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DTSTART;TZID=America/Los_Angeles:20231107T121500
DTEND;TZID=America/Los_Angeles:20231107T131000
DTSTAMP:20260412T031329
CREATED:20230908T055420Z
LAST-MODIFIED:20231024T041512Z
UID:3176-1699359300-1699362600@colleges.claremont.edu
SUMMARY:Frobenius coin-exchange generating functions (Matthias Beck\, San Francisco State University)
DESCRIPTION:We study variants of the Frobenius coin-exchange problem: Given n positive relatively prime parameters\, what is the largest integer that cannot be represented as a nonnegative integral linear combination of the given integers? This problem and its siblings can be understood through generating functions with 0/1 coefficients according to whether or not an integer is representable. In the 2-parameter case\, this generating function has an elegant closed form\, from which many corollaries follow\, including a formula for the Frobenius problem. We establish a similar closed form for the generating function indicating all integers with exactly k representations\, with similar wide-ranging corollaries. This is joint work with Leonardo Bardomero.
URL:https://colleges.claremont.edu/ccms/event/antc-seminar-matthias-beck-san-francisco-state-university/
LOCATION:Roberts North 102\, CMC
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
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BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20231114T121500
DTEND;TZID=America/Los_Angeles:20231114T131000
DTSTAMP:20260412T031329
CREATED:20230908T055625Z
LAST-MODIFIED:20231109T070158Z
UID:3177-1699964100-1699967400@colleges.claremont.edu
SUMMARY:f^*-vectors of lattice polytopes (Max Hlavacek\, Pomona College)
DESCRIPTION:The Ehrhart polynomial of a lattice polytope P counts the number of integer points in the nth integral dilate of P. The f^* -vector of P\, introduced by Felix Breuer in 2012\, is the vector of coefficients of the Ehrhart polynomial with respect to the binomial coefficient basis . Similarly to h and h^* -vectors\, the f^* -vector of P coincides with the f-vector (counting faces of every dimension) of its unimodular triangulations (if they exist). We give several inequalities that hold among the coefficients of f^*-vectors of polytopes. These inequalities resemble striking similarities with existing inequalities for the coefficients of f-vectors of simplicial polytopes. Even though f^* -vectors of polytopes are not always unimodal\, we describe several families of polytopes that carry the unimodality property.
URL:https://colleges.claremont.edu/ccms/event/antc-seminar-max-hlavacek-pomona-college/
LOCATION:Roberts North 102\, CMC
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20231121T121500
DTEND;TZID=America/Los_Angeles:20231121T131000
DTSTAMP:20260412T031329
CREATED:20231009T193529Z
LAST-MODIFIED:20231119T201433Z
UID:3282-1700568900-1700572200@colleges.claremont.edu
SUMMARY:On the Cox ring of a weighted projective plane blown-up at a point (Javier Gonzalez Anaya\, HMC)
DESCRIPTION:The Cox ring of a projective variety is the ring of all its meromorphic functions\, together with a grading of geometric origin. Determining whether this ring is finitely generated is a challenging task\, even for simple examples. In this talk\, we will discuss our efforts to tackle this problem for a specific class of varieties\, known as blow-ups of weighted projective planes (WPP). Through the lens of toric geometry\, a WPP is characterized by a rational plane triangle. This allows us to reinterpret the problem combinatorially and show that the solution often emerges from a parameter space of such triangles. This is joint work with José Luis González and Kalle Karu.
URL:https://colleges.claremont.edu/ccms/event/antc-seminar-javier-gonzalez-anaya-hmc/
LOCATION:Roberts North 102\, CMC
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
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BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20231128T121500
DTEND;TZID=America/Los_Angeles:20231128T131000
DTSTAMP:20260412T031329
CREATED:20231009T153250Z
LAST-MODIFIED:20231121T192204Z
UID:3281-1701173700-1701177000@colleges.claremont.edu
SUMMARY:What can chicken nuggets tell us about symmetric functions\, positive polynomials\, random norms\, and AF algebras? (Stephan Garcia\, Pomona)
DESCRIPTION:A simple question about chicken nuggets connects everything from analysis and combinatorics to probability theory and computer-aided design.  With tools from complex\, harmonic\, and functional analysis\, probability theory\, algebraic combinatorics\, and spline theory\, we answer many asymptotic questions about factorization lengths in numerical semigroups.  Our results yield uncannily accurate predictions\, along with unexpected results about symmetric functions\, trace polynomials\, and the statistical properties of certain AF C$^*$-algebras.
URL:https://colleges.claremont.edu/ccms/event/antc-seminar-stephan-garcia-pomona/
LOCATION:Roberts North 102\, CMC
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
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