Past Seminars › Seminar Series

Junior Number Theory Seminar (past)

Mon, 22/04
16:00 		Jan Vonk (Oxford) Junior Number Theory Seminar Add to calendar SR1
The eigencurve
Mon, 04/03
16:00 		Lillian Pierce (Oxford) Junior Number Theory Seminar Add to calendar SR1
A primer on Burgess bounds

We'll present a proof of the basic Burgess bound for short character sums, following the simplified presentation of Gallagher and Montgomery.
Mon, 25/02
16:00 		Paul-James White (undefined) Junior Number Theory Seminar Add to calendar SR1
Studying L-functions via the Trace formula
Mon, 11/02
16:00 		Netan Dogra (Oxford) Junior Number Theory Seminar Add to calendar SR1
TBC
Mon, 28/01
16:00 		James Maynard (Oxford) Junior Number Theory Seminar Add to calendar SR1
Primes represented by polynomials
Mon, 21/01
16:00 		Alastair Irving (Oxford) Junior Number Theory Seminar Add to calendar SR1
Prime Values of Linear Forms
Mon, 14/01
16:00 		Thomas Reuss (Oxford) Junior Number Theory Seminar Add to calendar SR1
An Introduction to the Square Sieve
Mon, 26/11/2012
16:00 		Simon Myerson (Oxford) Junior Number Theory Seminar Add to calendar SR1
Once Upon a Time in Egypt: How the Story of Rational Points Began

A nice bed-time story to end the term. It is often said that ideas like the group law or isogenies on elliptic curves were 'known to Fermat' or are 'found
in Diophantus', but this is rarely properly explained. I will discuss the first work on rational points on curves from the point of view of modern number
theory, asking if it really did anticipate the methods we use today.
Mon, 19/11/2012
16:00 		Thomas Reuss (Oxford) Junior Number Theory Seminar Add to calendar SR1
square-free values of f(p) where f is cubic
Mon, 12/11/2012
16:00 		James Maynard (Oxford) Junior Number Theory Seminar Add to calendar SR1
Sieve weights and the twin prime problem
Mon, 22/10/2012
16:00 		Alastair Irving (Oxford) Junior Number Theory Seminar Add to calendar SR1
An Introduction to Prime Detecting Sieves
Mon, 15/10/2012
16:00 		Lillian Pierce (Oxford) Junior Number Theory Seminar Add to calendar SR1
Simultaneous prime values of pairs of quadratic forms
Given a form $ F(x) $, the circle method is frequently used to provide an asymptotic for the number of representations of a fixed integer $ N $ by $ F(x) $. However, it can also be used to prove results of a different flavor, such as showing that almost every number (in a certain sense) has at least one representation by $ F(x) $. In joint work with Roger Heath-Brown, we have recently considered a 2-dimensional version of such a problem. Given two quadratic forms $ Q_1 $ and $ Q_2 $, we ask whether almost every integer (in a certain sense) is simultaneously represented by $ Q_1 $ and $ Q_2 $. Under a modest geometric assumption, we are able to prove such a result if the forms are in $ 5 $ variables or more. In particular, we show that any two such quadratic forms must simultaneously attain prime values infinitely often. In this seminar, we will review the circle method, introduce the idea of a Kloosterman refinement, and investigate how such "almost all" results may be proved.
Mon, 11/06/2012
16:00 		Jan Vonk Junior Number Theory Seminar Add to calendar SR1
Points on modular curves
Mon, 04/06/2012
16:00 		Alastair Irving Junior Number Theory Seminar Add to calendar SR1
Diophantine Approximation with Primes
Mon, 28/05/2012
16:00 		Frank Gounelas Junior Number Theory Seminar Add to calendar SR1
The congruent number problem
Which positive integers are the area of a right angled triangle with rational sides? In this talk I will discuss this classical problem, its reformulation in terms of rational points on elliptic curves and Tunnell's theorem which gives a complete solution to this problem assuming the Birch and Swinnerton-Dyer conjecture.

For any corrections/updates to these listings, please contact seminars [-at-] maths [dot] ox [dot] ac [dot] uk.

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