Previous Conferences & Workshops

In the second half of the 19th century, it was discovered that algebra and geometry had nothing to do with each other. I will discuss this fact and some consequences.

Solitons are particle-like solutions to dispersive evolution equations whose shapes persist as time evolves. In some situations, these solitons appear due to the balance between nonlinear effects and dispersion, in other situations their existence...

The "intersectivity lemma" states that if a ∈ (0,1) and A_n, n ∈ N,  are measurable sets in a probability space (X,m) satisfying  m(A_n) ≥ a for all n, then there exist a subsequence n_k, k ∈ N, which has positive upper density and such that the...

It is an open question as to whether the prime numbers contain the sum A+B of two infinite sets of natural numbers A, B (although results of this type are known assuming the Hardy-Littlewood prime tuples conjecture).  Using the Maynard sieve and the...

In this talk, I'll first give a broad overview of the history of combinatorial auctions within TCS, and then discuss some recent results.

Combinatorial auctions center around the following problem: There is a set M of m items, and N of n bidders...

In this talk, I will specify a Turing machine T and prove the following about it. 1. On input C/K a smooth projective hyperbolic curve over a number field, if T halts, then its output is C(K). 2. The Hodge, Tate, and Fontaine-Mazur conjectures imply...

The Lefschetz property is central in the theory of projective varieties, detailing a fundamental property of their Chow rings, essentially saying that the multiplication with a geometrically motivated class is of full rank.

We drop the keyword...

Let K be a convex body in $R^n$. In some cases (say when K is a cube), we can tile $R^n$ using translates of K. However, in general (say when K is a ball) this is impossible. Nevertheless, we show that one can always cover space "smoothly" using...

We prove that at least 2/21 of all integers can be written as a sum of two rational cubes, and at least 1/6 of all integers cannot. More generally, in any cubic twist family of elliptic curves, at least one 1/6 of curves have rank 0 and at least 1/6...