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UID:fc99b15a-24c3-4a23-8019-e0798f925387@nexttoyou
DTSTAMP:20261105T154023Z
DTSTART:20261112T083000Z
DTEND:20261112T213000Z
SUMMARY:Colloquium: Alexander Teplyaev
LOCATION:Hylan Building 1106a\, Hylan Building\, Rochester\, NY 14620
DESCRIPTION:Bridging Classical Analysis\, Fractals\, and Aperiodic Order\n
 \nRobert Strichartz’s work helped build a bridge from classical harmonic\
 nanalysis and partial differential equations to analysis on fractals.\nFo
 llowing this perspective\, I will describe how energy provides a\ncommon 
 starting point for defining Laplacians\, studying\neigenfunctions\, and c
 onstructing diffusion on spaces without smooth\ncoordinates. The Sierpińs
 ki gasket and related self-similar networks\nillustrate how geometric sca
 ling produces spectral gaps\, localized\neigenfunctions\, and diffusion w
 ith scaling laws different from those\nof Brownian motion in Euclidean sp
 ace.\n\nI will then turn to aperiodic order\, motivated by structures suc
 h as\nquasicrystals\, which exhibit organization without periodicity. The
 \ncollection of translates of an aperiodic pattern leads to a space\ncomb
 ining Euclidean and fractal features. Studying diffusion and\nLaplacians 
 on these pattern spaces reveals connections among analysis\,\nprobability
 \, and dynamical systems. Throughout the talk\, concrete\nexamples will i
 llustrate how geometry\, self-similarity\, and order\ninfluence analytic 
 behavior\, and how classical ideas extend to these\nunfamiliar settings. 
 The talk will be accessible to a broad\nmathematical audience\, including
  graduate students. No prior\nbackground in fractal analysis or aperiodic
  order will be assumed.\n\nhttp://next-to-u.app/events/fc99b15a-24c3-4a23
 -8019-e0798f925387
URL:http://next-to-u.app/events/fc99b15a-24c3-4a23-8019-e0798f925387
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