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DTSTART;TZID=America/Los_Angeles:20220913T121500
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DTSTAMP:20260405T063909
CREATED:20220902T001706Z
LAST-MODIFIED:20220906T231347Z
UID:2814-1663071300-1663074600@colleges.claremont.edu
SUMMARY:Kriz's theorem via dynamics of linear operators (Yunied Puig de Dios\, CMC)
DESCRIPTION:The existence of a set $A\subset \N_0$ of positive upper Banach density such that $A-A:=\{m-n:m\, n\in A\, m>n\}$ does not contain a set of the form $S-S$ with $S$ a piecewise syndetic is in essence the content of a popular result due to K\v r\'{i}\v z in 1987. Since then at least four different proofs of this result have been given\, and all of them give basically the example originally exhibited by K\v r\'{i}\v z when viewed appropriately. We obtain a generalization of K\v r\'{i}\v z’s result. Our approach differs completely from the previous ones\, as this would be the first proof of K\v r\'{i}\v z’s Theorem which does not rely on Lov\'{a}sz’s Theorem for chromatic numbers of Kneser graphs. Furthermore\, it is done via operator theory\, namely using dynamics of bounded linear operators on infinite-dimensional complex separable Banach spaces. As a consequence\, our example is genuinely different from the one exhibited  originally by K\v r\'{i}\v z.
URL:https://colleges.claremont.edu/ccms/event/krizs-theorem-via-dynamics-of-linear-operators-yunied-puig-de-dios-cmc/
LOCATION:Davidson Lecture Hall\, CMC\, 340 E 9th St\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
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DTSTART;TZID=America/Los_Angeles:20220914T161500
DTEND;TZID=America/Los_Angeles:20220914T173000
DTSTAMP:20260405T063909
CREATED:20220830T232626Z
LAST-MODIFIED:20220912T190511Z
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SUMMARY:Continuity Versus Uniform Continuity (Prof. Gerald Beer)
DESCRIPTION:Title: Continuity Versus Uniform Continuity \nSpeaker: Gerald Beer\, Department of Mathematics\, California State University \nAbstract: In this talk we discuss the class of metric spaces – called the UC-spaces – whose members have this characteristic property:  each continuous function f on X  must be uniformly continuous. \n\nGerald Beer\, PhD UCLA 1971 won the faculty prize for teaching assistants at UCLA.  He was a full professor at California State University Los Angeles\, where he won the Presidents Distinguished Professor Award. He has around 140 papers in refereed journals plus two books: (1) Applied Calculus for Business and Economics; (2) Topologies on Closed and Closed Convex Sets.  He is on the editorial boards of The Journal of Convex Analysis and Set-Valued and Variational Analysis. In 1983-1984\, he was a Fulbright Professor associated with the Mathematical Consortium of Manila\, and in 1986\, he was a National Academy of Sciences exchange scholar at the Bulgarian Academy of Sciences.  He had visiting positions at the University of California\, Davis\, University of Minnesota\, University of Milan\, University of Salerno\, University of Naples II\, University of Limoges\, University of Montpellier II\, University of Perpignan\, University of Complutense Madrid\, Politecnica Valencia\, UMH Elche\, and Auckland Institute of Technology. A conference honoring Professor Beer was held in Varenna\, Lake Como\, Italy on his 65th birthday.
URL:https://colleges.claremont.edu/ccms/event/continuity-versus-uniform-continuity-prof-gerald-beer/
LOCATION:Humanities Auditorium\, Scripps College\, and Zoom\, Claremont\, CA\, 91711\, United States
CATEGORIES:Colloquium
GEO:34.1035221214;-117.709766675
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