09:00 to 10:00 Wolfgang Lueck On the stable Cannon Conjecture The Cannon Conjecture for a torsionfree hyperbolic group $G$ with boundary homeomorphic to $S^2$ says that $G$ is the fundamental group of an aspherical closed $3$-manifold $M$.  It is known that then $M$ is a hyperbolic $3$-manifold.  We prove the stable version that for any closed manifold $N$ of dimension greater or equal to $2$  there exists a closed manifold $M$ together with a simple homotopy equivalence $M \to N \times BG$. If $N$ is aspherical and $\pi_1(N)$ satisfies the Farrell-Jones Conjecture, then $M$ is unique up to homeomorphism. This is joint work with Ferry and Weinberger. INI 1 10:00 to 11:00 Thomas Willwacher Configuration spaces of points and real Goodwillie-Weiss calculus The manifold calculus of Goodwillie and Weiss proposes to reduce questions about embedding spaces of manifolds to questions about mapping spaces of the (little-disks modules of) configuration spaces of points on those manifolds. We will discuss real models for these configuration spaces. Furthermore, we will see that a real version of the aforementioned mapping spaces is computable in terms of graph complexes. In particular, this yields a new tool to study diffeomorphism groups and moduli spaces. INI 1 11:00 to 11:30 Morning Coffee 11:30 to 12:30 Alexander Kupers Cellular techniques in homological stability 2: mapping class groups This is the second of two talks about joint work with S. Galatius and O Randal-Williams on applications higher-algebraic structures to homological stability. In it we apply the general theory to the example of mapping class groups of surfaces. After reproving Harer's stability result, I will explain how to prove the novel phenomenon of secondary homological stability; there are maps comparing the relative homology groups of the stabilization map for different genus and there are isomorphisms in a range tending to infinity with the genus. INI 1 12:30 to 13:30 Lunch at Churchill College 14:30 to 15:30 Victor Turchin Embeddings, operads, graph-complexes I will talk about the connection between the following concepts: manifold calculus, little discs operads, embedding spaces, problem of delooping, relative rational formality of the little discs, and graph-complexes. I will review main results on this connection by Boavida de Brito and Weiss, my coauthors and myself. At the end I will briefly go over the current joint work in progress of Fresse, Willwacher, and myself on the rational homotopy type of embedding spaces. Co-authors: Gregory Arone (Stockholm University), Julien Ducoulombier (ETH, Zurich), Benoit Fresse (University of Lille), Pascal Lambrechts (University of Louvain), Paul Arnaud Songhafouo Tsopméné (University of Regina), Thomas Willwacher (ETH, Zurich). INI 1 15:30 to 16:00 Afternoon Tea 16:00 to 17:00 Nathalie Wahl Homotopy invariance in string topology In joint work with Nancy Hingston, we show that the Goresky-Hingston coproduct, just like the Chas-Sullivan product, is homotopy invariant. Unlike the Chas-Sullivan product, this coproduct is a "compactified operation", coming from a certain compactification of the moduli space of Riemann surfaces. I'll give an idea of the ingredients used in the proof. INI 1
 10:00 to 11:00 Andre Henriques The complex cobordism 2-category and its central extensions I will introduce a symmetric monoidal 2-category whose objects are 0-manifolds, whose 1-morphisms are 1-dimensional smooth cobordisms, and whose 2-morphisms are Riemann surfaces with boundary and cusps. I will introduce a certain central extension by ℝ₊ and explain its relevance in chiral conformal field theory. Finally, I will explain the state of my understanding on the question of classification of such extensions by ℝ₊. INI 1 11:00 to 11:30 Morning Coffee 11:30 to 12:30 Sam Nariman Topological and dynamical obstructions to extending group actions. For any 3-manifold $M$ with torus boundary, we find finitely generated subgroups of $\Diff_0(\partial M)$ whose actions do not extend to actions on $M$; in many cases, there is even no action by homeomorphisms. The obstructions are both dynamical and cohomological in nature. We also show that, if $\partial M = S^2$, there is no section of the map $\Diff_0(M) \to \Diff_0(\partial M)$. This answers a question of Ghys for particular manifolds and gives tools for progress on the general program of bordism of group actions. This is a joint work with Kathryn Mann. INI 1 12:30 to 13:30 Lunch at Churchill College 13:30 to 14:30 Ryan Budney Some prospects with the splicing operad Roughly six years ago I described an operad that acts on spaces of long knots'. This is the space of smooth embeddings of R^j into R^n. The embeddings are required to be standard (linear) outside of a disc, and come equipped with a trivialisation of their normal bundles. This splicing operad gives a remarkably compact description of the homotopy-type of the space of classical long knots (j=1, n=3), that meshes well with the machinery of 3-manifold theory: JSJ-decompositions and geometrization. What remains to be seen is how useful this splicing operad might be when n is larger than 3. I will talk about what is known at present, and natural avenues to explore. INI 1 14:30 to 15:30 Diarmuid Crowley Relative kappa-classes Diff(D^n), the the space of diffeomorphisms of the n-disc fixed near the boundary has rich rational topology. For example, Weiss's discovery of surreal'' Pontrjagin classes leads to the existence of rationally non-trivial homotopy classes in BDiff(D^n). For any smooth n-manifold M, extension by the identity induces a map BDiff(D^n) \to BDiff(M). In this talk I will report on joint work with Wolfgang Steimle and Thomas Schick, where we consider the problem of computing the image of the `Weiss classes'' under the maps on homotopy and homology induced by extension. This problem naturally leads one to consider relative kappa-classes. Via relative kappa-classes, we show that the maps induced by extension are rationally non-trivial for a wide class of manifolds M, including aspherical manifolds (homology, hence also homotopy) and stably parallelisable manifolds (homotopy). When M is aspherical, our arguments rely on vanishing results for kappa-classes due to Hebestreit, Land, Lueck and Randal-Williams. INI 1