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UID:20250711T223810EDT-3141drlRwr@132.216.98.100
DTSTAMP:20250712T023810Z
DESCRIPTION:Title: Classical and emerging ideas in sparse high-dimensional 
 approximation.\n\nAbstract: Approximating functions of many variables from
  limited samples is a key task in modern computational mathematics and dat
 a science. This task is made intrinsically difficult by the so-called curs
 e of dimensionality\, a term introduced by R.E. Bellman in the 1970s that 
 refers to computational challenges arising in high dimensions. The objecti
 ve of this seminar is to introduce classical and emerging mathematical ide
 as in high-dimensional approximation.\n	\n	We will illustrate the rudiments 
 of sparse polynomial approximation theory\, motivating our study with appl
 ications to parametric differential equations. Specifically\, we will pres
 ent methods for computing sparse polynomial approximations of holomorphic 
 functions of many variables from limited Monte Carlo samples\, focusing on
  techniques based on least squares and compressed sensing and showing unde
 r what circumstances they are provably able to alleviate the curse of dime
 nsionality. Time permitting\, we will also discuss how these ideas come in
 to play in current research areas such as deep learning approximation theo
 ry and spectral methods for high-dimensional PDEs. This seminar is mainly 
 based on the book 'Sparse Polynomial Approximation of High-Dimensional Fun
 ctions'\, co-authored by the speaker with B. Adcock and C.G. Webster\, and
  published for SIAM in 2022 (http://www.sparse-hd-book.com).\n\n \n\nSemin
 ar location: 4336-4384 Pavillon Aisenstadt\, UdeM\n
DTSTART:20221018T180000Z
DTEND:20221018T190000Z
SUMMARY:Simone Brugiapaglia (Concordia University)
URL:/mathstat/channels/event/simone-brugiapaglia-conco
 rdia-university-342827
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