Forthcoming Seminars › Seminar Series

Number Theory Seminar

Thu, 16/10/2008
16:00 		Jimi Truelsen (Aarhus and Oxford) Number Theory Seminar Add to calendar L3
"Quantitative mass equidistribution for Eisenstein series on $ GL_2 $"
Thu, 23/10/2008
16:00 		Nic Niedermowwe (Oxford) Number Theory Seminar Add to calendar L3
The circle method with weights and Tschinkel's problem
We show how the circle method with a suitably chosen Gaussian weight can be used to count unweighted zeros of polynomials. Tschinkel's problem asks for the density of solutions to Diophantine equations with S-unit and integral variables.
Thu, 30/10/2008
16:00 		Tejaswi Navilarekallu (Amsterdam) Number Theory Seminar Add to calendar L3
"Galois action on L-values"
Thu, 06/11/2008
16:00 		David Solomon (Kings College London) Number Theory Seminar Add to calendar L3
"Annihilating Ideals for Class Groups of Number Fields"
"Stickelberger's famous theorem (from 1890) gives an explicit ideal which annihilates the imaginary part of the class group of an abelian field as a module for the group-ring of the Galois group. In the 1980s Tate and Brumer proposed a generalisation of Stickelberger's Theorem (and his ideal) to other abelian extensions of number fields, the so-called `Brumer-Stark conjecture'. I shall discuss some of the many unresolved issues connected with the annihilation of class groups of number fields. For instance, should the (generalised) Stickelberger ideal be the full annihilator, the Fitting ideal or what? And what can we say in the plus part (where Stickelberger's Theorem is trivial)?"
Thu, 13/11/2008
16:00 		Oscar Marmon (Chalmers University of Technology) Number Theory Seminar Add to calendar L3
On the density of solutions to Diophantine equations.
In a paper from 1994, 'The density of rational points on non-singular hypersurfaces', Heath-Brown developed a `multi-dimensional q-analogue' of van der Corput's method of exponential sums, giving good bounds for the density of solutions to Diophantine equations in many variables. I will discuss this method and present some generalizations.
Thu, 20/11/2008
16:00 		Kira Samol (Mainz) Number Theory Seminar Add to calendar L3
"Frobenius polynomials for Calabi-Yau equations"
Thu, 27/11/2008
16:00 		David Masser (Basel) Logic Seminar Add to calendar
Number Theory Seminar Add to calendar 		L3
Linear equations over multiplicative groups in positive characteristic, sums of recurrences, and ergodic mixing
Solving completely $ x+y-z=1 $ in unknowns taken from the group generated by a variable $ t $ with $ 1-t $ over a finite field is not so easy as might be expected. We present a generalization to arbitrary linear varieties and finitely generated groups (keywords effective Mordell-Lang). We also mention applications to (a) solving equations like $ u_n+v_m+w_l+f_k=0 $ in $ n,m,l,k $ for given recurrences $ u,v,w,f $; and to (b) finding the smallest order of non-mixing of a given algebraic $ {\bf Z}^s $-action. This is joint work with Harm Derksen.
Thu, 04/12/2008
16:00 		Trevor Wooley (Bristol) Number Theory Seminar Add to calendar L3
Exceptional sets for Diophantine inequalities
We report on work joint with Scott Parsell in which estimates are obtained for the set of real numbers not closely approximated by a given form with real coefficients. "Slim" technology plays a role in obtaining the sharpest estimates.

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

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