Past Events
A set of integers greater than 1 is primitive if no member in the set divides another. Erdős proved in the 1930s that the sum of 1/(a log a), ranging over a in A, is uniformly bounded over all choices of primitive sets A. In the 1980s he asked if this sum is maximized by the set of prime…
In this talk, I will show that for certain one-parameter families of initial conditions in R^3, when we run mean curvature flow, a genus one singularity must appear in one of the flows. Moreover, such a singularity is robust under perturbation of the family of initial conditions. This contrasts…
How is cloth stitching related to mountain climbing? Come to find out!
The world teems with examples of invasion, in which one steady state spatially invades another. Invasion can even display a universal character: fine details recur in seemingly unrelated systems. Reaction-diffusion equations provide a mathematical framework for these phenomena. In this talk, I…
Given a particular flavor of Floer homology, a natural question is to find a space-level upgrade for it, i.e. a naturally-defined (stable) homotopy type whose (co)homology recovers the usual Floer homology. In a series of two papers from 1995, Cohen-Jones-Segal show that one can recover the…
Abstract: We discuss a new, manifestly Poincare invariant, microlocal framework for analyzing propagation of massive waves near null infinity. The approach combines the "sc-calculus" of Parenti--Shubin--Melrose and the "double edge-calculus" of Lauter and Moroianu. One novelty is that spacetimes…
In 2013, Zhang showed that there exists some integer h for which p and p+h are both prime infinitely often. Equidistribution estimates for primes in arithmetic progressions to smooth moduli were a key ingredient of his work. In this talk, I will sketch what role these estimates play in proofs of…
I will talk about the quantum connection in positive characteristic for conical symplectic resolutions, in particular the conjecture of the equivalence of the p-curvature of such connections with (equivariant generalizations of) quantum Steenrod operations of Fukaya and Wilkins. The conjecture…
Prophet inequalities compare the expected performance of a stopping rule to a "prophet" who has complete knowledge of the future. The classical prophet inequality states that for a sequence of nonnegative random variables $X_1,\dots,X_n$ with known distributions, there is a stopping rule which…
We prove the infinitude of shifted primes p-1 without prime factors above p^{0.2844}. This refines p^{0.2961} from Baker and Harman in 1998. Consequently, we obtain an improved lower bound on the distribution of Carmichael numbers. Our main technical result is a new mean value theorem for primes…