Date : January 15th, 2020.
Place : The 3rd Area, Institutes of Engineering Sciences, F902, University of Tsukuba, Ikabaraki, Japan.
Access : From the Tsukuba station (Tsukuba Bus Center Terminal), there is a bus to Campus, and the nearest bus-stop from the venue is "The 3rd area".
This joint workshop is organized by Noboru Kunihiro (University of Tsukuba), Hiroshi Nozaki (Aichi University of Education), and Hyungrok Jo (University of Tsukuba). It aims to share ideas with each other about algebraic combinatorics, graph theory, and its cryptographic applications.
This workshop is supported by Invitational Fellowships for Research in Japan, Short-term, S19016 and JST CREST Grant Number JPMJCR14D6, CryptoMathCREST .
Title : Some recent results on Seidel matrices and signed graphs
Abstract :
In this talk I will discuss some recent results on Seidel matrices and signed graphs.
Title : Ramanujan graphs and their cryptographic applications
Abstract :
Ramanujan graph, one of expander graphs, is an optimal structure in a spectral sense, and it is used in many research areas very actively (pure mathematic, network theory, cryptography and so on). In this talk, I describe how to use the exlicit constructions of LPS (Lubotzky-Phillips-Sarnak) Ramanujan and its generalization, LPS-type Ramanujan graphs in cryptography. Especially, I introduce Cayley hash functions based on Ramanujan graphs and specify their security related to group word problems.
Title : Linear programming methods to obtain bounds on the order of regular graphs
Abstract :
We introduce some methods to obtain upper bounds on the order of a regular graph with given distinct eigenvalues. In particular, we can obtain upper bounds on the order of a regular graph with given spectral gap. Optimal graphs that attain the upper bound have high girth, and they are characterized as distance-regular graphs. These results are generalized to regular uniform hypergraphs.
Abstract :
In this talk, I will describe some open problems in spectral graph theory. These involve determining or bounding the second eigenvalue of graphs constructed from systems of equations over finite fields, determining the second or the smallest eigenvalue of some flip graphs or graphs without certain induced subgraphs.
Place : Tenryu honten
If you want to attend the banquet, please notify me of your attendance via jo.hyungrok.gb (at-mark) u.tsukuba.ac.jp until 2019. Dec. 13th (Friday).