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This page was the home of the Xtraordinary cohomology theory & K-theory Collective Discussion 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 En-algebra with a space of sections of a certain bundle. I will describe how to generalize non-abelian Poincaré duality to the case of En-algebras which are not group-like. While non-abelian Poincaré duality for group-like En-algebras can be viewed as the minimal theorem simultaneously generalizing Poincaré duality and May’s recognition principle for iterated loop spaces, this generalization can be viewed as the minimal generalization of the group-completion theorem and McDuff’s scanning result for configuration spaces of unordered particles in an open manifold.
4:40-5:40 -- En-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 En-cells and homological stability. Using this theory, we prove a local-to-global principle for homological stability, as well as give a new perspective on homological stability for various spaces including symmetric products and spaces of holomorphic maps.
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.
* the xkcd group -- making xkcd not stand for nothing since 2010!