GÖRAN
GUSTAFSSON Lectures in Mathematics
Enrico Bombieri Abstracts: |
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Lecture 1: From Dirichlet and Riemann to random matrices The first lecture will give a quick review of history, including some not so well-known facts, ending with a review of the analytic properties, some known and many conjectural, of the zeta function. It ends with the modern conjectures based on the theory of random matrices.
Lecture 2: The Rosetta Stone of L-functions The second lecture will present a review of the three basic ways of contructing L-functions, namely analytic (i.e.automorphic), geometric (i.e. motivic), algebraic (i.e. Galois representations), starting with the simplest examples.
Lecture 3: The explicit formula and the Riemann Hypothesis for curves over finite fields The third lecture begins with Riemann's formula for counting primes and its modern extensions and continues with the parallel theory for the zeta functions of curves over a finite fields, ending with the shortest elementary proof of the Riemann Hypothesis for curves over a finite field (Weil's theorem). |
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Sponsored by the Göran Gustafsson Foundation 2011-05-20 |