Topology Seminars

Fall 2018

Speaker: Paul Kainen (Georgetown University)
Date and time: Thursday, November 1, 5:15--6:30pm
Place: Gelman Library, room 608
Title:Even complexes have a spherical basis

Abstract: An n-complex is even if each n-1-cell is a face of a positive even number of n-cells.  It is shown that there exists a basis (w.r.t. symmetric difference) consisting of minimum topologicalsphere-subcomplexes (of the cube or simplex) such that each even subcomplex is the sum of a unique subset of the basis, and the cardinality of the basis is determined in two different ways. Algebraic topology is used in one of the arguments.

BioPaul Kainen got his Ph.D. in Algebraic Topology under direction of Peter J. Hilton (at Cornell in prehistoric days).  He works in graph theory and its enrichments to neural networks and also category theory.  He has taught at Georgetown Univ. since 1997 and previously has worked for Bell Laboratories and for a local systems engineering company.  Kainen is especially interested in the quantitative analysis of photonic technology in medicine. His Erdos-number is 1; he is co-author of The Four-Color Problem book.

Speaker: Takefumi Nosaka (Tokyo Institute of Technology)
Date and time: Tuesday, October 23, 5:15--6:30pm
Place: Gelman Library, room 608
Title: "Dijkgraaf-Witten invariants and Pachner moves"

Abstract: As a topological toy-model of the Chern-Simons invariant, Dijkgraaf and Witten suggested an invariant of 3-manifolds defined in a simple way.  However, the computation is seemingly not so easy if done from  definition. In this talk, I explain the definition and mention some technical difficulties. After that, I introduce some methods to compute the invariant. I will mention  M. Wakui approach using Pachner moves on 3-manifolds 

BioTakefumi Nosaka did his PhD under supervision of Tomotada Ohtsuki at RIMS at Kyoto University in 2012. Currently he is Assistant Professor at  Department of Mathematics, Tokyo Institute of Technology. He has many nice results in Knot Theory and Quandle Theory and recently published a book: T. Nosaka, Quandles and Topological Pairs: Symmetry, Knots, and Cohomology, SpringerBriefs in Mathematics, November, 2017.