SPOTLIGHT
Our Heights workshop took place in February and featured some wonderful talks both from the technical heightmachinery crowd( Kühne, Amoroso, and Wüstholz) and some who used heights in a softer manner to obtain wonderful results on equidistribution( Demarco, Daw, Shankar, etc.). One exceptionally wonderful talk that everyone enjoyed was by Boris Zilber who unveiled some of his new conjectures based on model theory, which try to generalize Zilber-Pink to the finite-field setting. This provided lots of new concrete problems to work on and there was much discussion on this for the rest of the conference.
The workshop on Efficient Congruencing had a variety of talks centered around Vinogradov ' s mean value theorem, exploring both the decoupling approach and the approach with translation-invariant systems, and how they relate.
We were also very lucky to have Umberto Zannier and Robert Vaughan give our Distinguished and Littlewood lecture series respectively. Zannier gave an extremely nice series of talks on the machinery of heights and its evolution over time. These were simultaneously very accessible( he began by carefully defining heights!) yet led to a series of open problems which seemed just out of reach.
The 2017 Littlewood Lecture series was given by Professor Robert Vaughan, FRS on the Hardy-Littlewood method. Vaughan masterfully described the method from every perspective— how it was viewed historically, the various advances which were brought to bear for Vinogradov’ s theorem and Waring’ s Problems, among others, and leading up to the most recent work on the subject. His talks were extremely clear while maintaining an impressively high level of technical precision. �
Robert Vaughan
— Jacob Tsimerman
Umberto Zannier
SPOTLIGHT
SIMON MYERSON is a post-doc from University College London who participated in the“ Unlikely Intersections, Heights, and Efficient Congruencing” Thematic Program. His project at Fields, as well as his other work, is in the field of analytical number theory, which he describes as“ giving rough estimates for the number of solutions to some arithmetic problem.”
“ You might be able to get an extremely unpleasant formula for the exact answer, which isn’ t going to tell you anything very useful, but you might be able to get a very simple, clear formula for the rough answer,” explains Simon. Fermat’ s last theorem( finally proven by Andrew Wiles in 1995) and the twin prime conjecture( still unproven) are two famous examples of analytic number theory problems.
Simon came to Fields hoping to broaden out from what he worked on in his PhD and found that the atmosphere of the Fields Institute was naturally conducive to collaboration.
“ What I’ m working on while [ at Fields ] is actually quite different than what I was working on previously. I’ m collaborating with several of the other post-docs on a couple of projects. One of them is actually something that I was curious about for a while, and it turned out that my office mate at Fields had worked in that area.”
When he’ s not working, you might find Simon expanding his felt rock collection.
“ It turns out that once you’ ve bought one felt rock you can’ t stop. You don’ t see them every day, so now when I see a felt rock I think‘ well I’ m the person who has felt rocks; I am obligated to buy this felt rock.’”
Simon is now back at UCL working on new applications of the circle method to Diophantine problems. �
— Malgosia Ip
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