Algebra seminar - From toric degenerations of the Grassmannian to its algebraic matroid
| Dates: | 17 October 2023 |
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| Times: | 14:00 - 15:00 |
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| What is it: | Seminar |
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| Organiser: | Department of Mathematics |
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| Who is it for: | University staff, External researchers, Current University students |
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| Speaker: | Oliver Clarke |
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Abstract: The coordinate ring of the Grassmannian under the Pluecker embedding is generated by maximal minors. These generators are natural as they satisfy 'straightening relations' that are akin to the (possibly) familiar reduction of S-polynomials for Groebner bases. However, these straightening relations depend on a choice of term order. If one changes the term order, it is computationally expensive to verify whether the maximal minors exhibit straightening relations. To explore this problem, we use matching fields: combinatorial gadgets that arise in tropical geometry. Associated to each matching field is a polytope. In this talk, I will relate the toric variety of this polytope with the combinatorics of the matching field and straightening relations of maximal minors. I will explain how this story relates to combinatorial mutations of Newton-Okounkov bodies and sheds light on the algebraic matroid of the Grassmannian.
Speaker
Oliver Clarke
Organisation: University of Edinburgh
Travel and Contact Information
Find event
Frank Adams 1
Alan Turing Building
Manchester
