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Speaker:
Alexander Buium
Affiliation:
U. of New Mexico/MPI
Date:
Wed, 2012-07-04 14:15 - 15:15
Location:
MPIM Lecture Hall
Parent event:
Number theory lunch seminar We develop an arithmetic analogue of linear partial differential equations in 2 independent "space-time" variables.
The spatial derivative is a Fermat quotient operator while the time derivative is a usual derivation. This allows
one to "flow" points in algebraic groups with coordinates in rings with arithmetic flavor. In particular we show
that elliptic curves possess certain canonical ``arithmetic flows" which are analogous to the convection, heat,
and wave equations. Canonical convection and heat (but no wave) equations also exist on modular curves;
the latter can be viewed as "unifying" Fourier and Serre-Tate expansions of modular forms.
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