Contact Lina Crocker (lina.crocker@uky.edu) for more information.

Meet Lina Crocker in the POT lobby at 11:45.

Contact Lina Crocker (lina.crocker@uky.edu) if you are attending.

Title: Representing discrete Morse functions with polyhedra



Abstract: Discrete Morse theory is a method of reducing a CW complex to a simpler complex with similar topological properties. Well-known approaches to this task are due to Banchoff, whose process involves embedding a polyhedron in Euclidean space and considering the projections of its vertices onto a straight line, and to Forman, whose process involves finding special functions from the face poset of a complex to the real numbers. In this talk, I will discuss a result by Bloch which gives a relationship between these two methods. In particular, given a discrete Morse function on a CW complex, there exists a corresponding polyhedral embedding of the barycentric subdivision of X such that the discrete Morse function and the projection of the vertices of the polyhedron onto a line give the same critical cells.



 

Speak Arabic with Native Arabic Speakers

تحدث باللغة الإنجليزية مع الناطقين بها.

Speak Arabic with Native Arabic Speakers

تحدث باللغة الإنجليزية مع الناطقين بها.

Recent discovery of topological insulators highlighted a new class of quantum phases, namely topological phases, characterized by exotic surface states and quantized response functions. While topological insulators are well understood, topological aspects of metals are less clear. In this talk, I’ll discuss a class of electronic topological semimetals, which are 3d analogies of graphene. They are solid state realizations of Weyl fermions, hence coined Weyl semimetals. I’ll discuss their topological properties, including surface Fermi arcs and bulk quantum Hall effects. In the presence of electronic interactions, charge density wave and superconductivity can develop in Weyl semimetals. I’ll show that these symmetry breaking states inherit the nontrivial topology from Weyl semimetals.

Information meeting for all Math majors and minors, and for all students interested in the Math program.