We will meet Wednesdays, 4-6 pm in A6/SR009. The first meeting is on April 20th.
The topic of the seminar will be "polytopes." We will learn about special classes and properties of polytopes, and why they are interesting, combinatorially, geometrically, from the viewpoint of linear optimization, etc.
The seminar will be held in English.
Here is an explanation to the "Three Things" Exercise by Ravi Vakil: http://math.stanford.edu/~vakil/threethings.html
Tentative Schedule:
| Date |
Topic |
Speaker |
| May 04 |
Flow Polytopes |
Jan |
| May 18 |
Transportation Polytopes
(and not weakly vertex-decomposable polytopes)
|
Joshua |
| June 08 |
0/1-Polytopes |
Deborah |
| June 22 |
fiber polytopes |
Farid |
| July 06 |
inscribable polytopes |
Jasper |
| July 13 |
|
Kyle |
Literature
Here are some possible topics:
-- neighborly polytopes
Padrol, A. (2013). Many neighborly polytopes and oriented matroids. Discrete & Computational Geometry, 50(4), 865-902.
-- transportation polytopes, and not weakly vertex-decomposable polytopes
De Loera, J. A., & Klee, S. (2012). Transportation problems and simplicial polytopes that are not weakly vertex-decomposable. Mathematics of Operations Research, 37(4), 670-674.
-- associahedra and their diameter
Pournin, L. (2014). The diameter of associahedra. Advances in Mathematics, 259, 13-42.
Sleator, D. D., Tarjan, R. E., & Thurston, W. P. (1988). Rotation distance, triangulations, and hyperbolic geometry. Journal of the American Mathematical Society, 1(3), 647-681.
-- flow polytopes
Baldoni-Silva, W., De Loera, J.A., & Vergne, M. (2004). Counting integer flows in networks. Found. Comput. Math. 4, 277-314.
Mészáros, K., & Morales, A. H. (2019). Volumes and Ehrhart polynomials of flow polytopes. Mathematische Zeitschrift, 293(3), 1369-1401.
-- fatness of 4-polytopes
Eppstein, D., Kuperberg, G., & Ziegler, G. M. (2003). Fat 4-polytopes and fatter 3-spheres (pp. 282-310). CRC Press.
-- fiber polytopes
Billera, L. J., & Sturmfels, B. (1992). Fiber polytopes. Annals of Mathematics, 135(3), 527-549.
-- inscribable polytopes
Padrol, A., & Ziegler, G. M. (2016). Six topics on inscribable polytopes. In Advances in discrete differential geometry (pp. 407-419). Springer, Berlin, Heidelberg.
-- 0/1 polytopes
Ziegler, G. M. (2000). Lectures on 0/1-polytopes. In Polytopes—combinatorics and computation (pp. 1-41). Birkhäuser, Basel.
-- random polytopes
Bárány, I. (1992). Random polytopes in smooth convex bodies. Mathematika, 39(1), 81-92.
-- q-simplicial p-simple polytopes
Paffenholz, A., & Ziegler, G. M. (2004). The Et-construction for lattices, spheres and polytopes. Discrete & Computational Geometry, 32(4), 601-621.