School of Mathematics

Taking up the terminology established in the first lecture, in 1970 Grothendieck showed that when two groups (G,H) form a Grothendieck pair, there is an equivalence of their linear representations. For recent work showing that certain groups are...

The incompressible 3D Euler equations have total kinetic energy conservation for smooth (spatially periodic) solutions. In the recent resolution of the Onsager conjecture by Isett, on the other hand, below certain threshold Hölder regularity, Euler...

I will explain a construction of a Legendrian version of embedded contact homology (ECH) for a sutured contact manifold Y along with a collection of Legendrians L contained in the boundary. The chain complex is generated by sets of Reeb orbits and...

I will discuss some questions of interest in neuroscience, seen through the lens of mathematics. No prior knowledge of neuroscience is needed for this talk. Two of the most basic visual capabilities of primates are orientation selectivity, i.e., the...

The degree mantra states that any non-zero univariate polynomial of degree at most d has at most d roots (counted with multiplicity). A generalization of this to the multivariate setting, proved by Dvir-Kopparty-Saraf-Sudan asserts that over any...

If a monomorphism of abstract groups H↪G induces an isomorphism of profinite completions, then (G,H) is called a Grothendieck pair, recalling the fact that Grothendieck asked about the existence of such pairs with G and H finitely presented and...

The classification of geometric structures on manifolds naturally leads to actions of automorphism groups, (such as mapping class groups of surfaces) on "character varieties" (spaces of equivalence classes of representations of surface groups).