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SUMMARY:Tempered holomorphic functions via condensed mathematics - Lucas V
 alle Thiele\, University of Cambridge
DTSTART:20260130T160000Z
DTEND:20260130T170000Z
UID:TALK234862@talks.cam.ac.uk
CONTACT:Kelly Wang
DESCRIPTION:In recent years\, Clausen and Scholze introduced condensed mat
 hematics\, a new framework for analytic geometry that unifies Archimedean 
 and non-Archimedean geometry and allows for Abelian categories of complete
  modules. In this talk\, I will give a gentle introduction to this theory 
 and explain how it can be used to rediscover the classical notion of a tem
 pered holomorphic function.\n\nA holomorphic function is tempered if it do
 es not grow too fast near the boundary of its domain. For example\, the fu
 nction 1/z is tempered on the punctured unit disc\, while exp(1/z) is not.
  Such functions play a key role in the theory of differential equations\, 
 particularly in the quest to find Riemann-Hilbert correspondences\, a stor
 y that goes back to Hilbert's 21st Problem. Even though this notion is ver
 y concrete and genuinely analytic\, we will see that condensed mathematics
  enables us to recover it in a categorical and largely "analysis-free" way
 .
LOCATION:MR13
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