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DTSTART;TZID=America/Los_Angeles:20261014T161500
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UID:10002368-1791994500-1791998100@colleges.claremont.edu
SUMMARY:CCMS Colloquium: Frobenius invariants — Austyn Simpson (Bates College)
DESCRIPTION:Abstract: Rings containing a finite field \(mathbb{F}_p\) (such as the ring of polynomials with coefficients in \(mathbb{F}_p\)) admit a map called the Frobenius homomorphism which sends every element to its \(p\)-th power. This operation encodes delicate information about the geometry of the zero sets of polynomial equations in prime characteristic\, such as whether they are smooth. In this talk\, I will survey some numerical invariants defined using limits and asymptotic properties of this homomorphism which quantify how non-smooth a polynomial is. I will also discuss the current capabilities of large language models at solving problems related to these invariants\, as well as a surprising appearance of the number \(frac{4}{3}+frac{5}{14sqrt{7}}\). \n\n\n\nFor questions about the event\, please contact your CCMS Colloquium chairs: \nProf. Robert Cass (Robert.Cass@ClaremontMcKenna.edu) or Prof. Qidi Peng (Qidi.Peng@cgu.edu) \nFor logistical questions\, contact Maxwell Kooiker (Maxwell.Kooiker@cgu.edu)\, the CCMS Colloquium Assistant.
URL:https://colleges.claremont.edu/ccms/event/ccms-colloquium-frobenius-invariants-austyn-simpson-bates-college/
LOCATION:Burkle 16\, Claremont Graduate University\, 1021 N. Dartmouth Ave.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Colloquium
ORGANIZER;CN="Qidi Peng":MAILTO:Qidi.Peng@cgu.edu
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