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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