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DTSTART;TZID=America/Los_Angeles:20241001T121500
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DTSTAMP:20260415T202518
CREATED:20240827T194511Z
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SUMMARY:Adinkras as Origami? (Edray Goins\, Pomona College)
DESCRIPTION:Around 20 years ago\, physicists Michael Faux and Jim Gates invented Adinkras as a way to better understand Supersymmetry.  These are bipartite graphs whose vertices represent bosons and fermions and whose edges represent operators which relate the particles.  Recently\, Charles Doran\, Kevin Iga\, Jordan Kostiuk\, Greg Landweber and Stefan M\'{e}ndez-Diez determined that Adinkras are a type of Dessin d’Enfant; they showed this by explicitly exhibiting a Belyi map as a composition $\beta: S \to \mathbb P^1(\mathbb C) \to \mathbb P^1(\mathbb C)$.  They computed the first arrow as a map from a certain compact connected Riemann surface $S$ to the Riemann sphere $\mathbb P^1(\mathbb C) \simeq S^2(\mathbb R)$\, and the second as a map which keeps track of the “coloring” of the edges.\n\nAdinkras naturally have square faces.  This keeps track of the non-commutative nature of the supersymmetric operators.  While Dessin d’Enfants correspond to triangular tilings of Riemann surfaces\, there is a similar construction — called “origami” — which correspond to square tilings.  In this project\, we attempt to discover how to express the construction of Doran\, et al. as a composition $\beta: S \to E(\mathbb C) \to \mathbb P^1(\mathbb C)$ for some elliptic curve elliptic curve $E$ such that the map corresponds to an “origami”\, that is\, a map which is branched over just one point.  This work is conducted as part of the Pomona Research in Mathematics Experience (DMS-2113782).
URL:https://colleges.claremont.edu/ccms/event/adinkras-as-origami-edray-goins-pomona-college/
LOCATION:Estella 2113
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
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DTSTART;TZID=America/Los_Angeles:20241008T121500
DTEND;TZID=America/Los_Angeles:20241008T131000
DTSTAMP:20260415T202518
CREATED:20240901T163937Z
LAST-MODIFIED:20240929T202957Z
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SUMMARY:Counting matrix points via lattice zeta functions (Yifeng Huang\, USC)
DESCRIPTION:​I will introduce two general problems and explain how they surprisingly connect with each other and with other aspects of mathematics (for a glimpse\, Sato—Tate\, hypergeometric functions\, moduli spaces of sheaves\, Catalan numbers\, Hall polynomials\, etc.)​.\n\nThe first problem is to count finite-field points on so called “varieties of matrix points”. They are created from a simple and fully elementary recipe and can yet easily get very complicated. The second problem is analogous to counting full-rank sublattices of $\mathbb{Z}^d$ with index $n$\, but with $\mathbb{Z}$ replaced by non-Dedekind rings\, such as non-maximal orders in number fields. (Containing joint work with Ken Ono\, Hasan Saad and joint work with Ruofan Jiang)
URL:https://colleges.claremont.edu/ccms/event/antc-talk-yifeng-huang-usc/
LOCATION:Estella 2113
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20241022T121500
DTEND;TZID=America/Los_Angeles:20241022T131000
DTSTAMP:20260415T202518
CREATED:20240909T190346Z
LAST-MODIFIED:20241016T201124Z
UID:3502-1729599300-1729602600@colleges.claremont.edu
SUMMARY:Making sandwiches: a novel invariant in D-module theory (David Lieberman\, HMC)
DESCRIPTION:In the field of commutative algebra\, the principal object of study is (unsurprisingly) commutative algebras. A somewhat unintuitive fact is that results about commutative algebras can be gleaned from an associated non-commutative algebra whose generators are very analytic in nature. This object is called the ring of differential operators\, often denoted by D. In a sense gives an algebraic way of constructing the partial derivative.\n\nAn important result in the study of D-modules is Bernstein’s inequality\, first proved by Joseph Bernstein in the 1970’s. The result gives a lower bound on the filtered dimension of a D-module\, which a provide insights about modules of commutative algebras. The goal of this talk is to present some novel singular settings where this inequality holds. To do this\, we will introduce an invariant called sandwich Bernstein-Sato polynomials. These are analogous to a well studied object called the Bernstein-Sato polynomial\, which is a generalization of the power rule taught in undergraduate calculus courses. Using sandwich Bernstein-Sato polynomials\, we will show that Bernstein’s inequality holds true for the differential operators of the coordinate ring of the Segre product of projective spaces.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-david-lieberman-hmc/
LOCATION:Estella 2113
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
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BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20241029T121500
DTEND;TZID=America/Los_Angeles:20241029T131000
DTSTAMP:20260415T202518
CREATED:20240903T234219Z
LAST-MODIFIED:20241023T053311Z
UID:3487-1730204100-1730207400@colleges.claremont.edu
SUMMARY:Sequences with identical autocorrelation spectra (Daniel Katz\, Cal State Northridge)
DESCRIPTION:In this talk\, we explore sequences and their autocorrelation functions. Knowing the autocorrelation function of a sequence is equivalent to knowing the magnitude of its Fourier transform.  Resolving the lack of phase information is called the phase problem.  We say that two sequences are equicorrelational to mean that they have the same aperiodic autocorrelation function.  We investigate the necessary and sufficient conditions for two sequences to be equicorrelational\, where\nwe take into consideration the alphabet from which their terms are drawn.  There are trivial forms of equicorrelationality arising from modifications that predictably preserve the autocorrelation\, for example\, negating the sequence or writing the sequence in reverse order and then complex conjugating every term.  By an exhaustive search of binary sequences up to length $44$\, we find that nontrivial equicorrelationality among binary sequences does occur\, but is rare.  We say that a positive integer $n$ is {\it unequivocal} to mean that there is no pair of nontrivially equicorrelational binary sequences of length $n$; otherwise $n$ is {\it equivocal}.  For integers $n \leq 44$\, we found that the unequivocal ones are $1$–$8$\, $10$\, $11$\, $13$\, $14$\, $19$\, $22$\, $23$\, $26$\, $29$\, $37$\, and $38$.  We prove that any multiple of a equivocal number is also equivocal\, and pose open questions as to whether there are finitely or infinitely many unequivocal numbers and whether the probability of nontrivial equicorrelationality occurring tends to zero as the sequence length tends to infinity.  (This is joint work with Adeebur Rahman and Michael J Ward.)
URL:https://colleges.claremont.edu/ccms/event/antc-talk-daniel-katz-cal-state-northridge-2/
LOCATION:Estella 2113
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
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