Department of Mathematics - Master Calendar

Algebraic Geometry Seminar

Event Type
Seminar/Symposium
Sponsor
Algebraic Geometry Group, Department of Mathematics
Location
207 Psychology Building
Date
Nov 11, 2025   3:00 pm  
Speaker
Bruce Reznick
Views
18
Originating Calendar
Algebraic Geometry Calendar

Title: Higher Order Arithmetic-Geometric Inequalities

Abstract: If the set {v(k)} in R^d consists of a simplex and a single interior point, and if you impose the condition that the sum of c(k) x^v(k) vanishes to the second order at (1,\dots,1) and is definite, then the resulting polynomial is, up to a multiple, a version of the arithmetic-geometric inequality for the monomials x^{v(k)}. There is a sense in which this is an iff condition. In this talk, we explore geometric conditions on larger point-sets {v(k)} so that imposing a higher even-order vanishing at (1,\dots,1) leads to an inequality, and present a few preliminary results and a lot of pictures. A riddle, wrapped in a mystery, inside an enigma.

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