Quebec Mathematical Sciences Colloquium

April 17, 2009 from 16:00 to 18:00 (Montreal/Miami time) On location

Arithmetic Laplacian

Colloquium presented by Alexandru Buium (University of New Mexico)

We develop an arithmetic analogue of elliptic partial differential equations. The role of the space coordinates is played by a family of primes, and that of the space derivatives along the various primes are played by corresponding Fermat quotient operators subjected to certain commutation relations. This leads to arithmetic linear partial differential equations on algebraic groups that are analogues of certain operators in analysis constructed from Laplacians. We classify all such equations on one dimensional groups, in particular on elliptic curves, and analyze their spaces of solutions.


Room 6214, Pavillon André Aisenstadt, 2920 ch. de la Tour, Université de Montréal