Title: Topology, DNA, and persistent homology

Date and Location: Sept 17, 2026 @ A-211 @ 11:30AM

Abstract: In this talk, we will present several applications of topology. Namely,

• A different approach to the problems of randomness and chirality of

the packed DNA in icosahedral bacteriophages.

• Sedimentation and electrophoretic migration of circular DNA molecules.

• Prediction of breast cancer outcome and survival by topology-based

biomarkers.

On this last application, the topological tool of persistence homology is

utilized. The last portion of the talk will be devoted to a brief introduction

of persistence homology.

Title: Introduction To Toric Topology

Date and Location: Oct 9, 2026 @ A-211 @ 10: 45 AM 

Abstract: Toric topology is a very active area that lies at the intersection of topology, algebraic geometry, differential topology, combinatorics, and several other fields. Roughly speaking, a quasitoric manifold is a complex manifold equipped with a torus action whose orbit space is a simple convex polytope. The aim of this talk is to introduce the basic ideas of toric topology and to explore some of the algebraic-topological aspects of these fascinating manifolds. Examples will be presented and then general statements about their cohomology rings and homotopy groups will be discussed. I will present some open problems in the field, in particular, the rigidity conjetures that have been the focus of intense research. Time permitting, I will give a brief overview of stable splitting of certain toric spaces that are related to quasitoric manifolds.

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