## Contact Info

Pure MathematicsUniversity of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x33484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

The Pure Math colloquium is held roughly every other week during the fall and winter terms. The talks are at 4:00 pm on Mondays in the Math and Computer Building (MC) 5501, and are preceded by refreshments with the speaker at 3:30 pm in MC 5403.

**Monday, February 27th**

**Trevor Wooley, University of Bristol **

“A translation-invariant perspective on arithmetic (and) harmonic analysis”

We learn about translation-invariance at mathematical birth. Thus, given a three-term arithmetic progression, such as 10, 20, 30, we learn that one can obtain another such progression by shifting every entry by the same integer, as in the triple 17, 27, 37. Very recently, a method has emerged that applies non-linear translation-invariant equations to analyse Fourier series having polynomial arguments (such as Weyl sums) – the p-adic or congruence based version of this method is known as efficient congruencing, while the real interval based version is the decoupling method of Bourgain, Demeter and Guth. There are many circumstances in which this method achieves the best possible estimates, with consequent applications of Diophantine type such as Waring’s problem, equidistribution of polynomial sequences modulo one, and discrete Fourier restriction problems. In this talk, while we outline the underlying ideas, we emphasise applications. We will discuss and speculate concerning as many different problems as time permits.

Here is an archive of past colloquia.

University of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x33484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

University of Waterloo

University of Waterloo

43.471468

-80.544205

200 University Avenue West

Waterloo,
ON,
Canada
N2L 3G1