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SUMMARY:Peter Kropholler (University of Southampton)
DTSTART:20200603T100000Z
DTEND:20200603T110000Z
DTSTAMP:20260425T012513Z
UID:CANTA/1
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/CANTA
 /1/">Amenable groups and Noetherian group rings</a>\nby Peter Kropholler (
 University of Southampton) as part of Royal Holloway CANTA-Launch\n\n\nAbs
 tract\nIn joint work with Karl Lorensen and Dawid Kielak\, we study an old
  question of Reinhold Baer\nwhich dates back to around 1960.\nwhich are th
 e groups such that the integral group ring is Noetherian. We shall see\nth
 at as well satisfying the maximal condition on subgroups (which Baer knew)
 \, they\nalso must be amenable. This then connects the question to some in
 teresting\nBurnside groups constructed by Ivanov and Olshanskii.\n \nI lov
 e this topic because it touches on two important and apparently very\ndiff
 erent things in 20th century mathematics: the Banach-Tarski paradox and\nt
 he roots of non-commutative algebraic geometry.\n
LOCATION:https://stable.researchseminars.org/talk/CANTA/1/
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BEGIN:VEVENT
SUMMARY:Leo Ducas (CWI Amsterdam)
DTSTART:20200603T150000Z
DTEND:20200603T160000Z
DTSTAMP:20260425T012513Z
UID:CANTA/2
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/CANTA
 /2/">An Algorithmic Reduction Theory for Binary Codes</a>\nby Leo Ducas (C
 WI Amsterdam) as part of Royal Holloway CANTA-Launch\n\n\nAbstract\nJoint 
 work (in Progress) with\nThomas Debris-Alazard and Wessel van Woerden\n\nL
 attice reduction is the task of finding a basis of short and somewhat orth
 ogonal vectors of a given lattice. In 1985 Lenstra\, Lenstra and Lovasz pr
 oposed a polynomial time algorithm for this task\, with an application to 
 factoring rational polynomials. Since then\, the LLL algorithm has found c
 ountless application in algorithmic number theory and in cryptanalysis.\n\
 nThere are many analogies to be drawn between Euclidean lattices and linea
 r codes over finite fields. In this work\, we propose to extend the range 
 of these analogies by considering the task of reducing the basis of a bina
 ry code. In fact\, all it takes is to choose the adequate notion mimicking
  Euclidean orthogonality (namely orthopodality)\, after which\, all the re
 quired notions\, arguments\, and algorithms unfold before us\, in quasi-pe
 rfect analogy with lattices.\n
LOCATION:https://stable.researchseminars.org/talk/CANTA/2/
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BEGIN:VEVENT
SUMMARY:Lillian Pierce (Duke University)
DTSTART:20200611T150000Z
DTEND:20200611T160000Z
DTSTAMP:20260425T012513Z
UID:CANTA/3
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/CANTA
 /3/">On some open questions in number theory: from the perspective of mome
 nts</a>\nby Lillian Pierce (Duke University) as part of Royal Holloway CAN
 TA-Launch\n\n\nAbstract\nMany questions in number theory can be phrased lo
 osely in the following terms: “how often can this function take large va
 lues?” We will talk about some open questions in number theory where we 
 want to show that the answer is “never.” In particular\, we will discu
 ss some interesting situations where we can upgrade information that a fun
 ction “rarely takes large values” to information that it “never take
 s large values.” This perspective allows us to see some new connections 
 between open conjectures in number theory.\n
LOCATION:https://stable.researchseminars.org/talk/CANTA/3/
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