Previous Special Year Seminar

The non-orientable genus (a.k.a crosscap number) of a knot is the smallest genus over all non-orientable surfaces spanned by the knot. In this talk, I’ll describe joint work with Christine Lee, in which we obtain two-sided linear bound of the...

We will discuss methods of decomposing knot and link complements into polyhedra. Using hyperbolic geometry, angled structures, and normal surface theory, we analyze geometric and topological properties of knots and links.

Given a trivalent graph embedded in 3-space, we associate to it an instanton homology group, which is a finite-dimensional $\mathbf{Z}/2$ vector space. The main result about the instanton homology is a non-vanishing theorem, proved using techniques...

Given a trivalent graph embedded in 3-space, we associate to it an instanton homology group, which is a finite-dimensional $\mathbf{Z}/2$ vector space. The main result about the instanton homology is a non-vanishing theorem, proved using techniques...

Given a variety $Y$ with a rectangular Lefschetz decomposition of its derived category, I will discuss an interesting relation between the derived categories of a cyclic cover of $Y$ and its branch divisor. As examples, I will describe the cases of...

Let $R$ be a regular semi-local domain, containing a field. Let $G$ be a reductive group scheme over $R$. We prove that a principal $G$-bundle over $R$ is trivial, if it is trivial over the fraction field of $R$. If the regular semi-local domain $R$...

I will try to tell the story of the projective line minus three points from the point of view of periods, and if time permits, discuss some open problems.

This is joint work with G .Garkusha. Using the machinery of framed sheaves developed by Voevodsky, a triangulated category of framed motives is introduced and studied. To any smooth algebraic variety $X$, the framed motive $M_{fr}(X)$ is associated...

Starting from an example in which the Hitchin correspondence can be written down explicitly, we look at what might be said relating the incidence complex of the boundary of the character variety, and the Hitchin map.

I will try to tell the story of the projective line minus three points from the point of view of periods, and if time permits, discuss some open problems.