Presentations

Throughout the semester students will be asked to give 30-40 minute presentations during class based on topics relevant to the course. Students are welcome to propose their own topics. They may also choose from the (hopefully growing) list of topics below. Some topics deal directly with symmetric functions, some deal with related topics (quasisymmetric functions, nonsymmetric functions), and some are just other areas of research that fall under the umbrella term "algebraic combinatorics." I am happy to talk with you about any of these topics (or others).

• Chromatic symmetric functions (Stanley's original paper, a recent quasisymmetric generalization) - Logan
• Stanley symmetric functions (Stanley's original paper, Wikipedia, a recent paper in the area)
• Macdonald's reduced word identity (a bijective proof, a more general bijective proof)
• Plethystic notation (a combinatorial approach) - Jongwon
• Basic Schubert calculus (Fulton's Young Tableaux textbook (which you can borrow from me), a survey article, some nice slides) - George
• Permutation patterns
• Coxeter combinatorics
• Rook theory / non-symmetric functions - Ellen
• LLT polynomials
• The hook formula and generalizations (a recent generalization by Greta and collaborators) - lecture
• RSK and unions of increasing sequences (Greene's original paper) - lecture
• Combinatorial Hopf algebras or monoids (Ardila-Aguiar's recent paper, Ardila's JMM slides)
• Inversion number of standard tableaux (Jim's original paper with Laura Stevens, Jim and Emily's recent development)
• Specht modules - Stephen