The geometry of convex polytopes and polyhedra is relevant in several areas of mathematics, both pure and applied. This includes, e.g., linear and combinatorial optimization, (toric) algebraic geometry, tropical geometry and (discrete) differential geometry.

Participants will present an original recent paper in the area. The target audience of the seminar are students in a master program in mathematics and graduate students of the Berlin Mathematical School. Yet the list of participants is closed by now.

All presentations will take place on Thursday July 20, 2017 in MA 621. We will start at 9:00 sharp! Each presentation will take about one hour. Everybody is welcome to attend.

9:00

Fabian Frickenstein

Adam Bohn, Yuri Faenza, Samuel Fiorini, Vissarion Fisikopoulos, Marco Macchia, Kanstantsin Pashkovich:
Enumeration of 2-level polytopes,
arXiv:1703.01943

10:05

Jorge Alberto Olarte

Vladimir Grujić, Marko Pešović:
Face enumeration on matroid base polytopes,
arXiv:1704.06715

11:10

Marco Buhlheller

Gaku Liu:
Mixed volumes of hypersimplices,
Electron. J. Combin. 23
(2016), no. 3, Paper 3.19, 19 pp.

14:30

Johanna Steinmeyer

Frédéric Bihan, Ivan Soprunov:
Criteria for strict monotonicity of the mixed volume of convex polytopes,
arXiv:1702.07676

15:35

Sybille Meyer

Daniel Irving Bernstein, Colby Long:
L-Infinity optimization in tropical geometry and phylogenetics,
arXiv:1606.03702

16:40

Paul Vater

Benoît Bertrand, Lucía López de Medrano, Jean-Jacques Risler:
On the total curvature of tropical hypersurfaces,
Algebraic and combinatorial aspects of tropical geometry, pp. 21-43,
Contemp. Math., 589, Amer. Math. Soc., Providence, RI, 2013.

- Takayuki Hibi, Liam Solus: Facets of the r-stable (n,k)-hypersimplex, Ann. Comb. 20 (2016), no. 4, 815-829.
- Christophe Hohlweg, Vincent Pilaud, Salvatore Stella: Polytopal realizations of finite type g-vector fans arXiv:1703.09551
- Raman Sanyal, Christian Stump: Lipschitz polytopes of posets and permutation statistics, arXiv:1703.10586

- Sylvie Corteel, Jang Soo Kim, Karola Mészáros: Volumes of generalized Chan-Robbins-Yuen polytopes, arXiv:1704.02701
- Ivan Soprunov, Artem Zvavitch: Bezout inequality for mixed volumes, arXiv:1507.00765

- Andries E. Brouwer, Jan Draisma, Bart J. Frenk: Lossy gossip and composition of metrics, Discrete Comput. Geom. 53 (2015), no. 4, 890-913.
- Stéphane Gaubert, Frédéric Meunier: Carathéodory, Helly and the others in the max-plus world, Discrete Comput. Geom. 43 (2010), no. 3, 648-662.
- Ralph Morrison, Ngoc M. Tran: The tropical commuting variety, Linear Algebra Appl. 507 (2016), 300-321.
- Yaroslav Shitov: A counterexample on tropical linear spaces, Linear Algebra Appl. 511 (2016), 19-21.
- Ngoc M. Tran: Enumerating Polytropes, arXiv:1310.2012

- Spencer Backman: Riemann-Roch Theory for Graph Orientations, arXiv:1401.3309
- Philip Brinkmann, Günter M. Ziegler: A flag vector of a 3-sphere that is not the flag vector of a 4-polytope, Mathematika 63 (2017), no. 1, 260-271.
- M.A. Dickmann: A Combinatorial Geometric Structure on the Space of Orders of a Field: I, European Journal of Combinatorics 18:6 (1997), 613-634.
- M.A. Dickmann, A. Petrovich: Fans in the Theory of Real Semigroups, II. Combinatorial Theory, arXiv:1703.07433.
- Matthias Lenz: On powers of Plücker coordinates and representability of arithmetic matroids, arXiv:1703.10520