Upcoming Seminars

Title: Secants, Gorenstein ideals, and stable complexes
Seminar: Algebra
Speaker: Brooke Ullery of Emory University
Contact: David Zureick-Brown, david.zureick-brown@emory.edu
Date: 2022-09-06 at 4:00PM
Venue: MSC N304
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Abstract:
As Bertram describes in his thesis, certain rank two vector bundles on curves can be parametrized by a projective space into which the curve itself embeds. The idea is that the least so-called ``stable" bundles correspond to points on the embedded curve, the next most unstable lie on the first secant variety, then on the second secant variety, and so on. In this talk, I'll describe joint work with Bertram in which we generalize this to $\mathbb{P}^2$ by replacing vector bundles with complexes of vector bundles. This leads to a surprising connection between height three Gorenstein ideals, secant varieties (and their generalizations), and stability conditions on the bounded derived category of coherent sheaves on $\mathbb{P}^2$.
Title: Jordan Decompositions of Tensors
Seminar: Algebra
Speaker: Luke Oeding of Auburn University
Contact: David Zureick-Brown, david.zureick-brown@emory.edu
Date: 2022-09-19 at 4:00PM
Venue: MSC W301
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Abstract:
The Jordan normal form for similar matrices is a powerful classification tool as it provides a test to determine which matrices are similar (in the same orbit), and whether one orbit contains another or not. We expand on an idea of Vinberg to take a tensor space and the natural Lie algebra which acts on it and embed them into an auxiliary algebra. Viewed as endomorphisms of this algebra we associate adjoint operators to tensors. We show that the group actions on the tensor space and on the adjoint operators are consistent, which endows the tensor with a Jordan decomposition. We utilize aspects of the Jordan decomposition to study orbit separation and classification in examples that are relevant for quantum information. My talk will contain many examples and open questions.
Title: Athens-Atlanta joint Number Theory Seminar
Seminar: Algebra
Speaker: Alina Bucur and Samit Dasgupta of USCD and Duke
Contact: David Zureick-Brown, david.zureick-brown@emory.edu
Date: 2022-11-07 at 4:00PM
Venue: MSC W301
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Abstract: