Algebra Seminar

Friday, February 5, 2016
1:15 PM - 2:30 PM (ET)
Exley Science Center Tower ESC 618
Event Type
Canalia, Caryn

Michael Wijaya, Dartmouth College: A function-field analogue of Conway's topograph

Abstract: In "The Sensual (Quadratic) Form", Conway introduced a new visual method to display values of a binary quadratic form Q(x,y)=ax^2+bxy+cy^2 with integer coefficients.  This topograph method, as he calls it, leads to a simple and elegant method of classifying integral binary quadratic forms and answering some basic questions about them.  In this talk, I will present an analogue of Conway's topograph method for binary quadratic forms with coefficients in F_q[T], where q is an odd prime power.  The constructions will take place on the Bruhat-Tits tree of SL(2), which is an analogue of the real hyperbolic plane. 

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