Past Junior Number Theory Seminar

19 November 2007
15:00
Abstract
Defined in terms of $\zeta(\frac{1}{2} +it)$ are the Riemann-Siegel functions, $\theta(t)$ and $Z(t)$. A zero of $\zeta(s)$ on the critical line corresponds to a sign change in $Z(t)$, since $Z$ is a real function. Points where $\theta(t) = n\pi$ are called Gram points, and the so called Gram's Law states between each Gram point there is a zero of $Z(t)$, and hence of $\zeta(\frac{1}{2} +it)$. This is known to be false in general and work will be presented to attempt to quantify how frequently this fails.
  • Junior Number Theory Seminar
12 November 2007
15:00
Abstract
I will review the construction of algebraic de Rham cohomology, relative de Rham cohomology, and the Gauss-Manin connection. I will then show how we can find a basis for the cohomology and the matrix for the connection with respect to this basis for certain families of curves sitting in weighted projective spaces.
  • Junior Number Theory Seminar

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