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DTSTART;TZID=America/Los_Angeles:20200123T121500
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DTSTAMP:20260408T100201
CREATED:20191008T203742Z
LAST-MODIFIED:20200120T195443Z
UID:1599-1579781700-1579785000@colleges.claremont.edu
SUMMARY:Dragging the roots of a polynomial to the unit circle (Sinai Robins\, University of Sao Paulo)
DESCRIPTION:Several conditions are known for a self-inversive polynomial that ascertain the location of its roots\, and we present a framework for comparison of those conditions. We associate a parametric family of polynomials p_α(x) to each such polynomial p\, and define cn(p)\, il(p) to be the sharp threshold values of α that guarantee that\, for all larger values of the parameter\, p_α(x) has\, respectively\, all roots in the unit circle and all roots interlacing the roots of unity of the same degree.  Interlacing implies circle rootedness\, hence il(p) ≥ cn(p)\, and this inequality is often used for showing circle rootedness. Both il(p) and cn(p) turn out to be semi-algebraic functions of the coefficients of p\, and some useful bounds are also presented\, entailing several known results about roots in the circle. The study of il(p) leads to a rich classification of real self-inversive polynomials of each degree\, organizing them into a complete polyhedral fan. We have a close look at the class of polynomials for which il(p) = cn(p)\, whereas in general the quotient il(p)/cn(p) is shown to be unbounded as the degree grows. Several examples and open questions are presented.  This is joint work with Arnaldo Mandel.
URL:https://colleges.claremont.edu/ccms/event/antc-seminar-sinai-robins-university-of-sao-paulo/
LOCATION:Emmy Noether Room\, Millikan 1021\, Pomona College\, 610 N. College Ave.\, Claremont\, California\, 91711
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
GEO:34.099908;-117.7142522
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DTSTART;TZID=America/Los_Angeles:20200128T121500
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CREATED:20200124T175017Z
LAST-MODIFIED:20200124T232945Z
UID:1791-1580213700-1580217000@colleges.claremont.edu
SUMMARY:Castelnuovo-Mumford regularity of edge ideals of graphs (Siamak Yassemi\, University of Tehran)
DESCRIPTION:Let K be a field and S = K[x_1\,…\,x_n] be the polynomial ring in n variables over K. For a graded S-module M with minimal free resolution the Castelnuovo-Mumford regularity  is defined. We survey a number of recent studies of the Castelnuovo-Mumford regularity of the ideals related to a graph and their (symbolic) powers. Our focus is on the bounds and exact values for the regularity in terms of combinatorial data from associated graphs. This research program has produced many exciting results and\, at the same time\, opened many further interesting questions and conjectures.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-by-siamak-yassemi-university-of-tehran/
LOCATION:Emmy Noether Room\, Millikan 1021\, Pomona College\, 610 N. College Ave.\, Claremont\, California\, 91711
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
GEO:34.099908;-117.7142522
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