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Inequalities: Posets, Tableaux, Symmetric Functions

Algebra & Discrete Mathematics

Speaker: Prof. Curtis Greene, Haverford College
Location: 2112 Math Science Building
Start time: Mon, Apr 15 2019, 2:10PM

This talk will pursue several threads linking topics in the title. Originally we were motivated by symmetric function inequalities of the form f(X) >= g(X) where the inequality must hold for all nonnegative substitutions of the variables. The literature on this topic is too vast to permit a comprehensive survey, but we will mention several interesting open problems and conjectures. We will focus on a "positivity principle" that seems to hold for most symmetric function inequalities of this type involving familiar combinatorial families (monomial, Schur, etc.). Where we have proofs, they involve interesting combinatorics (posets and tableaux), and also the FKG inequality from statistical mechanics.

Please note the unusual time (2pm) and room.