Termine

Markus Stroppel will give a lecture series on advanced topics in locally compact groups. The lectures take place on Monday at 14:15 in room SR 1D They will start on Monday, November 17. The planned topics are: * the scale function and tidy subgroups * automorphism groups of trees

Abstract: An E_1 Calabi-Yau object A in a symmetric monoidal infinity-category C is a dualizable E_1 algebra together with an S^1-cyclic trace that exhibits a self duality of A. Examples include the cochain complex of any closed oriented manifold. By work of Barkan and Steinebrunner, every E_1 Calabi-Yau object in C defines a 2-d open field theory with values in C, which are symmetric monoidal functors from the open bordism category on disks to C. In joint work with Barkan and Steinebrunner, we show that any open field theory F extends canonically to an open-closed field theory whose value at the circle is the THH of the E_1 Calabi-Yau object A associated to F. As a corollary, we obtain an action of the moduli spaces of surfaces on the THH of E_1 Calabi-Yau algebras. This provides a space level refinement of previous work of Costello (over Q) and Wahl (over Z). Time permitting, I will discuss ongoing work with Andrea Bianchi on canonical local to global extensions of TFTs associated with E_\infty Calabi-Yau objects.

I will review some classical examples of groups whose strictly descending chains of subgroups are finite. Some recent constructions of such groups (having large cardinality) will also be explained. Set-theoretic consistency will play a role in some of the stated results. This is joint work with Saharon Shelah.

In this talk, we study the rigidity properties of a differential inclusion in linearized elasticity. We will introduce and discuss a set K of three diagonal strains that are pairwise incompatible but with non-trivial (symmetrized) rank-1-convex hull. This is called a T3 structure. We first prove that K is rigid at the level of exact solutions, namely that Lipschitz maps whose gradient is locally in K must be affine. After this, we study the scaling behaviour of the corresponding singularly-perturbed elastic energy, giving quantitative information on the flexibility of K in the sense of approximate solutions. This is based on a joint work with R. Indergand, D. Kochmann, A. Rüland, and C. Zillinger.

Kolloquium über Geschichte und Didaktik der Mathematik

The space of elastic curves is an infinite-dimensional Banach space equipped with a Riemannian metric. Using a global Isometry the space can be better understood and geodesics can be computed.