Junior Number Theory Seminar
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Mon, 17/01/2011 16:00 |
Lillian Pierce (Oxford) |
Junior Number Theory Seminar  |
SR1 |
| An old conjecture of Hardy and Littlewood posits that on average, the number of representations of a positive integer N as a sum of k, k-th powers is "very small." Recently, it has been observed that this conjecture is closely related to properties of a discrete fractional integral operator in harmonic analysis. This talk will give a basic introduction to the two key problems, describe the correspondence between them, and show how number theoretic methods, in particular the circle method and mean values of Weyl sums, can be used to say something new in abstract harmonic analysis. | |||
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Mon, 31/01/2011 16:00 |
Frank Gounelas (Oxford) |
Junior Number Theory Seminar |
SR1 |
| The main aim of this talk will be to present a proof of the Tsen-Lang theorem on the existence of points on complete intersections and sketch a proof of the Grabber-Harris-Starr theorem giving the existence of a section to a fibration of a rationally connected variety over a curve. Time permitting, recent work of de Jong and Starr on rationally simply connected varieties will be discussed with applications to the number theory of hypersurfaces. | |||
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Mon, 07/02/2011 16:00 |
Damiano Testa (Oxford) |
Junior Number Theory Seminar |
SR1 |
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Mon, 14/02/2011 16:00 |
Johan Bredberg (Oxford) |
Junior Number Theory Seminar |
SR1 |
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Mon, 21/02/2011 16:00 |
James Maynard (Oxford) |
Junior Number Theory Seminar |
SR1 |
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Mon, 28/02/2011 16:00 |
Markus Hanselmann (Oxford) |
Junior Number Theory Seminar |
SR1 |
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Mon, 07/03/2011 16:00 |
Alastair Irving (Oxford) |
Junior Number Theory Seminar |
SR1 |
