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SUMMARY:Minhyong Kim (Warwick and Korea Institute for Advanced Study)
DTSTART:20200501T140000Z
DTEND:20200501T150000Z
DTSTAMP:20260404T094832Z
UID:CGTAColloquium/1
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/CGTAC
 olloquium/1/">Principal bundles in diophantine geometry</a>\nby Minhyong K
 im (Warwick and Korea Institute for Advanced Study) as part of Colloquium 
 of the Centre for Geometry\, Topology\, and Applications (Southampton)\n\n
 \nAbstract\nPrincipal bundles and their moduli have seen a remarkable arra
 y of application in geometry and topology over the past 50 years or so. Th
 eir uses in number theory are perhaps less well known. This talk will give
  a brief introduction to arithmetic principal bundles with a focus on appl
 ication to Diophantine geometry\, the geometric study of rational or integ
 ral solutions to polynomial equations.\n
LOCATION:https://stable.researchseminars.org/talk/CGTAColloquium/1/
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SUMMARY:Jie Wu (Hebei Normal University\, China)
DTSTART:20210507T140000Z
DTEND:20210507T150000Z
DTSTAMP:20260404T094832Z
UID:CGTAColloquium/2
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/CGTAC
 olloquium/2/">Modular cohomotopy groups</a>\nby Jie Wu (Hebei Normal Unive
 rsity\, China) as part of Colloquium of the Centre for Geometry\, Topology
 \, and Applications (Southampton)\n\n\nAbstract\nCohomotopy (cohomology) t
 heory can be viewed as a (non-abelian) generalized cohomology theory\, tha
 t has various applications such as its deep connections with framed cobord
 ism via unstable and framed version of Pontrjagin-Thom construction. The (
 integral) cohomotopy sets/groups have been extensively studied. In this ta
 lk\, after giving a breif review on cohomotopy theory\, we propose the stu
 dy on modular cohomotopy theory\, which has canonical connections with int
 egral cohomotopy theory via double suspensions and Anick fibre sequences. 
 Finally\, we will report our recent progress on modular cohomotopy theory.
  This is a joint work with Pengcheng Li and Jianzhong Pan.\n
LOCATION:https://stable.researchseminars.org/talk/CGTAColloquium/2/
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