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DTSTART;TZID=America/Los_Angeles:20231003T121500
DTEND;TZID=America/Los_Angeles:20231003T131000
DTSTAMP:20260415T115240
CREATED:20230901T053808Z
LAST-MODIFIED:20230901T053808Z
UID:3170-1696335300-1696338600@colleges.claremont.edu
SUMMARY:Cellular resolutions of the diagonal and exceptional collections for toric D-M stacks (Reginald Anderson\, CMC)
DESCRIPTION:Beilinson gave a resolution of the diagonal for complex projective space\, which gives a strong\, full exceptional collection of line bundles as a generating set for the derived category of coherent sheaves. Bayer-Popescu-Sturmfels generalized Beilinson’s resolution of the diagonal by giving a cellular resolution of the diagonal for a proper subclass of smooth toric varieties which they called “unimodular.” In joint work with Gabe Kerr\, we extended this resolution of the diagonal to smooth projective toric varieties by showing that the cokernel of Bayer-Popescu-Sturmfels’ resolution is torsion with respect to the irrelevant ideal. In this talk\, we show that Bayer-Popescu-Sturmfels’ resolution yields a strong\, full\, exceptional collection of line bundles for unimodular projective toric surfaces\, and that our extended resolution of the diagonal yields a strong\, full exceptional collection of line bundles for a smooth\, non-unimodular projective toric surface.
URL:https://colleges.claremont.edu/ccms/event/cellular-resolutions-of-the-diagonal-and-exceptional-collections-for-toric-d-m-stacks-reginald-anderson-cmc/
LOCATION:Roberts North 102\, CMC
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
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DTSTART;TZID=America/Los_Angeles:20231024T121500
DTEND;TZID=America/Los_Angeles:20231024T131000
DTSTAMP:20260415T115240
CREATED:20231003T045008Z
LAST-MODIFIED:20231003T234122Z
UID:3269-1698149700-1698153000@colleges.claremont.edu
SUMMARY:Deep hole lattices and isogenies of elliptic curves (Lenny Fukshansky\, CMC)
DESCRIPTION:For a lattice L in the plane\, we define the affiliated deep hole lattice H(L) to be spanned by a shortest vector of L and the furthest removed vector from the lattice contained in the triangle with sides corresponding to the shortest basis vectors. We study the geometric and arithmetic properties of deep hole lattices\, which turn out to be quite interesting. In particular\, we construct sequences of deep hole lattices corresponding to elliptic curves over a fixed number field. In the case of CM elliptic curves\, we prove that all elliptic curves generated by this sequence are isogenous to each other and produce bounds on the degree of isogeny. Finally\, we produce a counting estimate for the planar lattices with a prescribed deep hole lattice. Joint work with Pavel Guerzhoy and Tanis Nielsen.
URL:https://colleges.claremont.edu/ccms/event/deep-hole-lattices-and-isogenies-of-elliptic-curves-lenny-fukshansky-cmc/
LOCATION:Roberts North 102\, CMC
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
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DTSTART;TZID=America/Los_Angeles:20231031T121500
DTEND;TZID=America/Los_Angeles:20231031T131000
DTSTAMP:20260415T115240
CREATED:20230921T041133Z
LAST-MODIFIED:20231013T160601Z
UID:3248-1698754500-1698757800@colleges.claremont.edu
SUMMARY:On the spectra of syntactic structures (Isabella Senturia\, Yale University)
DESCRIPTION:We explore the application of spectral graph theory to the problem of characterizing linguistically-significant classes of tree structures. We focus on various classes of syntactically-defined tree graphs\, and show that the spectral properties of different matrix representations of these classes of trees provide insight into the linguistic properties that characterize these classes. More generally\, our goal is to provide another route to understanding the mathematical structure of natural language\, one that does not come from extensive definitions and rules defined via linguistic extrapolation\, but instead is extracted directly from computation on the syntactically-defined graphical structures.
URL:https://colleges.claremont.edu/ccms/event/antc-seminar-via-zoom-isabella-senturia-yale-university/
LOCATION:On Zoom
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
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