演讲人：Paul Horn、Huabin Ge、Luc Vinet、Satoshi Tsujimoto
讲座时间：2016-12-09 09:00:00
讲座地点：信息楼三层343研讨室
讲座内容
2016“图论和数学物理研讨会”由中国人民大学信息学院数学系主办。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.