Algebra Seminar
Title and Abstract: TBD
Date:
-
Location:
POT 745
Type of Event (for grouping events):
algebra seminar
Algebra Seminar
Title: Ideals from hypersurface arrangements
Abstract:
A hyperplane arrangement in projective space is a finite set of hyperplanes. It is defined by a polynomial $f$, which is a product of linear forms defining the individual hyperplanes. It is well-known that free arrangements have favorable properties. A hyperplane arrangement is free precisely if its Jacobian ideal is Cohen-Macaulay, an algebraic property we define in the talk. The Jacobian ideal is generated by the partial derivatives of $f$.
We consider the Cohen-Macaulayness of two ideals that are related to the Jacobian ideal: its top-dimensional part and its radical. In joint work with Migliore and Schenck we showed that the related ideals are Cohen-Macaulay under a mild hypothesis. We discuss extensions for hypersurface arrangements where the polynomial $f$ is a product of irreducible forms whose degrees are at least one. These results were obtained jointly with Migliore.
Date:
-
Location:
POT 745
Type of Event (for grouping events):
Algebra Seminar
Date:
-
Location:
POT 745
Type of Event (for grouping events):
Algebra Seminar
Title and Abstract: TBD
Date:
-
Location:
POT 745
Type of Event (for grouping events):
Algebra Seminar
Title and Abstract: TBD
Date:
-
Location:
TBD
Type of Event (for grouping events):
Algebra Seminar
Title and Abstract: TBD
Date:
-
Location:
POT 745
Type of Event (for grouping events):
Algebra Seminar
Title and Abstract: TBD
Date:
-
Location:
POT 745
Type of Event (for grouping events):
Algebra Seminar
Title: Hilbert Schemes and Newton-Okounkov Bodies
Abstract: Hilbert schemes of points in the plane parametrize finite, closed subschemes of C^2 with a fixed length. In this talk, I will explain how to compute the Newton-Okounkov bodies of these Hilbert schemes, which are certain unbounded polyhedra encoding geometric information about the Hilbert schemes. Finally, I will share what is known for Hilbert schemes of points on complete toric surfaces.
Date:
-
Location:
POT 745
Type of Event (for grouping events):
Algebra Seminar
Title. Smooth limits of plane curves and Markov numbers
Abstract. When can we guarantee that smooth proper limits of plane curves are still plane curves? Said a different way --- When is the locus of degree d plane curves closed in the (noncompact) moduli space of smooth genus g curves? It is relatively easy to see that if d>1, then d must be prime. Mori suggests that this may be enough in higher dimensions. Interestingly, in low dimensions, this is not sufficient. For example, Griffin constructed explicit families of quintic plane curves with a smooth limit that is not a quintic plane curve. In this talk we propose the following conjecture: Smooth proper limits of plane curves of degree d are always plane curves if d is prime and d is not a Markov number. We discuss the motivation and evidence for this conjecture which come from Hacking and Prokhorov's work on Q-Gorenstein limits of the projective plane.
Date:
-
Location:
POT 745
Type of Event (for grouping events):
Algebra Seminar
Title: Lexicodes Over Principal Ideal Rings
Abstract: Let R be a finite principal left ideal ring. Place a lexicographic ordering on the vectors in the free left R-module R^n with respect to some basis B. The code produced by searching through this list, greedily collecting vectors satisfying some property P, is called a lexicode. For decades, several iterations of a greedy algorithm have appeared, to produce maximal lexicodes with nice properties. The most recent, in 2014, was generalized to work over finite chain rings. In this talk, I will present a new version of the greedy algorithm, generalized to produce lexicodes over a much larger class of rings.
Date:
Location:
POT 745
