Student Homotopy Seminar 

1/7

1/14

1/21

Abstract: We will begin with an overview of an old problem, due to Baez and Dolan, that applied higher category theory to the study of mathematical physics (via topological quantum field theories). I will show how to reduce the statement of the Baez-Dolan Stabilization Hypothesis from a statement in higher category theory (we choose the setting of Rezk’s Theta_n spaces) to one in abstract homotopy theory. I’ll then sketch how to prove the Stabilization Hypothesis using semi-model categories, n-operads, and Cisinski’s locally constant presheaves. A key new ingredient is a result that does left Bousfield localization for non-left proper model categories. This is joint work with Michael Batanin.

1/28

Abstract: The box product is a formal multiplication for cosimplicial objects that is known to induce A_{\infty} monoid structure on the totalization of certain cosimplicial objects. In this talk, I will give a description of the box product and as an application show how it can be used to induce an A_{\infty}-monoid structure on the space of based loops on a pointed space X given by concatenation. Using this example as inspiration, I will then outline an argument for giving \partial_* Id — the symmetric sequence of Goodwillie derivatives of the identity functor — a “homotopy coherent” operad structure.

2/4

2/11

2/18

2/25

3/3

3/10

3/17

3/24

3/31

4/7

4/14

4/21

4/28