**Speaker:** Ken Baker (U. Miami)

**Date: **Friday March 7th. 3-4pm.

**Location: **DSB C128.

**Speaker:** Ryan Budney

**Title: **A coming census of triangulated smooth 4-manifolds.

**Speaker:** Sam Churchill

**Title:** 4-manifolds bounding 3-manifolds

**Date:** Friday October 4th, 3pm-4pm

**Location:** CLE A211

**Speaker:** Joseph Cheng (UBC)

**Title:** Poincare duality for orbifolds in Morava K-theory

**Abstract:** It was showed by Greenlees and Sadofsky that the classifying spaces of ﬁnite groups are self-dual with respect to Morava K-theory K(n). Their duality map was constructed using a transfer map. I will describe the map and its generalization which would induce a K(n)-version of Poincare duality for classifying spaces of orbifolds. Some examples of K(n)-fundamental class and intersection product will be given. If time permits, I will explain the similarity of this duality map with that of the Spanier-Whitehead duality for manifolds from the point of view of diﬀerentiable stacks.

**Date:** Friday September 27th

**Time:** 3pm--4pm

**Location:** CLE A211

**Speaker:** Robin Koytcheff

**Title:** A coloured operad for string link infection

**Abstract:** This talk builds on the work of Budney on operads and knot spaces described in the past two seminars. In particular, we build on his operad for splicing of knots, which we will briefly review. Infection of knots or links by string links is a generalization of splicing from knots to links and is useful for studying concordance of knots. In joint work with Burke, we have constructed a coloured operad that encodes this infection operation. This work has motivated us to prove a prime decomposition for 2-component string links in joint work with Burke and Blair. This suggests the possibility of proving further decomposition theorems analogous to those of Budney; this last item is work in progress.

**Date:** Friday September 13th

**Time:** 3pm-4pm

**Location:** CLE A211

**Speaker:** Ryan Budney

**Title:** Spaces of embeddings. Part 1 of 2

**Abstract:** I will describe recent work on the homotopy-type of spaces of embeddings, primarily the space of embeddings of the circle in the 3-sphere. The talk will consist of an introduction to operads, and the basics of what is known about knots and embedding spaces. I will describe how Schubert's connect-sum decomposition can be elaborated into an action of the 2-cubes operad on knot spaces, and how that relates to the homotopy-type of knot spaces via geometrization. This inspired a further operad called the splicing operad, which has further insights into the topology of knot spaces, and deeper connections to geometrization. Towards the end of this 2-part talk I will discuss how there appears to be nice connections to the tools coming from the calculus of functors for describing embedding spaces.

**Date:** Friday August 23rd

**Time:** 3pm-4pm

**Location:** CLE A211

**Speaker:** Ryan Budney

**Title:** Spaces of embeddings. Part 2 of 2

**Abstract:** See previous talk.

**Date:** Friday August 30th, 3pm-4pm

**Location:** CLE A211

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