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DTSTART;TZID=America/Los_Angeles:20230207T121500
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UID:3066-1675772100-1675775400@colleges.claremont.edu
SUMMARY:Orthogonality defect and coherence of cyclotomic lattices (Lenny Fukshansky\, CMC)
DESCRIPTION:There are two different measures of how far a given Euclidean lattice is from being orthogonal — the orthogonality defect and the average coherence. The first of these comes from the study of sphere packing while the second is motivated by frame theory\, but both of them have applications in digital communications\, especially in coding theory and cryptography. It is interesting to understand how the two are related. We investigate this question on an important class of cyclotomic lattices\, where some nice formulas can be derived and certain empirical observations can be made. Joint work with David Kogan.
URL:https://colleges.claremont.edu/ccms/event/orthogonality-defect-and-coherence-of-cyclotomic-lattices-lenny-fukshansky-cmc/
LOCATION:Davidson Lecture Hall\, CMC\, 340 E 9th St\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
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UID:3065-1676981700-1676985000@colleges.claremont.edu
SUMMARY:On zeros of multilinear polynomials (Max Forst\, CGU)
DESCRIPTION:Consider rational polynomials in multiple variables that are linear with respect to some of the variables. In this talk we discuss the problem of finding a zero of such polynomials that are bounded with respect to a height function. For a system of such polynomials satisfying certain technical conditions we prove the existence of a bounded height simultaneous zero. For a single such polynomial we prove the existence of a zero of bounded height lying outside of a prescribed algebraic set. Based on joint work with Lenny Fukshansky.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-max-forst-cgu-2/
LOCATION:Davidson Lecture Hall\, CMC\, 340 E 9th St\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
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