Vorkenntnisse in Diskreter Geometrie und/oder Konvexgeometrie erforderlich.
Working/good knowledge of Discrete or/and Convex Geometry is needed.
Die online Vorbesprechung findet am (first online meeting will be at)
Dienstag, 21.04.2020, 16:00 s.t..
If you are interested in participating, please send me an email so that I can provide you with the “how´´ .
Vorlesungszeiten: Dienstag, 10-12, online
Vorlesungsbeginn: April, 21st; if you are interested in participating, please send me an email so that I can provide you with the “how´´ .
Inhalt: Covering numbers, Dvoretzky’s theorem, reverse Brunn-Minkowski theorem, L_p/dual-Brunn-Minkowski theory, volume distribution in convex bodies
Vorkenntnisse: Fundierte Kenntnisse in der Konvexgeometrie
Literatur: (vorläufig)
Shiri Artstein-Avidan, Apostolos Giannopoulos and Vitali Milman, Asymptotic Geometric Analysis, Part I, AMS 2015.
Guillaume Auburn and Stanislaw J. Szarek, Alice and Bob meet Banach, AMS 2017.
Silouanos Brazitikos, Apostolos Giannopoulos, Petros Valettas and Beatrice-Helen Vritsiou, Geometry of isotropic convex bodies, AMS 2014.
Richard Gardner, Geometric Tomography, Cambridge 2006.
Alexander Koldobsky, Fourier analysis in convex geometry, AMS 2005.
Rolf Schneider, Convex bodies: The Brunn-Minkowsi theory, Cambridge 2014.
Bei Fragen, bitte e-mail an mich.
Vorlesungszeiten (times&locations): Donnerstag, 10-12 & Freitag, 10-12, online ((average)weekly format: lectures 3 + exercises 1)
Vorlesungsbeginn (start): April 23rd; if you are interested in participating, please send me an email so that I can provide you with the “how´´ .
Inhalt (content): Lattices, reduction theory, packing and covering of convex bodies,
successive&covering minima, transference theorems, lattice points and convex bodies
Vorkenntnisse (requirements): Diskrete Geometrie I & II, bzw. fundierte Kenntnisse über strukturelle und metrische Eigenschaften konvexer Mengen. Discrete Geometry I/II, or solid knowledge on structural and metrical/analytic properties of convex sets.
Literatur: (vorläufig/preliminary)
John William Scott Cassels, An Introduction to the Geometry of Numbers, 1971.
Peter Manfred Gruber, Convex and Discrete Geometry, 2007.
Peter Manfred Gruber and Cornelius Gerrit Lekkerkerker, Geometry of Numbers, 1987.
Laszlo Lovász: An Algorithmic Theory of Numbers, Graphs, and Convexity, 1986.
Carl Ludwig Siegel, Lectures on the Geometry of Numbers, 1988.
If you have any questions, please send me an email.