Search results found for "gasc"in "Events"

Displaying 1 - 10 of 12 results

GASC Seminar “Moment Maps of Toric Varieties, Linear Precision, and Maximum Likelihood Degree One” by David Cox (Amherst College)

Abstract: My talk will start from a question about moment maps of toric varieties (from symplectic geometry). To get some preliminary insight, I will relate the question to the concept of strict linear precision (from geometric modeling). However, the best result so far uses a result of June Huh on maximum likelihood degree one (from algebraic statistics). I will also discuss the more general notion of rational linear precision and…
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GASC seminar “Syzygies of the Veronese and Pinched Veronese modules” by Ivan Martino

Syzygies of the Veronese and Pinched Veronese modules There has been a lot of effort to find the graded Betti numbers of the Veronese ring and Veronese modules. I am going to define the (pinched) Veronese modules and present a sample of literature results, like the work of Ein and Lazarsfeld, Ottaviani and Paoletti and, Bruns, Conca and R\ ̈omer. In the second part of the talk, I will show…
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GASC Seminar “Trace Modules and Rigidity Conjectures” by Haydee Lindo (Williams College)

Abstract: I will discuss some on-going work examining the relationship between trace modules and modules having no self-extensions, that is Ext_R^1(M,M) = 0, over commutative Noetherian rings. The findings will be applied to a conjecture by Auslander and Reiten in the context of self-injective commutative rings. Abstract for the pretalk: The well-known trace map on matrices can be generalized to a map for a general module over a commutative ring.…
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GASC Seminar “Singular locus of a class of dual varieties” by Emre Sen

Singular locus of a class of dual varieties For a given irreducible projective variety X, the closure of the set of all hyperplanes containing tangents to X is the projectively dual variety X*. We study the singular locus of projectively dual varieties of certain Segre-Plucker embeddings. We give a classification of the irreducible components of the singular locus of several representation classes. Basically, they admit two types of singularities: cusp…
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GASC Seminar “Some Results on the Ideal Theory of Affine Grassmannians” by Dinakar Muthiah (University of Massachusetts, Amherst)

Abstract: I will discuss some results on the ideal theory of affine Grassmannians. The talk will focus on a proof (joint with Alex Weekes and Oded Yacobi) of a conjecture of V. Kreiman, V. Lakshmibai, P. Magyar, and J. Weyman about the equations cutting out type-A affine Grassmannians inside the Sato Grassmannian. I will also briefly discuss some related results (joint with Joel Kamnitzer, Alex Weekes, and Oded Yacobi) about…
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GASC seminar: “Minimal extending modules of torsion classes- by Shijie Zhu (Northeastern)

``Minimal extending modules of torsion classes'', by Shijie Zhu: Abstract: Torsion classes of finitely generated modules over a finite dimensional algebra form a lattice. We characterize the notion of cover relations, complete join irreducible elements and canonical join representations in the context of the lattice of torsion classes by minimal extending modules. As an application, we study the algebra $RA_n$ whose lattice of torsion classes is isomorphic to the weak…
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GASC Seminar “The Combinatorics of Torsion Classes” by Emily Barnard (Northeastern)

Abstract: This is the first of a two part series. (The second talk will be given by Shijie Zhu on November 27.) Let be a finite-dimensional associative algebra. The set of torsion classes over mod , ordered by containment, form a complete lattice denoted tors . Recently, there has been much interest in the combinatorial structure of tors , specifically when is the preprojective algebra (W) for W a finite,…
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GASC Seminar “Orthogonal tensor decomposition” by Elina Robeva

Orthogonal tensor decomposition A symmetric tensor is orthogonally decomposable if it can be written as a linear combination of tensor powers of n orthonormal vectors. Such tensors are interesting because their decomposition can be found efficiently. We study their spectral properties and give a formula for all of their eigenvectors. We also give equations defining the variety of all real symmetric orthogonally decomposable tensors. Analogously, we study nonsymmetric orthogonally decomposable…
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GASC Seminar “Homotopy Group Actions and Group Cohomology” by Alejandro Adem

Homotopy Group Actions and Group Cohomology Understanding the symmetries of a topological space is a classical problem in mathematics. In this talk we will consider the somewhat more flexible notion of a group action up to homotopy. This leads to interesting interactions between topology, group theory and representation theory. This is joint work with Jesper Grodal. Schedule of the talk: 11:45 - Pre-seminar (25 minutes) 12:15 - Seminar
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GASC Seminar “The Lé Numbers of One-Parameter Families of Parameterized Hypersurfaces” by Brian Hepler

The Lé Numbers of One-Parameter Families of Parameterized Hypersurfaces We investigate one-parameter deformations of functions on affine space whose defining hypersurfaces can be parameterized by a finite morphism that is generically one-to-one. Such hypersurfaces must necessarily have critical loci of codimension one. With the mild assumption of isolated polar activity at the origin, we are able to completely express the Lé numbers of the special fiber in terms of the…
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