We motivate the study of metric spaces with a unique convex geodesic bicombing, which we
call CUB spaces. These encompass many classical notions of nonpositive curvature, such …

A bstract We study 3D pure Einstein quantum gravity with negative cosmological constant, in
the regime where the AdS radius l is of the order of the Planck scale. Specifically, when the …

We prove that the hyperelliptic Torelli group is generated by Dehn twists about separating
curves that are preserved by the hyperelliptic involution. This verifies a conjecture of Hain …

We prove that satellite operations that satisfy a certain positivity condition and have winding
number other than one are not homomorphisms. The argument uses the $ d $-invariants of …

We give a new proof of a celebrated theorem of Dennis Johnson that asserts that the kernel
of the Johnson homomorphism on the Torelli subgroup of the mapping class group is …

For k≥ 1, let ℐ g 1 (k) be the k th term in the Johnson filtration of the mapping class group of
a genus g surface with one boundary component. We prove that for all k≥ 1, there exists …

These are lecture notes for a series of talks at the 2019 TASI school. They contain
introductory material to the general subject of Chern-Simons theory. They are meant to be …

We show that the smallest noncyclic quotients of braid groups are symmetric groups, proving
a conjecture of Margalit. Moreover, we recover results of Artin and Lin about the …

For any surface† of infinite topological type, we study the Torelli subgroup I.†/of the mapping
class group MCG.†/, whose elements are those mapping classes that act trivially on the …

Let ℐ g,* denote the Torelli group of the genus g≥ 2 surface S g with one marked point. This
is the group of homotopy classes (rel basepoint) of homeomorphisms of S g fixing the …