401-3520-21L  Sphere Packings, Lattices and Codes

SemesterFrühjahrssemester 2021
DozierendeD. Radchenko
Periodizitäteinmalige Veranstaltung
KommentarNumber of participants limited to 12.

KurzbeschreibungSeminar on Sphere Packings, Lattices and Codes
LernzielTo learn about the sphere packing problem and its connection to various other topics such as error-correcting codes, combinatorial and spherical designs, and modular forms.
InhaltSome of the tentative topics include: sphere packing problem; the kissing number problem; error-correcting codes; Shannon capacity; finite projective planes; binary Golay code; spherical designs; theta functions of lattices; linear programming bounds for spherical codes and sphere packings.
LiteraturJ.H. Conway, N.J. Sloane, Sphere Packings, Lattices and Groups, 3rd edition, Springer-Verlag New York, 2017.
W. Ebeling, Lattices and Codes: A Course Partially Based on Lectures by Friedrich Hirzebruch, third edition, Springer Spektrum, Wiesbaden, 2013.
D. Zagier, Elliptic modular forms and their applications, in "The 1-2-3 of Modular Forms" (K. Ranestad, ed.), Universitext, Springer, Berlin, 2008.
C. Zong, Sphere Packings, Universitext, Springer-Verlag New York, 1999.
Voraussetzungen / BesonderesMany of the topics are self-contained and require only basic knowledge of linear algebra and analysis. Some of the later talks require basic knowledge of complex analysis. Some degree of familiarity with modular forms is also helpful, but not strictly necessary.