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SUMMARY:Emmanuel Breuillard (University of Cambridge)
DTSTART:20210211T220000Z
DTEND:20210211T230000Z
DTSTAMP:20260423T024019Z
UID:JNTS/12
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/JNTS/12/">A 
 subspace theorem for manifolds</a>\nby Emmanuel Breuillard (University of 
 Cambridge) as part of Columbia CUNY NYU number theory seminar\n\n\nAbstrac
 t\nIn the late 90's Kleinbock and Margulis solved a long-standing conjectu
 re due to Sprindzuk regarding diophantine  approximation on submanifolds o
 f $\\Bbb R^n$. Their method used homogeneous  dynamics via the so-called n
 on-divergence estimates for unipotent  flows on the space of lattices. Thi
 s new point of view has revolutionized metric diophantine approximation. I
 n this talk I will discuss how these ideas can be used to revisit the cele
 brated Subspace Theorem of W. Schimidt\, which deals diophantine approxima
 tion for linear forms with algebraic coefficients and is a far-reaching ge
 neralization of Roth's theorem. Combined with a certain understanding of t
 he geometry at the heart of Schmidt's Subspace Theorem\, in particular the
  notion of Harder-Narasimhan filtration and related ideas borrowed from Ge
 ometric Invariant Theory\, the Kleinbock-Margulis method leads to a metric
  version of the Subspace Theorem\, where the linear forms are allowed to d
 epend on a parameter. This result encompasses much previous work about dio
 phantine exponents of submanifolds. If time permits I will also discuss co
 nsequences for diophantine approximation on Lie groups. Joint work with Ni
 colas de Saxc\\'e (Paris 13).\n
LOCATION:https://researchseminars.org/talk/JNTS/12/
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