Number Theory Seminar
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Thu, 14/10/2010 16:00 |
Dr S Siksek (Dept. Mathematics, University of Warwick) |
Number Theory Seminar  |
L3 |
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Let C be a smooth plane cubic curve over the rationals. The Mordell--Weil Theorem can be restated as follows: there is a finite subset B of rational points such that all rational points can be obtained from this subset by successive tangent and secant constructions. It is conjectured that a minimal such B can be arbitrarily large; this is indeed the well-known conjecture that there are elliptic curves with arbitrarily large ranks. This talk is concerned with the corresponding problem for cubic surfaces. |
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Thu, 21/10/2010 16:00 |
Dr A Gorodnik (Bristol) |
Number Theory Seminar |
L3 |
| Given a polynomial function f defined on a variety X, we consider two questions, which are non-commutative analogues of the Prime Number Theorem and the Linnik Theorem: - how often the values of f(x) at integral points in X are almost prime? - can one effectively solve the congruence equation f(x)=b (mod q) with f(x) being almost prime? We discuss a solution to these questions when X is a homogeneous variety (e.g, a quadratic surface). | |||
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Thu, 28/10/2010 16:00 |
Dr M. Belolipetsky (University of Durham) |
Number Theory Seminar |
L3 |
| While studying growth of lattices in semisimple Lie groups we encounter many interesting number theoretic problems. In some cases we can show an equivalence between the two classes of problems, while in the other the true relation between them is unclear. On the talk I will give a brief overview of the subject and will then try to focus on some particularly interesting examples. | |||
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Thu, 04/11/2010 16:00 |
Dr A. Diaconu (University of Durham) |
Number Theory Seminar |
L3 |
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Thu, 11/11/2010 16:00 |
Roger Heath-Brown (Oxford) |
Number Theory Seminar |
L3 |
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Thu, 18/11/2010 16:00 |
Dr S Zwegers (University College, Dublin) |
Number Theory Seminar |
L3 |
| We consider certain q-series depending on parameters (A,B,C), where A is a positive definite r times r matrix, B is a r-vector and C is a scalar, and ask when these q-series are modular forms. Werner Nahm (DIAS) has formulated a partial answer to this question: he conjectured a criterion for which A's can occur, in terms of torsion in the Bloch group. For the case r=1, the conjecture has been show to hold by Don Zagier (MPIM and CdF). For r=2, Masha Vlasenko (MPIM) has recently found a counterexample. In this talk we'll discuss various aspects of Nahm's conjecture. | |||
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Thu, 25/11/2010 16:00 |
Dr J. Markloff (Bristol) |
Number Theory Seminar |
L3 |
