19062
Lecture
WiSe 13/14: (V) Aufbaumodul Diskrete Geometrie III
Raman Sanyal
Additional information / Pre-requisites
The target audience are students with a solid background in discrete geometry and/or convex geometry (en par with Discrete Geometry I & II). The topic of this course is a state-of-art of advanced topics in discrete geometry that find applications and incarnations in differential geometry, topology, combinatorics, and algebraic geometry.
Voraussetzungen: Preferably Discrete Geometry I and II. Background in discrete geometry (polytopes, subdivisions, h-vectors) and convex geometry (mixed volumes, Brunn-Minkowski, Aleksandrov-Fenchel) should suffice. close
Voraussetzungen: Preferably Discrete Geometry I and II. Background in discrete geometry (polytopes, subdivisions, h-vectors) and convex geometry (mixed volumes, Brunn-Minkowski, Aleksandrov-Fenchel) should suffice. close
Comments
This is the third in a series of three courses on discrete geometry. This advanced course centers around the g-Theorem, that is, the complete characterization of face numbers of simplicial convex polytopes. Combining ideas from the combinatorics (Discrete Geometry I) and the convex geometry (Discrete Geometry II) of polytopes naturally leads to McMullen's polytope/weight algebra. In this setup the g-Theorem and its proof can be clearly phrased. If time permits we will also address connections of the `algebra of polytopes' to intersection theory in toric and tropical geometry.
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Suggested reading
will be announced in class.
16 Class schedule
Regular appointments
Tue, 2013-10-15 10:00 - 12:00
Tue, 2013-10-22 10:00 - 12:00
Tue, 2013-10-29 10:00 - 12:00
Tue, 2013-11-05 10:00 - 12:00
Tue, 2013-11-12 10:00 - 12:00
Tue, 2013-11-19 10:00 - 12:00
Tue, 2013-11-26 10:00 - 12:00
Tue, 2013-12-03 10:00 - 12:00
Tue, 2013-12-10 10:00 - 12:00
Tue, 2013-12-17 10:00 - 12:00
Tue, 2014-01-07 10:00 - 12:00
Tue, 2014-01-14 10:00 - 12:00
Tue, 2014-01-21 10:00 - 12:00
Tue, 2014-01-28 10:00 - 12:00
Tue, 2014-02-04 10:00 - 12:00
Tue, 2014-02-11 10:00 - 12:00