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SUMMARY:Mini cours: Optimization\, lattices\, spherical designs
DTSTART:20230208T090000Z
DTEND:20230208T110000Z
DTSTAMP:20260424T152800Z
UID:indico-event-9409@indico.math.cnrs.fr
DESCRIPTION:Speakers: Frank Vallentin (Collogne)\n\nLattices (discrete sub
 groups of n-dimensional Euclidean spaces) are ubiquitous objects in mathem
 atics.One typical class of lattice problems is finding a good lattice with
  respect to some parameter\, for instance minimizing packing density\, max
 imizing covering density\, minimizing potential energy\, minimizing the qu
 antization constant. When locally looking at these optimization problems t
 he concept of spherical designs (finite point sets on the sphere which pro
 vide excellent cubature formulas for polynomials) often plays a central ro
 le. I will look at this phenomenon in depth.Another typical problem for la
 ttices is algorithmic. For instance the closest vector problem (given a la
 ttice and a point in Euclidean space\, what is the closest lattice vector 
 to this given point?). In general the closest vector problem is NP-hard. I
  will show that one can solve the closest vector problem in polynomial tim
 e for special classes of lattices.One new approach to efficiently solve th
 e closest vector problem for other classes of lattices could go via the co
 ncept of least distortion metric embeddings: How to embed the flat torus g
 iven by a lattice into Euclidean space with minimal metric distortion. I w
 ill show how a semidefinite optimization approach can be used to find and 
 analyze least distortion Euclidean embeddings of flat tori.Quand et où
  :- Mercredi 08 Février : 10h-12h\, Salle Pellos (1R2 - 207)-
  Jeudi 09 Février : 10h-12h\, Salle Cavailles (1R2 - 132) \n\n
 https://indico.math.cnrs.fr/event/9409/
LOCATION:Salle Pellos (1R2 - 207) le mercredi et Salle Cavailles (1R2 - 13
 2) le jeudi
URL:https://indico.math.cnrs.fr/event/9409/
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