Seminar: Polyhedral Geometry
Summer 2017
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.
Presentations
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
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.
Further References
Special Classes of Polytopes and Fans
Metric Properties of Polytopes
-
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
Tropical Geometry
-
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
Beyond Polytopes and Polyhedral Fans
- 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