May 5, 2022: main talk at 2:00 in SR5 at the MI
Federico Vigolo (University of Münster)
Coarse structures, groups and automorphisms
This talk is an introduction to coarse structures, coarse groups and their automorphisms. Coarse structures provide a general language to study the large scale geometry of spaces, and we may say that coarse groups are spaces with operations that behave like groups on a large scale. This point of view opens multiple lines of research and leads to numerous open questions. Drawing from some analogies among SL(n,Z), Out(F_n) and mapping class groups, in this talk I will especially focus on questions regarding groups of coarse automorphisms.
May 12, 2022: main talk at 2:00 in SR5 at the MI
Kostantinos Tsouvalas (IHES)
Cartan projections of fiber products and non quasi-isometric embeddings
Several important classes of groups are known to admit discrete faithful linear representations which are quasi-isometric embeddings (e.g. Anosov hyperbolic groups and more generally convex co-compact subgroups). In this talk, we will be interested in groups with the opposite behaviour. We are going to exhibit some constructions of linear finitely generated (and presented) subgroups P of direct products of hyperbolic groups, with the property that every linear representation of P (over a local field) cannot be a quasi-isometric embedding. The main tool for the proof is an upper estimate for the norm of the Cartan projection of multiple commutators in direct products.
June 2, 2022
Open Slot
June 23, 2022
Mercator Workshop (Link)
July 7, 2022: main talk at 1:00 in SRB at the MI
Richard Kenyon (Yale University)
Dimers, webs and SL_n local systems
We consider SL_n-local systems on graphs on surfaces and show how the associated Kasteleyn matrix can be used to compute probabilities of various topological events involving the overlay of n independent dimer covers (or “n-webs”). This is joint work with Dan Douglas and Haolin Shi.
July 14, 2022: main talk at 2:00 in SR5 at the MI
Cancelled
July 21, 2022: main talk at 5:00 on Zoom
Karen Butt (University of Michigan)
Quantitative marked length spectrum rigidity
The marked length spectrum of a closed Riemannian manifold of negative curvature is a function on the free homotopy classes of closed curves which assigns to each class the length of its unique geodesic representative. Conjecturally, the marked length spectrum determines the metric up to isometry (Burns--Katok). This is known to be true in some special cases, namely in dimension 2 (Otal, Croke), in dimension at least 3 if one of the metrics is locally symmetric (Hamenstadt, Besson--Courtois--Gallot), and in any dimension if the metrics are assumed to be sufficiently close in a suitable C^k topology (Guillarmou--Knieper--Lefeuvre). Even in these cases, there is more to be understood about to what extent the marked length spectrum determines the metric. Namely, if two manifolds have marked length spectra which are not equal but are close, is there some sense in which the metrics are close to being isometric? In this talk, we will provide some (quantitative) answers to this question, refining the known rigidity results for surfaces and for locally symmetric spaces of dimension at least 3.