Erica Flapan (Pomona College, CA, USA)

Qiuyu Ren (Stanford University, CA, USA)

Mayuko Yamashita (Perimeter Institute for Theoretical Physics, Waterloo, Canada)

Tian Yang (Texas A&M University, TX, USA)

TBA

Speaker: Erica Flapan (Pomona College)

Title:  The Topology of Entangled Molecules

Abstract:  Spatial graph theory is the study of the topology of graphs embedded in R^3. It can be thought of as a generalization of knot theory, but it was actually motivated by chemists trying to understand the symmetries of flexible molecules. In this talk, we will explain the role of spatial graph theory in classifying the symmetries of molecular M¨obius ladders and other entangled synthetic molecules. Then we explore knots, links, and non-planar graphs that have been identified in protein structures and present mathematical models explaining how protein knots might occur.

Speaker: Qiuyu Ren (Stanford University)

Title: TBA

Abstract: TBA

Speaker: Mayuko Yamashita (Perimeter Institute for Theoretical Physics, Canada)

Title: TBA

Abstract: TBA

Speaker: Tian Yang (Texas A&M University)

Title: Volume Conjecture and some recent progress

Abstract: In this talk, I will first give an overview of the Volume Conjecture, which connects two seeming different approaches to 3-dimensional topology – the hyperbolic geometry and the quantum invariants. Then I will talk about a recent joint work with Tianyue Liu, Shuang Ming, Xin Sun and BaojunWu, where we define a family of quantum invariants for hyperbolic 3-manifolds with cusp ends and with totally geodesic boundary from the representation theory of the a quantum group, called the modular double of U_qsl(2;R), and prove that asymptotically these new invariants behave exactly in the way that the Volume Conjecture predicted.