Previous Conferences & Workshops

We present several classification results for Lagrangian tori, all proven using the splitting construction from symplectic field theory. Notably, we classify Lagrangian tori in the symplectic vector space up to Hamiltonian isotopy; they are either...

I'll outline recent results with Steven Sivek classifying the Stein fillings, up to topological homotopy equivalence, of the canonical contact structure on the unit cotangent bundle of a surface. The proof begins with Li, Mak and Yasui's technology...

A covering space $C \\to M$ is classified by a subgroup of the fundamental group of $M$. If we refuse to choose a basepoint, then $C \\to M$ is equivalent to a functor from the fundamental groupoid of $M$ to $\\mathsf{Set}$. Suppose $(M,S)$ is a...

The conventional perturbative approach and the nonperturbative lattice approach are the two standard yet very distinct formulations of quantum gauge theories. Since in dimension two Yang-Mills theory has a rigorous continuum limit of the lattice...

This talk will be about some phenomena that occur as (singular) hyperbolic structures on 3-manifolds collapse to and transition through other geometric structures. Typically, the collapsed structures are much more flexible than the hyperbolic...

We prove an average-case depth hierarchy theorem for Boolean circuits over the standard basis of AND, OR, and NOT gates. Our hierarchy theorem says that for every $d \geq 2$, there is an explicit $n$-variable Boolean function $f$, computed by a...

One way to construct new 3-manifolds is by surgery on a knot in the 3-sphere; that is, we remove a neighborhood of a knot, and reglue it in a different way. What 3-manifolds can be obtained in this manner? We provide obstructions using the Heegaard...

We prove an average-case depth hierarchy theorem for Boolean circuits over the standard basis of AND, OR, and NOT gates. Our hierarchy theorem says that for every $d \\geq 2$, there is an explicit $n$-variable Boolean function $f$, computed by a...

We will describe how to get almost toric fibrations for all del Pezzo surfaces (endowed with monotone symplectic form), in particular for $\\mathbb{CP}^2\\#k\\overline{\\mathbb{CP}}^2$ for $4\\le k \\le 8$, where there is no toric fibrations. From...