Course Announcement - Fall 2017

Math 270: Geometric and Topological Combinatorics

Instructor: Bernd Sturmfels

Contact: bernd at math, 925 Evans, phone messages 642 6550
Office hours: Mondays 9:30-11am, and by appointment

Lectures: Tuesdays and Thursdays, 8:00-9:30, in 9 Evans

First Day of Lectures: Thursday, August 24.
Last Day of Lectures: Tuesday, October 10.

Prerequisites: Mathematical maturity of an advanced graduate student. Interest in the MSRI program.

Description: This 2-unit course is offered under the header Hot Topics in Mathematics. Our topic is that
of the concurrent MSRI program with the same title. We offer a lightning introduction to research themes
in Geometric and Topological Combinatorics. This will enable students to participate in MSRI activities.

Format: The course consists of 13 lectures. Each lectures introduce the audience to a different book.
Our 13 books are listed below, and they are on reserve at the math library. I will lecture on selected topics
from that book. Participants are encouraged to form study groups, work out problems, and collaborate.

Book Groups: The following six groups (leaders parenthesized) will start during the first week of September:
IDEALS (Maddie Weinstein), MATROIDS (Charles Wang), POLYTOPES (Anna Seigal), DISCRIMINANTS
(Chris Eur), TRIANGULATIONS (Nic Brody), and ORIENTED MATROIDS (Melissa Sherman-Bennett).

Grading: The passing grade (S) will be awarded for participation and nicely written book reports.
Contents and format are flexible: you set your own standards. Submission deadline is November 27.

Wrap-up Meeting: We will meet on Monday, November 27. Book groups will report on their findings.

August 24: Lectures on Geometric Combinatorics (by Rekha Thomas)
August 29: A Course in Topological Combinatorics (by Mark De Longueville)
August 31, 8-9: Lectures on Polytopes (by Günter Ziegler)
September 5, 8-9: Computing the Continuous Discretely (by Matthias Beck, Sinai Robins)
September 7: No Class - Please attend Introductory Workshop at MSRI
September 12: Matroid Theory (by James Oxley)
September 14: Oriented Matroids (by A Björner, M Las Vergnas, B Sturmfels, N White, G Ziegler)
September 19: Combinatorics and Commutative Algebra (by Richard Stanley)
September 21: Arrangements of Hyperplanes (by Peter Orlik, Hiroaki Terao)
September 26: Triangulations (by Jesus De Loera, Jörg Rambau, Francisco Santos)
September 28: Gröbner Bases and Convex Polytopes (by Bernd Sturmfels)
September 28: (4-5pm) Please attend my Colloquium Lecture on Tensors
October 3: Essentials of Tropical Combinatorics (by Michael Joswig)
October 5: Discriminants, Resultants and Multidimensional Determinants (by I Gel'fand, M Kapranov, A Zelevinsky)
October 5: (4-5pm) Please attend Caroline Klivans' Colloquium Lecture
October 10: No Class - Please attend Workshop at MSRI
October 12: No Class - Please attend Workshop at MSRI
November 27 (Monday): 2-4pm, 740 Evans: Wrap-up meeting