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This page was the home of the **X**traordinary cohomology theory & **K**-theory **C**ollective **D**iscussion group^{*} for the spring 2015 semester.

All talks at Berkeley were on Berkeley time (i.e. they started 10 minutes late).

This xkcd group meeting is joint with the Stanford topology progress seminar.

N.B.: Talk times are exact, i.e. *not* on Berkeley time.

**3:20-4:20 -- A generalization of non-abelian Poincaré duality**

Salvatore and Lurie's non-abelian Poincaré duality theorem equates the topological chiral homology of a group-like *E _{n}*-algebra with a space of sections of a certain bundle. I will describe how to generalize non-abelian Poincaré duality to the case of

**4:40-5:40 -- E_{n}-cells and their applications**

When studying objects with additional algebraic structure, e.g. algebras over an operad, it can be helpful to consider cell decompositions adapted to these algebraic structures. I will talk about joint work with Jeremy Miller on the relationship between

**6:00-7:00 -- Counting Riemann surfaces with homotopy theory**

One way to count curves satisfying certain conditions is to express these conditions as cycles on the moduli space of curves, and compute the intersection product. One obstacle to this is that the moduli space may not have the "expected dimension", which in particular means that the above product may not be well defined. In this talk, we'll see how homotopic methods can be used in order to circumvent this issue and obtain a rigorous procedure for curve counting.

*Daniel Lowengrub*

^{*} the xkcd group -- making xkcd not stand for nothing since 2010!