View Proposal #271
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| ID | 271 |
|---|---|
| First Name | Aba |
| Last Name | Mbirika |
| Institution | University of Iowa |
| Speaker Category | graduate student |
| Title of Talk | Cool combinatorics arising on a cohomology hunt! |
| Abstract | Can cool combinatorics arise in a hunt for the cohomology ring of a variety? Yes indeed! In 1992, De Mari, Proces, and Shayman introduce Hessenberg varieties. These are a natural generalization of the famed Springer variety. Much is known about the cohomology ring of the Springer variety, but little is known in the case of a general Hessenberg. We provide a step in this direction by inspecting a certain subfamily of Hessenbergs called the Peterson variety. We conjecture that the cohomology ring of a Peterson variety has the presentation of a graded quotient of a polynomial ring modulo a special ideal with very nice combinatorial properties. Along the way, cute combinatorics pops up in the form of Dyck paths, Catalan numbers, etc. We also discuss tantalizing recent work that might help confirm our conjecture. |
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| Suitable for undergraduates? | ??? |
| Day Preference | |
| Computer Needed? | |
| Bringing a laptop? | |
| Overhead Needed? | |
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| Date Submitted | 10/6/2009 |
| Year | 2009 |