Binghamton University's Graduate Conference in Algebra and Topology

October 13-14 , 2018


Graduate students of all levels and faculty are invited to register to give a 30 minute talk. Talks may be expository or on current research.

For more information, email gradconf@math.binghamton.edu .


Keynote Speaker
William Menasco
University at Buffalo

Title: The geometry of the curve complex.

Abstract: Let S_g be a closed oriented surface of genus g \geq 2 and C^1(S_g) be its curve complex---vertices are homotopy classes of essential simple closed curves with two vertices sharing an edge if they have disjoint representatives. In this talk we will survey some of the results on the coarse geometry of the curve complex: that C^1(S_g) is path connected; that the vertices, C^0(S_g), have a natural metric; that this metric on C^0(S_g) is unbounded; and, that this metric on C^0(S_g) is delta-hyperbolic. Finally, we will talk about recent results of Birman-Margalit-M on an algorithm for computing distance in C^0(S_g).


Keynote Speaker
Nataša Jonoska
University of South Florida

Title: How biology can incite new ideas in algebra and topology

Abstract: In the last couple of decades, it has become evident that algebraic and topological approaches are well suited for modeling certain biological processes. The specificities of processes in molecular biology have required mathematicians to look into notions and problems that might not have been considered before and have brought new mathematical ideas. We will start with one of Tom Head’s pioneering concepts on splicing systems showing connections between DNA recombinant processes and formal language theory. Then we will discuss how some concepts in spatial/topological graph theory have developed from modeling DNA rearrangements.

Keynote Speaker
Jean-François Lafont
Ohio State University

Title: Totally geodesic submanifolds in closed hyperbolic manifolds

Abstract: I will briefly describe the various constructions of closed hyperbolic manifolds, with a focus on the arithmetic vs. non-arithmetic dichotomy. I will then illustrate this dichotomy by discussing two results on the structure of submanifolds inside these manifolds.


Keynote Speaker
Ruth Charney
Brandeis University

Title: A geometric approach to Artin groups

Abstract: Artin groups arise naturally as fundamental groups of hyperplane complements. They form a large and diverse collection of groups which include braid groups, free groups, free abelian groups and many more. While some classes of Artin groups are well understood, many remain mysterious, with even very basic questions unanswered. In this talk I will explain why Artin groups are interesting and review what is known and not known about these groups. I will then discuss some geometric techniques for studying these questions (including some recent joint work with Rose Morris-Wright).