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DTSTART;TZID=America/Los_Angeles:20210907T123000
DTEND;TZID=America/Los_Angeles:20210907T132000
DTSTAMP:20260406T235655
CREATED:20210823T221435Z
LAST-MODIFIED:20210830T213551Z
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SUMMARY:Region colorings in knot theory (Sam Nelson\, CMC)
DESCRIPTION:In this talk we will survey recent developments in the use of ternary algebraic structures known as Niebrzydowski Tribrackets in defining invariants of knots\, with some perhaps surprising applications.
URL:https://colleges.claremont.edu/ccms/event/antc-seminar-sam-nelson-cmc/
LOCATION:On Zoom
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
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DTSTART;TZID=America/Los_Angeles:20210914T123000
DTEND;TZID=America/Los_Angeles:20210914T132000
DTSTAMP:20260406T235655
CREATED:20210822T191624Z
LAST-MODIFIED:20210829T182323Z
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SUMMARY:On Hermite's problem\, Jacobi-Perron type algorithms\, and Dirichlet groups (Oleg Karpenkov\, Liverpool)
DESCRIPTION:In this talk we introduce a new modification of the Jacobi-Perron algorithm in the three dimensional case. This algorithm is periodic for the case of totally-real conjugate cubic vectors. To the best of our knowledge this is the first Jacobi-Perron type algorithm for which the cubic periodicity is proven. This provides an answer in the totally-real case to the question of algebraic periodicity for cubic irrationalities posed in 1848 by Ch.Hermite. \nWe will briefly discuss a new approach which is based on geometry of numbers. In addition we point out one important application of Jacobi-Perron type algorithms to the computation of independent elements in the maximal groups of commuting matrices of algebraic irrationalities.
URL:https://colleges.claremont.edu/ccms/event/antc-seminar-pavel-guerzhoy-university-of-hawaii/
LOCATION:On Zoom
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
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DTSTART;TZID=America/Los_Angeles:20210921T123000
DTEND;TZID=America/Los_Angeles:20210921T131000
DTSTAMP:20260406T235655
CREATED:20210831T205637Z
LAST-MODIFIED:20210906T215314Z
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SUMMARY:The magic of the number three: three explanatory proofs in abstract algebra (Gizem Karaali\, Pomona)
DESCRIPTION:When first learning how to write mathematical proofs\, it is often easier for students to work with statements using the universal quantifier. Results that single out special cases might initially come across as more puzzling or even mysterious. Explanatory proofs\, in the sense of Steiner\, transform what might initially seem mysterious or even magical into lucid mathematics. In this talk we explore three specific statements from abstract algebra that involve the number three\, whose proofs are explanatory. This is joint work with Samuel Yih PO’18.
URL:https://colleges.claremont.edu/ccms/event/antc-seminar-gizem-karaali-pomona/
LOCATION:On Zoom
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
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DTSTART;TZID=America/Los_Angeles:20210928T123000
DTEND;TZID=America/Los_Angeles:20210928T132000
DTSTAMP:20260406T235655
CREATED:20210827T004513Z
LAST-MODIFIED:20210921T181604Z
UID:2224-1632832200-1632835200@colleges.claremont.edu
SUMMARY:An algebraic introduction to the Kauffman bracket skein algebra (Helen Wong\, CMC)
DESCRIPTION:The Kauffman bracket skein algebra was originally defined as a generalization of the Jones polynomial for knots and links on a surface and is one of the few quantum invariants where the connection to hyperbolic geometry is fairly well-established.  Explicating this connection to hyperbolic geometry requires an understanding of the non-commutative structure of the skein algebra\, especially at roots of unity.  We’ll present some of the known (and not known) properties of the skein algebra.  Highlights include the Chebyshev polynomials\, quantum tori\, $SL(2\, \mathbb C)$ and other interesting algebraic objects.
URL:https://colleges.claremont.edu/ccms/event/antc-seminar-helen-wong-cmc/
LOCATION:On Zoom
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
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