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DTSTART;TZID=America/Los_Angeles:20221101T121500
DTEND;TZID=America/Los_Angeles:20221101T131000
DTSTAMP:20260411T121230
CREATED:20220906T211012Z
LAST-MODIFIED:20221031T180722Z
UID:2839-1667304900-1667308200@colleges.claremont.edu
SUMMARY:A tale of two worlds: parking functions &  reduction algebras (Dwight Anderson Williams II\, Pomona)
DESCRIPTION:“A Tale of Two Cities” is a novel told in three books/parts. Here we describe three projects related both to published work and ongoing pieces: \nPROJECT 1: In the world of combinatorics\, parking functions are combinatorial objects arising from the situation of parking cars under a parking strategy. In this part of the talk\, we will refresh the notion of classical parking functions given by the classical parking rules/strategy. We will then state an interesting correspondence between certain classical parking functions and so-called ideal states of the famous Tower of Hanoi game. This work is to appear in The American Mathematical Monthly with the following co-authors: Y. Aguillon\, D. Alvarenga\, P.E. Harris\, S. Kotapati\, J.C. Martinez Mori\, C. Monroe\, Z. Saylor\, and C. Tieu. \nPROJECT 2: In the world of algebra\, we shed light on representation theory of Lie superalgebras by constructing reduction algebras. These algebras provide structures to study in their own right\, and we give an example in presenting the diagonal reduction algebra of $osp(1|2)$\, first described in a joint paper with Jonas T. Hartwig. \nPROJECT 3: Continuing down an algebraic pathway\, we summarize the general framework given by Zhelobenko to apply representation theory of reduction algebras as a method to solve equations. Fixing equations important to the study of physics has led to recent work with Jonas T. Hartwig and Erin Dolecheck\, as well\, Irmak Bukey.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-dwight-anderson-williams-ii-pomona/
LOCATION:Davidson Lecture Hall\, CMC\, 340 E 9th St\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
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BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20221108T121500
DTEND;TZID=America/Los_Angeles:20221108T131000
DTSTAMP:20260411T121230
CREATED:20220824T204820Z
LAST-MODIFIED:20221031T203245Z
UID:2787-1667909700-1667913000@colleges.claremont.edu
SUMMARY:Factoring translates of polynomials (Arvind Suresh\, University of Arizona - Tucson)
DESCRIPTION:Given a degree d polynomial f(x) in Q[x]\, consider the subset S_f  of Q consisting of rational numbers t for which the translated polynomial f(x) – t factors completely in Q[x]. For example\, if f is linear or quadratic then S_f is always infinite\, but if degree of f is at least 3\, then interesting things can happen. In this talk\, we discuss a connection between the set S_f and the classical Prouhet–Tarry–Escott problem (which asks for integer solutions to certain symmetric family of equations)\, and we present two infinite families of polynomials f for which S_f is infinite (upon replacing Q with certain number fields). Time permitting\, we outline how these can then be used to produce algebraic curves over number fields having a record number of rational points (relative to their genus).
URL:https://colleges.claremont.edu/ccms/event/antc-talk-arvind-suresh-university-of-arizona-tucson/
LOCATION:Davidson Lecture Hall\, CMC\, 340 E 9th St\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20221115T121500
DTEND;TZID=America/Los_Angeles:20221115T131000
DTSTAMP:20260411T121230
CREATED:20220823T003904Z
LAST-MODIFIED:20221102T220943Z
UID:2786-1668514500-1668517800@colleges.claremont.edu
SUMMARY:Minimal Mahler measure in number fields (Kate Petersen\, University of Minnesota Duluth)
DESCRIPTION:The Mahler measure of a polynomial is the modulus of its leading term multiplied by the moduli of all roots outside the unit circle.  The Mahler measure of an algebraic number b\, M(b) is the Mahler measure of its minimal polynomial. By a result of Kronecker\, an algebraic number b satisfies M(b)=1 if and only if b is a root of unity. Famously\, Lehmer asked if there are algebraic numbers with Mahler measures arbitrarily close to 1 (but not equal to 1). We will investigate the minimal Mahler measure of a number field.  For a number field K this is the smallest Mahler measure of a non-torsion generator for K\, written M(K). There are known upper and lower bounds for M(K) in terms of the degree and discriminant of K.  Focusing on cubics\, we will discuss how these bounds correspond to other properties of the number field\, and the sharpness of these bounds.  This is joint work with Lydia Eldredge.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-kate-petersen-university-of-minnesota-duluth/
LOCATION:Davidson Lecture Hall\, CMC\, 340 E 9th St\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20221129T122500
DTEND;TZID=America/Los_Angeles:20221129T131500
DTSTAMP:20260411T121230
CREATED:20221110T030247Z
LAST-MODIFIED:20221124T032038Z
UID:2989-1669724700-1669727700@colleges.claremont.edu
SUMMARY:Partial orders on standard Young tableaux( Gizem Karaali\, Pomona)
DESCRIPTION:Young diagrams are all possible arrangements of n boxes into rows and columns\, with the number of boxes in each subsequent row weakly decreasing. For a partition λ of n\, a standard Young tableau S of shape λ is built from the Young diagram of shape λ by filling it with the numbers 1 to n\, each occurring exactly once in such a way that the numbers are strictly increasing across rows (left to right) and down columns. Young diagrams with n cells are in one-to-one correspondence with the irreducible representations of the symmetric group Sn\,; the standard Young tableaux count the dimensions of these irreps and thus are some of the most essential objects of combinatorial representation theory and algebraic combinatorics. In this talk\, based on joint work with Isabella Senturia (PO’20) and Müge Taskin\, I will describe a handful of partial orders already defined on SYTn\, the set of all standard Young tableaux with n cells\, and propose a new one.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-gizem-karaali-pomona-2/
LOCATION:On Zoom
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
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