph $K_{2n}$ is colored by perfect matchings, then the resulting graph can be decomposed into spanning trees so that each tree contains one edge of each color. After many years of inactivity there has recently been a fair amount of recent work on the conjecture, with the best result (due to the speaker) saying that one may decompose a positive fraction of the graph into rainbow spanning trees.In this talk, I’ll discuss recent work with my graduate student Lauren Nelson, where we prove an analogous result for a much more general class of graphs, requiring a bound only on the spectral gap and minimum degree. In particular, I’ll describe how spectral and isoperimetric information can be used to guarantee the existence of many disjoint rainbow trees in graphs. The proof combines probabilistic and spectral methods.

Soliton Box-Ball Systems in Automata

Satoshi Tsujimoto

Takahashi-Satsuma’s box-ball system (BBS) is one of the important ultradiscrete systems in Soliton theory.

First we briefly review the relationship between BBS and automata group. We will take a further look at BBS from an automata perspective. As a consequence we will introduce several 0-1 valued dynamical systems sharing the several important properties with BBS.

Quantum state transport, entanglement generation and orthogonal polynomials

Luc Vinet

The transport with high fidelity of quantum states from one location to another is fundamental in quantum computing and information. Entangled states are also essential ressources for protocol such as teleportation. I will show how the theory of orthogonal polynomials enters in the design of spin chains or optical lattices that realize these tasks. No knowledge of quantum physics will be assumed.

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