Mathematics Program and Computer Science Program Present
EVENT CANCELED
Juggling, Refinements, and Symmetries for Volumes of Flow Polytopes
Wednesday, March 1, 2023
RKC 111
12:00 pm – 1:00 pm EST/GMT-5
12:00 pm – 1:00 pm EST/GMT-5
Alejandro Morales, University of Massachusetts
Flow polytopes are an important class of polytopes in combinatorics whose lattice points and volumes have interesting properties and relations to other parts of geometric and algebraic combinatorics. These polytopes were recently related to (multiplex) juggling sequences of Butler, Graham, and Chung. The Chan-Robbins-Yuen (CRY) polytope is a flow polytope with normalized volume equal to the product of consecutive Catalan numbers, one of the most well-known sequences in combinatorics. Zeilberger proved this by evaluating the Morris constant term identity, but no combinatorial proof is known. In this talk we will talk about the connection between juggling and (flow) polytopes and introduce a new refinement of the Morris identity with combinatorial interpretations both in terms of lattice points and volumes of flow polytopes. Alejandro Morales is originally from Colombia and got his B.Math. from the University of Waterloo and a Ph.D. from MIT, working with Professor Alexander Postnikov. After postdocs at Université du Québec à Montréal and UCLA, he started a tenure-track position at UMass, Amherst where he is part of the Discrete Mathematics group. Morales works in enumerative and algebraic combinatorics and uses bijections, symmetric functions, and tools from algebra to study several objects including linearizations of posets, polytopes associated to graphs, and factorizations of permutations. Morales' research is funded by grants of the National Science Foundation and is a handling Editor of the mathematician owned journal Combinatorial Theory. You can see videos, slides, code, and conjectures of the work of Morales here: ahmorales.combinatoria.co
For more information, call 845-758-6822, or e-mail [email protected].
Time: 12:00 pm – 1:00 pm EST/GMT-5
Location: RKC 111