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Monday, November 2, 2020 — 11:30 AM EST
Title: Monogamy Violations in Perfect State Transfer
| Speakers: | Sabrina Lato & Christino Tamon |
| Affiliations: | University of Waterloo & Clarkson Unversity |
| Zoom: | Contact Soffia Arnadottir |
Abstract:
Continuous-time quantum walks on a graph are defined using a Hermitian matrix associated to a graph. For a quantum walk on a graph using either the adjacency matrix or the Laplacian, there can be perfect state transfer from a vertex to at most one other vertex in the graph.
Thursday, November 5, 2020 — 1:00 PM EST
Title: Filtering Grassmannian cohomology via k-Schur functions
| Speakers: | Huda Ahmed and Yuanning Zhang |
| Affiliation: | New York University and UC Berkeley |
| Zoom: | Contact Karen Yeats |
Abstract:
This talk concerns the cohomology rings of complex Grassmannians. In 2003, Reiner and Tudose conjectured the form of the Hilbert series for certain subalgebras of these cohomology rings. We build on their work in two ways. First, we conjecture two natural bases for these subalgebras that would imply their conjecture using notions from the theory of k-Schur functions. Second we formulate an analogous conjecture for Lagrangian Grassmannians.
Joint work with Michael Feigen, Victor Reiner, and Ajmain Yamin.
Thursday, November 5, 2020 — 1:00 PM EST
Title: Packings of partial difference sets
| Speaker: | Jonathan Jedwab |
| Affiliation: | Simon Fraser University |
| Zoom: | Contact Karen Yeats |
Abstract:
Partial difference sets are highly structured group subsets that occur in various guises throughout design theory, finite geometry, coding theory, and graph theory. They admit only two possible nontrivial character sums and so are often studied using character theory.
Friday, November 6, 2020 — 3:30 PM EST
Title: Constructing broken SIDH parameters: a tale of De Feo, Jao, and Plut's serendipity
| Speaker: | Chloe Martindale |
| Affiliation: | University of Bristol |
| Zoom: | Please email Emma Watson |
Abstract:
This talk is motivated by analyzing the security of the cryptographic key exchange protocol SIDH (Supersingular Isogeny Diffie-Hellman), introduced by 2011 by De Feo, Jao, and Plut. We will first recall some mathematical background as well as the protocol itself. The 'keys' in this protocol are elliptic curves, which are typically described by equations in x and y of the form y^2 = x^3 + ax + b.