Date  Speaker  Title (click for abstract) 
Sep. 1st  No seminar 

Sep. 8th  No seminar  Run Monday schedule

Sep. 15th  Yanwen Luo (Rutgers)  The space of geodesic triangulations on surfaces

Sep. 22nd  Dragomir Saric (CUNY)  The Heights theorem for integrable quadratic differentials on infinite Riemann surfaces

Sep. 29th  Tian Yang (TAMU)  A relative version of the TuraevViro
invariants and hyperbolic polyhedral metrics

Oct. 6th  No seminar 

Oct. 13th  Lvzhou Chen (UT Austin)  Stable commutator lengths of integral chains in rightangled Artin groups

Oct. 20th  Shaosai Huang (University of Wisconsin Madison)  Topological rigidity of the first Betti number and Ricci flow smoothing

Oct. 27th  Ryan Spitler (McMaster) 

Nov. 3rd  Jiayin Pan (UCSB) 

Nov. 10th  HuaiDong Cao (Lehigh University) 

Nov. 17th  Michael Landry (WUSTL) 

Nov. 24th  No Seminar  Happy Thanksgiving!

Dec. 1st  Tye Lidman (North Carolina State University) 

Dec. 8th 

Date  Speaker  Title (click for abstract) 
Jan. 19th  No seminar 

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Feb. 23rd 


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March 9th 


March 16th  No Seminar  Spring break!

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April 27th 

The space of geodesic triangulations on surfacesIn 1959, Smale showed that the group of diffeomorphisms of the closed 2disk which are identity on the boundary is a contractible space. In 1984, Bloch, Connelly, and Henderson proved the discrete version of this theorem: the space of simplexwise linear homeomorphisms of a convex polygon is contractible. 
The Heights theorem for integrable quadratic differentials on infinite Riemann surfacesAn integrable holomorphic quadratic differential on a Riemann surface induces a measured foliation of the surface by horizontal trajectories. A quadratic differential associates to each homotopy class of a closed curve its height, i.e.the infimum of the transverse measure over the homotopy class. Marden and Strebel proved that the space of quadratic differentials is in a one to one correspondence to the heights maps when the Riemann surface is of parabolic type. 
A relative version of the TuraevViro invariants and hyperbolic polyhedral metricsWe define a relative version of the TuraevViro invariants for an ideally triangulated compact 3manifold with nonempty boundary and a coloring on the edges, and propose the Volume Conjecture for these invariants whose asymptotic behavior is related to the volume of the manifold in the hyperbolic polyhedral metric with singular locus the edges and cone angles determined by the coloring. As the main result of this talk, we prove the conjecture in the case that the cone angles are sufficiently small. This suggests an approach of solving the Volume Conjecture for the TuraevViro invariants of hyperbolic 3manifold with totally geodesic boundary. 
Stable commutator lengths of integral chains in rightangled Artin groupsThe stable commutator length (scl) is an invariant for group elements, and it carries topological and dynamical information. Topologically, an integral 1chain in a group G is a formal sum of loops in the K(G,1) space, and its scl is the least complexity of surfaces bounding the union of these loops. Aiming for effective lower bounds of the index of special subgroups (say in hyperbolic 3manifold groups), we give lower bounds for scl of integral chains in rightangled Artin groups (RAAGs) and rightangled Coxester groups (RACGs). We show that the infimal positive scl of integral chains in any RAAG/RACG is positive, and its size explicitly depends on the defining graph of the RAAG/RACG up to a multiplicative constant 12. In particular, the size is nonuniform among RAAGs/RACGs, but it is uniform among *hyperbolic* RACGs. If time permits, I will also explain a connection between scl in RAAGs and the socalled fractional stability number of graphs. This is joint work with Nicolaus Heuer. 
Topological rigidity of the first Betti number and Ricci flow smoothingThe infranil fiber bundle is a typical structure appeared in the collapsing geometry with bounded sectional curvature. In this talk, I will discuss a topological condition on the first Betti numbers that guarantees a torus fiber bundle structure (a special type of infranil fiber bundle) for collapsing manifolds with only Ricci curvature bounded below. The main technique applied here is smoothing by Ricci flows. This covers my joint with Bing Wang. 