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DTSTART;TZID=America/Los_Angeles:20220405T123000
DTEND;TZID=America/Los_Angeles:20220405T132000
DTSTAMP:20260416T080342
CREATED:20220125T062030Z
LAST-MODIFIED:20220326T052025Z
UID:2556-1649161800-1649164800@colleges.claremont.edu
SUMMARY:Covering by polynomial planks (Alexey Glazyrin\, University of Texas Rio Grande Valley)
DESCRIPTION:In 1932\, Tarski conjectured that a convex body of width 1 can be covered by planks\, regions between two parallel hyperplanes\, only if the total width of planks is at least 1. In 1951\, Bang proved the conjecture of Tarski. In this work we study the polynomial version of Tarski’s plank problem. \nWe note that the recent polynomial proofs of the spherical and complex plank covering problems by Zhao and Ortega-Moreno give some general information on zeros of real and complex polynomials restricted to the unit sphere. As a corollary of these results\, we establish several generalizations of the Bang plank covering theorem.\nUsing the polynomial approach\, we also prove the strengthening of the Fejes Tóth zone conjecture on covering a sphere by spherical segments\, closed parts of the sphere between two parallel hyperplanes. In particular\, we show that the sum of angular widths of spherical segments covering the whole sphere is at least π. \nThis is a joint work with Roman Karasev and Alexandr Polyanskii.
URL:https://colleges.claremont.edu/ccms/event/antc-seminar-alexey-glazyrin-university-of-texas-rio-grande-valley/
LOCATION:On Zoom
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
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BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20220412T123000
DTEND;TZID=America/Los_Angeles:20220412T132000
DTSTAMP:20260416T080342
CREATED:20211213T015630Z
LAST-MODIFIED:20220225T220354Z
UID:2510-1649766600-1649769600@colleges.claremont.edu
SUMMARY:Geometrization of Markov numbers (Oleg Karpenkov\, University of Liverpool)
DESCRIPTION:In this talk we link discrete Markov spectrum to geometry of continued fractions. As a result of that we get a natural generalization of classical Markov tree which leads to an efficient computation of Markov minima for all elements in generalized Markov trees.
URL:https://colleges.claremont.edu/ccms/event/antc-seminar-oleg-karpenkov-university-of-liverpool/
LOCATION:TBA
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
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DTSTART;TZID=America/Los_Angeles:20220419T123000
DTEND;TZID=America/Los_Angeles:20220419T132000
DTSTAMP:20260416T080342
CREATED:20220124T234622Z
LAST-MODIFIED:20220413T160024Z
UID:2553-1650371400-1650374400@colleges.claremont.edu
SUMMARY:A conjugacy criterion for two pairs of 2 x 2 matrices over a commutative ring (Bogdan Petrenko\, Eastern Illinois University)
DESCRIPTION:I will explain how to apply presentations of algebras (together with some classical results from non-commutative algebra) to obtain some 5 polynomial invariants telling us when two pairs of 2×2 matrices over a commutative ring are conjugate\, assuming that each of these pairs generate the matrix algebra. This talk is based on my joint paper with Marcin Mazur (Binghamton University):  Separable algebras over infinite fields are 2-generated and finitely presented\, Arch. Math. 93 (2009)\, 521-529.
URL:https://colleges.claremont.edu/ccms/event/antc-seminar-bogdan-petrenko-eastern-illinois-university/
LOCATION:On Zoom
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20220426T123000
DTEND;TZID=America/Los_Angeles:20220426T132000
DTSTAMP:20260416T080342
CREATED:20220127T053038Z
LAST-MODIFIED:20220421T192843Z
UID:2570-1650976200-1650979200@colleges.claremont.edu
SUMMARY:Bounds for nonzero Littlewood-Richardson coefficients (Müge Taskin\, Boğaziçi University\, Turkey)
DESCRIPTION:As  $\lambda$ runs through all integer partitions\, the set of   Schur functions $\{s_{\lambda}\}_\lambda$ forms a basis in the ring of symmetric functions. Hence the rule $$s_{\lambda}s_{\mu}=\sum c_{\lambda\,\mu}^{\gamma} s_{\gamma}$$ makes sense and the coefficients $c_{\lambda\,\mu}^{\gamma}$ are called \textit{Littlewood-Richardson (LR) coefficients}. The calculations of Littlewood-Richardson coefficients has been an important problem from the first time they were introduced\, due to their important role in representation theory of symmetric groups and enumerative geometry. \nIn this talk we will explain some of the main features of these coefficients and provide a summary of the characterizations given by Littlewood and Richardson (1934)\, Berenstein- Zelevinsky ()1988) and Knutson-Tao (1999). Then we will explain our approach to a seemingly easier problem\, that is\, the determination of  triples $(\lambda\,\mu\,\gamma)$  of partitions for which $c_{\lambda\,\mu}^{\gamma}$ is non zero. Our method describes some upper and lower bounds for triples $(\lambda\,\mu\,\gamma)$ with nonzero  $c_{\lambda\,\mu}^{\gamma}$\, by using  Young diagram combinatorics and especially\, the indispensable Dominance order. This is joint work with R. Bedii Gümüş and supported by Tübitak/1001/115F156.
URL:https://colleges.claremont.edu/ccms/event/antc-seminar-muge-taskin-bogazici-university-turkey/
LOCATION:On Zoom
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
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