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FORCE ADD IS CLOSED. More information can be found here.
New Change of Major Policy. Next Open Period: December 19,2016 - January 27, 2017
Featured ResearchNick Loehr - Dr. Loehr's research areas are bijective and algebraic combinatorics. The main problem in bijective combinatorics is to prove that two finite sets have the same size by exhibiting a specific one-to-one correspondence between them. Some of the most elegant proofs in mathematics occur in this field. The illustration depicts a colored, directed tree growing around a cylinder. This tree appears in a bijective proof of a recently discovered identity in the theory of integer partitions.
Algebraic combinatorics deals with the interplay between combinatorics and certain areas of abstract algebra, including representation theory, symmetric functions, Lie algebras, and algebraic geometry. An intricate combinatorial calculus has been developed for computing with symmetric functions and related constructs by drawing and operating on suitable pictures of partitions, tableaux, parking functions, lattice paths, etc. Quantum analogues of these combinatorial objects lead to deep results about Macdonald polynomials, the Bergeron-Garsia nabla operator, Hilbert schemes, and more.