IU/PU/IUPUI Joint Topology Seminar

November 8, 2014
IUPUI
Indianapolis, IN, USA

The first meeting of the IU/PU/IUPUI Joint Topology Seminar will be held at IUPUI in Indianapolis, Indiana on Saturday November 8, 2014. Talks will begin at 10am and end at 12:30pm, and we plan to go to lunch afterwards.

Registration

If you plan to attend, please email Dan Ramras (dramras at iupui.edu), and indicate if you will need a parking pass and if you plan to come to lunch. We can provide parking passes, which allow you to park in the lots in front of the LD building. (Note that most parking spots on the IUPUI campus require a permit, even on weekends.)

Confirmed Speakers

Ralph Kaufmann, Purdue University: Feynman categories and Hopf algebras
Kate Ponto, University of Kentucky: Amazing consequences of simple properties of the trace

Schedule:

10am: Ralph Kaufmann

11:30am: Kate Ponto

Abstracts:

Ralph Kaufmann, Feynman categories and Hopf algebras

We give the definition of Feynman categories. These are a universal framework for studying operads, PROPs, modular operads, and even twisted modular operads and algebras over operads in the same way. We discuss universal operations on them such as (dual) transforms and for them such as brackets and master equations. We also studied the respective model category theory. We furthermore explain how to distill Hopf algebras from Feynman categories. This is partially joint work with B. Ward and partially with I. Galvez-Carrillo and A. Tonks.

Kate Ponto, Amazing consequences of simple properties of the trace

For a fibration (with a connected base space) the Euler characteristic of the total space is the product of the Euler characteristics of the base and the fiber. The Euler characteristic is also additive on subcomplexes. Combining these we have a description of the Euler characteristic of a G-space in terms of the quotients of the isotropy subspaces. The generalizations of the Euler characteristic to fixed point invariants, primarily the Lefschetz number and Reidemeister trace, are similarly additive and multiplicative. Classically these results were proven using a variety of techniques.

Mike Shulman and I have shown that all of these results are consequences of a simple formal observation and some topological input. The formal observation is a generalization of the invariance of trace under change of basis. The topological input is a little more complicated.

Directions

All talks will be held in LD 026 (basement of the math building) on the IUPUI campus in downtown Indianapolis. Note that the LD building and the SL building are joined; LD rooms are on the southern side (further from Michigan St.).

Parking information:

Campus Map

Organizers

Dan Ramras (dramras at iupui dot edu)
Mike Mandell (mmandell at indiana dot edu)
David Gepner (dgepner at purdue dot edu)

Please contact us with questions.

Email: dramras at iupui dot edu