Colloquium September 12

Colloquium September 12
Date: Friday September 12

Time: 16:00 to 17:00

Place: 210 McBryde, TBA

Speaker: Frank Sottile of Univ of Massachusetts

Title: Enumerative Real Algebraic Geometry

Abstract

Consider the following hard problem: Give meaningful information about the number r of real solutions to a system of multivariate polynomial equations. Quite often much more is known than merely that r is between 0 and the number d of complex solutions. This stronger information is typically available when the system has some geometric structure. Enumerative real algebraic geometry treats this hard problem for systems coming from geometry.

In this talk, I will survey some of what is known. In particular, I will discuss recent better understanding of the bounds of 0 and d. A picture is emerging: for systems from geometry, the upper bound of d can always be obtained, and in many cases there are non-trivial lower bounds on the number of real solutions, with certain gaps that have been discovered experimentally.

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