Activities

Conferences attended

Generally, I identify as a problem solver rather than a theory builder, and all of my papers are in some way explicitly motivated by a particular problem. I find the easiest way to become acquainted with a new area of mathematics is to pick a problem and work on it for a while. Here is a nonexhaustive list of problems that I have devoted a reasonable amount of time (at least a few days) in the past and the author. If you manage to solve them or are interested in working with me on one, I would be delighted to know!

1. Is every n-connected X that is formal rationally formal over F_p as an E_n-algebra (Mandell) [I initially started the p-adic de Rham complex paper as a failed attempt to resolve this problem]
2. What functors have a final coalgebra sequence that converges in \omega+\omega steps in Met and Ab (Ademek, Milius and Moss) [We solved the second but not the first]
3. Does every Heyting algebra arise as Sub(1) of a topos? (Pitts)
4. Are there integers greater than 42 such that the partition function p(n) divides n! ? (Heffernan and MacHale) [Probably no for statistical reasons]
5. Are there triples (n, n+1, n+2) such that (A_F(n), A_F(n+1), A_F(n+2)) are all integral? (Luca and Marques) [Probably no for statistical reasons]
6. Are there two-point selections on the real line that where the induced sigma algebra coincides with the Lesbague measurable sets? (Salvador García-Ferreira) [The homotopy type of two point selections is something I would like to explore, but not helpful here!]
7. Let X be a connected space (homotopy type), and LX its free loop space. Can LX be finitely dominated without X being contractible ? (Maxime Ramzi) [V. Saunier and I think we have a possible method to do this modulo future developments in group theory]
8. The Hadamard conjecture.
9. Is there a nice complex that computes the homology of Perm (Tamaroff)?