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SUMMARY:Henry Towsner (U Penn)
DTSTART:20200709T180000Z
DTEND:20200709T190000Z
DTSTAMP:20260423T035749Z
UID:OLS/11
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OLS/11/">Sho
 uld we believe in nonstandard analysis?</a>\nby Henry Towsner (U Penn) as 
 part of Online logic seminar\n\n\nAbstract\nNonstandard analysis has been 
 the one of the focal points for debate about the role of the axiom of choi
 ce in mathematics.  I'll argue that this discussion often conflates two di
 stinct issues - the question of whether mathematical arguments are valid\,
  and the question of whether all mathematical objects should be understood
  to "exist" in the same way.  I'll discuss various ways of showing that mo
 st uses of nonstandard analysis in mathematics don't actually use the axio
 m of choice\, and how this perspective can be used to obtain new mathemati
 cal results (including applications\, joint with William Simmons\, to find
 ing new bounds for primality testing in polynomial rings).  On the other h
 and\, I'll argue (based on joint work with Kenny Easwaran) that the same p
 erspective argues against interpreting nonstandard values too literally wh
 en considering applications with real-world interpretations.\n
LOCATION:https://researchseminars.org/talk/OLS/11/
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