matthias beck

professor of mathematics
kumi does math
san francisco state universityfreie universität berlin

Discrete Geometry II: Lattice-Point Enumeration in Polyhedra

FU Berlin Summer 2021

Online Class Wed & Thu 10:15-11:45
Instructor Matthias Beck
Online Exercise Session Tue 8:30-10:00
Teaching Assistant Sophie Rehberg
Office Villa
Online office hours TBD

Course description. This is the second in a series of three courses on discrete geometry. This advanced course will cover a selection of topics from enumerative geometric combinatorics, centered around volume computation for polyhedra. In the discrete setting, this computation is based on Ehrhart's theory of counting lattice points in polytopes. We will witness an interplay of methods from combinatorics, geometry, and number theory, with an emphasis on actually computing discrete volume functions.

Prerequisites. Linear algebra, polyhedral geometry (convex polytopes, faces, polarity, etc.) as covered in Discrete Geometry I.

References. We will mostly follow

but there are several other good references:

Online musings. The FU currently does not allow our course to be in person, so I will stream (and record) every lecture via FU WebEx. Please check the FU guidelines dealing with the Corona virus frequently. The exercise discusssions will also be on FU WebEx; see the FU Whiteboard for more information and a link to our class sessions.

Exercises & final exam. We will post (on the FU Whiteboard sites) weekly homework problems; they will be due each Friday. To obtain the Aktive Teilnahme stamp, you will need to reach at least a 50% total score on the homework. The final exam will be a 48-hour take-home exam starting at 12:00 on 20 July 2021, posted here and on the FU Whiteboard sites. The Nachklausur will also be a 48-hour take-home exam starting at 12:00 on 21 September 2021; anyone wishing to take the Nachklausur needs to register (email to the instructor) by 1 September 2021.

I want to ensure that each of you accomplishes the goals of this course as comfortably and successfully as possible. At any time you feel overwhelmed or lost, please come and talk with me. Always ask lots of questions in class; my courses are interactive, whether in person or online.

department of mathematics
san francisco state university
1600 holloway ave
san francisco, ca 94132



institut für mathematik
diskrete geometrie
freie universität berlin
arnimallee 2
14195 berlin