School of Mathematics

The double bubble plumbing, first studied by Smith and Wemyss, is a Stein neighborhood of two Lagrangian 3-spheres intersecting cleanly along an unknotted circle in some 6-dimensional symplectic manifold. Depending on the identification of the...

How many algebraic integers of bounded height have a minimal polynomial with a given Galois group? One approach to this problem is via Malle's conjecture. In this talk we will discuss an alternative approach using a construction with the Galois...

A real plane algebraic curve C is called expressive if its defining polynomial has the smallest number of critical points allowed by the topology of the set of real points of C. We give a necessary and sufficient criterion for expressivity (subject...

We present a combinatorial approach to the Deligne-Mumford-Knudsen compactification of the moduli space of n distinct points on the projective line P1. The idea is to choose a totally symmetric embedding of the orbits of generic points into a high...

We show that various classical theorems of linear incidence geometry, such as the theorems of Pappus, Desargues, Möbius, and so on, can be interpreted as special cases of a general result that involves a tiling of a closed oriented surface by...

The Boone-Higman conjecture (1973) predicts that a finitely generated group has solvable word problem if and only if it embeds in a finitely presented simple group. The "if" direction is true and easy, but the "only if" direction has been open for...

Parallels between elliptic and parabolic theory of partial differential equations have long been explored. In particular, since elliptic theory can be seen as a steady-state version of parabolic theory, if a parabolic estimate holds, then by...

In this talk we discuss a relation between the contact version

of the Hofer norm and positive loops of contactomorphisms.

This leads to a new criterion for the existence of contractible positive

loops in terms of open book decompositions and previously...

For every finite set of points in the plane, if every line going through any two of them contains a third, then they all lie on a single line. This ``local-to-global" theorem (which you can play with proving)  has many generalizations, to higher...

I will explain how several different moduli spaces of bundles on a smooth projective curve have abelian motives. Our starting point is a formula for the motive of the stack of vector bundles on the curve in Voevodsky's category of motives with...