Convergence of Ricci flows with bounded scalar curvature, Richard Bamler.
It is a basic fact that the Riemannian curvature becomes unbounded at every finitetime singularity of the Ricci flow. Sesum showed that the same is true for the Ricci curvature. It has since remained a conjecture whether also the scalar curvature becomes unbounded at any singular time.
In this talk I will show that, given a uniform scalar curvature bound, the Ricci flow can only degenerate on a set of codimension bigger or equal to 4, if at all. This result is a consequence of a structure theory for such Ricci flows, which relies on and generalizes recent work of Cheeger and Naber.

Certifying the Thurston norm via SL(2, C)twisted homology, Ian Agol.
We study when the Thurston norm is detected by twisted Alexander
polynomials associated to representations of the 3manifold group to
SL(2,C). Specifically, we show that the hyperbolic torsion polynomial
determines the genus for a large class of hyperbolic knots in the
3sphere which includes all special arborescent knots and many knots
whose ordinary Alexander polynomial is trivial. This theorem follows
from results showing that the tautness of certain sutured manifolds
can be certified by checking that they are a product from the point of
view of homology with coefficients twisted by an SL(2,
C)representation.

Notions of differential calculus on metric measure spaces, Nicola Gigli.
I shall discuss in which sense generic metric measure spaces possess a weak firstorder differential structure. Building on this, I will then turn to spaces with Ricci curvature bounded from below and illustrate how a secondorder calculus can be built on them. In particular, concepts like Hessian, covariant derivative and Ricci curvature will all be well defined.

Algebraic degrees of pseudoAnosov stretch factors, Balazs Strenner.
Consider a mapping of the torus that stretches and compresses it in
two directions. (These are called Anosov maps.) The lift of such a map
to the universal cover is the action of a matrix in SL(2,Z) on the
plane and the stretch factor is an eigenvalue of the matrix. Therefore
only quadratic algebraic integers can be stretch factors of the torus.
For higher genus surfaces, the topology of the surface still imposes
constraints on the possible algebraic degrees of the stretch factors,
but now a wider variety of degrees may appear. In this talk, I will
explain a construction that realizes stretch factors of all possible
degrees.

On growth of iterated monodromy groups: a geometric point of view, Misha Hlushchanka.
Iterated monodromy group (IMG) is a selfsimilar group associated to every branched covering f of the 2sphere (in particularly to every rational map). It was observed that even very simple maps generate groups with complicated structure and exotic properties which are hard to find among groups defined by more classical methods. For instance, IMG(z^2+i) is a group of intermediate growth and IMG(z^21) is an amenable group of exponential growth. Unfortunately, we still face a lack of general theory which would unify and explain these nice examples.
In the talk I will first make a detour to the theory of growth of groups and overview the current state of studies of algebraic properties of IMGs. Then I will concentrate on a specific example of a rational map, whose Julia set is given by the whole Riemann sphere, and prove that its IMG has exponential growth. The proof is based on the Geometry of the tilings associated to the map. This is a joint project with Mario Bonk and Daniel Meyer.
