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UID:www.tcs.tifr.res.in/event/1644
DTSTAMP:20251230T040224Z
SUMMARY:Lattice packing of spheres in high dimensions using a stochasticall
 y evolving ellipsoid
DESCRIPTION:Speaker: Boaz Klartag (The Weizmann Institute of Science)\n\nAb
 stract: \nWe prove that in any dimension n there exists an origin-symmetri
 c ellipsoid of volume $c n^2$ that contains no points of $Z^n$ other than 
 the origin. Here $c > 0$ is a universal constant. Equivalently\, there exi
 sts a lattice sphere packing in $R^n$ whose density is at least $c n^2 / 2
 ^n$. Previously known constructions of sphere packings in $R^n$ had densit
 ies of the order of magnitude of $n / 2^n$\, up to logarithmic factors. Ou
 r proof utilizes a stochastically evolving ellipsoid that accumulates at l
 east  $c n^2$ lattice points on its boundary\, while containing no lattic
 e points in its interior except for the origin.\nShort Bio:Boaz Klartag 
 is a professor in the Department of Mathematics at the Weizmann Institute 
 of Science. He obtained his PhD in 2004 from Tel Aviv University under t
 he supervision of Prof. Vitali Milman. His research interests lie in conve
 x geometry\, analysis\, and high-dimensional phenomena. Klartag's contrib
 utions include his work on the central limit theorem for convex sets\, Bou
 rgain's slicing problem\, needle decompositions in Riemannian geometry\, a
 nd the approximation of data by C^m-smooth functions. He has received nume
 rous accolades\, including the European Mathematical Society (EMS) Prize\,
  the Salem Prize\, and the Erdős Prize. Before joining Weizmann\, he held
  faculty positions at Princeton University and Tel Aviv University and was
  a Clay Research Fellow as well as a member of the Institute for Advanced 
 Study. He has also held visiting positions at the Fondation Sciences Math
 ématiques de Paris (FSMP)\, the Mathematical Sciences Research Institute 
 (MSRI)\, the Fields Institute at the University of Toronto\, Princeton Uni
 versity\, and ETH Zurich. \n
URL:https://www.tcs.tifr.res.in/web/events/1644
DTSTART;TZID=Asia/Kolkata:20251230T123000
DTEND;TZID=Asia/Kolkata:20251230T133000
LOCATION:via Zoom in A201
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