Topology Seminar—Fall 2023

The seminar meets each Tuesday at 3:05 pm in LOV 0231, unless otherwise noted.

Schedule and talks

• Sep 5
  • Organizational Meeting
• Sep 12 & Sep 19
  • Sam Ballas
  • Frame theory on vector bundles
  • Vector valued information can be transmitted by describing the coordinates of vectors in a fixed basis, however this method of transmission is not very robust since corruption of a single coordinate can drastically alter the description of the vector. To combat this it is often desirable to have a spanning set that is larger than a basis (such an object is called a frame) to provide a description of vectors that is more robust with respect to signal corruption. The study of frames for vector fields and their properties is called Frame Theory, and is an active area of current research. In recent work with Tom Needham and Clayton Shonkwiler, we develop a frame theory for vector bundles. The idea being that given a vector bundle one wishes to find a collection of sections that pointwise span the fibers. Finding such objects is somewhat subtle since by definition, non-trivial vector bundles don’t admit global bases of sections. More interestingly, we will see that it is always possible to find a frame with sufficiently many vectors and that the minimal numbers of sections in a frame is obstructed by algebraic topological invariants of the vector bundle.
• Sep 26 & Oct 3
  • Brandon Doherty
  • Cubical models of higher categories without connections
  • We will discuss the cubical Joyal model structures on the categories of cubical sets both with and without connections, by which cubical sets model the theory of (infinity,1)-categories, and the proofs that these model structures are Quillen equivalent to the Joyal model structure on simplicial sets. If time permits, we will also discuss the comical model structures on marked cubical sets which model (infinity,n)-categories for arbitrary n, and the proof that these are equivalent to the corresponding complicial model structures on marked simplicial sets.
• Oct 10
  • Mario Gómez Flores
• Oct 17
  • Pierre-Louis Blayac (University of Michigan)
• Oct 24
  • Ronno Das
• Oct 31
  • Florian Stecker
• Nov 7
• Nov 14
  • Jared Miller
• Nov 21
• Nov 28
• Dec 5
  • Oishee Banerjee