eilbeck-ws15

Contact

Carl von Ossietzky Universität Oldenburg
Institut für Mathematik
26111 Oldenburg
olcrypt@uol.de

Contact

Carl von Ossietzky Universität Oldenburg
Institut für Mathematik
26111 Oldenburg
olcrypt@uol.de

Coordinators

Prof. Dr. Florian Hess
florian.hess@uol.de
Phone: +49 (0) 441 798-2906


Prof. Dr. Andreas Stein
andreas.stein@uol.de
Phone: +49 (0) 441 798-3232

eilbeck-ws15

Talk

Chris Eilbeck (Heriot-Watt University)

10.12.2015 - W01 0-012 (Wechloy), 16 Uhr c.t.

Generalizations of the Weierstrass sigma function, discriminants, and heat equations

Abstract: The solutions of many interesting nonlinear wave equations can be written down in terms of Weierstrass $\wp$ functions and their generalizations to higher genus. In turn the $\wp$ functions are just the 2nd logarithmic derivatives of a entire function, the Weierstrass $\sigma$ function generalized to genus $g$. We discuss the properties of the $\sigma$ function associated with a plane curve of genus $g$. These functions satisfy sets of interesting linear parabolic PDEs. These PDEs can be used to form linear but complicated recurrence relations for the coefficients of the sigma expansion. A connection with the discriminant of the associated curve is also highlighted.

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