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DTSTART;TZID=America/Los_Angeles:20190205T121500
DTEND;TZID=America/Los_Angeles:20190205T131000
DTSTAMP:20260413T170003
CREATED:20181205T171033Z
LAST-MODIFIED:20190123T223504Z
UID:963-1549368900-1549372200@colleges.claremont.edu
SUMMARY:Lattices from group frames and vertex transitive graphs (Lenny Fukshansky\, CMC)
DESCRIPTION:Tight frames in Euclidean spaces are widely used convenient generalizations of orthonormal bases. A particularly nice class of such frames is generated as orbits under irreducible actions of finite groups of orthogonal matrices: these are called irreducible group frames. Integer spans of rational irreducible group frames form Euclidean lattices with some very nice geometric properties\, called strongly eutactic lattices. We discuss this construction\, focusing on an especially interesting infinite family in arbitrarily large dimensions\, which comes from vertex transitive graphs. We demonstrate several examples of such lattices from graphs that exhibit some rather fascinating properties. This is joint work with D. Needell\, J. Park and J. Xin.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-lenny-fukshansky-cmc/
LOCATION:Millikan 2099\, Pomona College\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
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BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20190212T121500
DTEND;TZID=America/Los_Angeles:20190212T131000
DTSTAMP:20260413T170003
CREATED:20181227T132155Z
LAST-MODIFIED:20190120T184543Z
UID:994-1549973700-1549977000@colleges.claremont.edu
SUMMARY:Subgraph statistics (Benny Sudakov\, ETH Zurich)
DESCRIPTION:Given integers $k\,l$  and a graph $G$\, how large can be the fraction of $k$-vertex subsets of $G$ which span exactly $l$ edges?  The systematic study of this very natural  question  was recently initiated by Alon\, Hefetz\, Krivelevich and Tyomkyn who also proposed several interesting conjectures on this topic. \n\nIn this talk we discuss a theorem which proves one of their conjectures and implies an asymptotic version of another.  We also make some first steps towards analogous question for hypergraphs. Our proofs involve some Ramsey-type arguments\, and a number of different probabilistic tools\, such as polynomial anticoncentration inequalities and  hypercontractivity. \nJoint work with M. Kwan and T. Tran.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-benny-sudakov-eth-zurich/
LOCATION:Millikan 2099\, Pomona College\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
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BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20190219T121500
DTEND;TZID=America/Los_Angeles:20190219T131000
DTSTAMP:20260413T170003
CREATED:20190123T071222Z
LAST-MODIFIED:20190203T022044Z
UID:1141-1550578500-1550581800@colleges.claremont.edu
SUMMARY:Knowledge\, strategies\, and know-how (Pavel Naumov\, CMC)
DESCRIPTION:An agent comes to a fork in a road. There is a sign that says that one of the two roads leads to prosperity and another to death. The agent must take the fork\, but she does not know which road leads where. Does the agent have a strategy to get to prosperity? On one hand\, since one of the roads leads to prosperity\, such a strategy clearly exists. On the other\, the agent does not know what the strategy is. \nIf a coalition of agents has a strategy\, it knows that it has a strategy\, and it also knows what this strategy is\, then we say that the coalition has a know-how strategy. In this talk I will discuss several of my recent papers on modal logics that describe the interplay between coalition knowledge\, strategies\, and know-how strategies.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-pavel-naumov-cmc/
LOCATION:Millikan 2099\, Pomona College\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
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BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20190226T121500
DTEND;TZID=America/Los_Angeles:20190226T131000
DTSTAMP:20260413T170004
CREATED:20190112T015039Z
LAST-MODIFIED:20190218T190711Z
UID:1047-1551183300-1551186600@colleges.claremont.edu
SUMMARY:When is the product of Siegel eigenforms an eigenform? (Jim Brown\, Occidental College)
DESCRIPTION:Modular forms are ubiquitous in modern number theory.  For instance\, showing that elliptic curves are secretly modular forms was the key to the proof of Fermat’s Last Theorem.  In addition to number theory\, modular forms show up in diverse areas such as coding theory and particle physics.  Roughly speaking\, a modular form is a complex-valued function defined on the complex upper half-plane that satisfies a large number of symmetries.  A modular form has two invariants: weight and level.  If one fixes a weight and level\, the collection of modular forms of that weight and level form a finite-dimensional complex vector space.  One has a collection of operators on these spaces referred to as Hecke operators.  A natural question is if one takes two eigenforms of these operators and multiplies them\, when is the product still an eigenform?  It was shown in independent work by Duke and Ghate that there is a finite list of pairs of eigenforms whose product is again an eigenform.  In this talk we will report on the case when one replaces modular forms with the more general case of Siegel modular forms.  This is work that was partially conducted during an REU in summer 2018.  No prior familiarity with modular forms is assumed.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-jim-brown-occidental-college/
LOCATION:Millikan 2099\, Pomona College\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
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