Previous Conferences & Workshops

We shall discuss two new results concerning gauge-theoretic invariants of "standard" four-manifolds, namely closed, connected, four-dimensional, orientable, smooth manifolds with \(b^1 = 0\) and \(b^+ \geq 3\) and odd. We first describe how the SO(3...

We construct a new Euler system from a collection of special 1-cycles on certain Shimura 3-folds associated to \(U(2,1) \times U(1,1)\) and appearing in the context of the Gan--Gross--Prasad conjectures. We study and compare the action of the Hecke...

What are the possible Hodge numbers of a smooth complex projective variety? We construct enough varieties to show that many of the Hodge numbers can take all possible values satisfying the constraints given by Hodge theory. For example, there are...

I will explain how infinite sequences of flops give rise to some interesting phenomena: first, an infinite set of smooth projective varieties that have equivalent derived categories but are not isomorphic; second, a pseudoeffective divisor for which...

Beauville and Voisin proved that decomposable cycles (intersections of divisors) on a projective K3 surface span a 1-dimensional subspace of the (infinite-dimensional) group of 0-cycles modulo rational equivalence. I will address the following...

Report on R. Virk's arXiv:1406.4855v3. This is a fun, short and simple note with variations on the well-known theme by G. Laumon that the Euler characteristics with and without compact supports coincide.

Monotone submodular maximization over a matroid (MSMM) is a fundamental optimization problem generalizing Maximum Coverage and MAX-SAT. Maximum Coverage is NP-hard to approximate better than \(1-1/e\), an approximation ratio obtained by the greedy...

My talk will be a broad introduction to what is the (mostly conjectural) higher dimensional generalization of Abel's theorem on divisors on Riemann surfaces, namely, the relationship between the structure of the group of algebraic cycles on a...