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DTSTART;TZID=America/Los_Angeles:20251104T121500
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SUMMARY:Classifying possible density degree sets of hyperelliptic curves (Jasmine Camero\, Emory University)
DESCRIPTION:Let $C$ be a nice (smooth\, projective\, geometrically integral) curve over a number field $k$. The single most important geometric invariant of a curve is the genus\, which can control various arithmetic properties of a curve. A celebrated result of Faltings implies that all points on $C$ come in families of bounded degree\, with finitely many exceptions. This result symbolized an advancement in the study of arithmetic information about curves and serves as the guiding philosophy of arithmetic geometry by highlighting the idea that “geometry governs arithmetic.” We explore the behavior of parameterized points and deduce consequences for the arithmetic of hyperelliptic curves\, specifically focusing on classifying the density degree sets of such curves.
URL:https://colleges.claremont.edu/ccms/event/classifying-possible-density-degree-sets-of-hyperelliptic-curves-jasmine-camero-emory-university/
LOCATION:Estella 2099
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
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DTSTART;TZID=America/Los_Angeles:20251111T121500
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CREATED:20250827T221608Z
LAST-MODIFIED:20251022T171318Z
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SUMMARY:Elementary probability via bundles (Wai Yan Pong\, Cal State Dominguez Hills)
DESCRIPTION:This talk explores elementary probability and statistics through the language of category theory. We introduce a category of Bundles and use it to reinterpret several results typically covered in an introductory course on probability and statistics. This approach naturally reveals the underlying geometric structures common to these results. The talk is accessible to anyone familiar with linear algebra\, and we hope teachers of probability will find this perspective fresh and interesting.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-wai-yan-pong-cal-state-dominguez-hills-2/
LOCATION:Estella 2099
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
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DTSTART;TZID=America/Los_Angeles:20251118T121500
DTEND;TZID=America/Los_Angeles:20251118T131000
DTSTAMP:20260423T003353
CREATED:20250808T232856Z
LAST-MODIFIED:20251113T200129Z
UID:3779-1763468100-1763471400@colleges.claremont.edu
SUMMARY:Non-vanishing of L-functions over function fields (Alexandra Florea\, UC Irvine)
DESCRIPTION:I will talk about some results concerning the non-vanishing of $L$-functions associated to fixed order characters $\ell$ at the central point over functions fields. Quadratic characters have been studied a lot over the years\, and very good non-vanishing results are available in this case\, due to work of Soundararajan. When focusing on cubic and higher order characters\, much less is known. In this talk\, I will explain how one can obtain a positive proportion of non-vanishing for any fixed order $\ell$ characters\, which goes to $0$ as $\ell$ goes to infinity. This is based on joint work with C. David and M. Lalin.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-alexandra-florea-uc-irvine/
LOCATION:Estella 2099
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
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