Please adhere to the current German and Berlin Corona policies.
On Friday there will be an invited talk and several tutorials, demos and helpdesk sessions for polymake users.
Participants are encouraged to use a laptop with an installed version of polymake in the tutorials. If you have any polymake problem you want to get help during the workshop please describe your problem during the sign up process.
Please fill out the registration form!
| Friday | |||
|---|---|---|---|
| 09:00-09:30 | Registration (MA 313) | ||
| 09:30-10:30 | Talk: Khovanskii bases and Toric degenerations of Cox rings (MA 313) | ||
| Marta Panizzut | |||
| 10:30-11:00 | Break and Helpdesk (MA 313) | ||
| 11:00-12:00 | Tut: Polymake Basics (MA 313) | Tools (MA 621) | |
| Mara Belotti | Benjamin Lorenz, Lars Kastner | ||
| 12:00-14:00 | Lunch and Coffee | ||
| 14:00-15:00 | Tut: Oscar.jl (MA 313) | Markov bases in polymake (MA 621) | |
| Claudia Yun | Antony Della Vecchia | ||
| 15:00-15:30 | Break and Helpdesk (MA 313) | ||
| 15:30-16:30 | Use cases: | ||
| 1. Phylogenetics in polymake (MA 313) | |||
| Andrei Comăneci | |||
| 2. Regular subdivisions and tropical hypersurfaces (MA 313) | |||
| Sylvain Spitz | |||
| 16:30-18:15 | Helpdesk (MA 621) | ||
| ~18:45 | Dinner (self paid, at Café Hardenberg) | ||
We study combinatorial properties of toric degenerations of Cox rings of blow-ups of 3-dimensional projective space at points in general positions. We focus in particular on Ehrarht-type formulas for the multigraded Hilbert functions of these spaces. From our computations, it follows that the presentation ideal of the Cox ring of the blow up of the projective space at seven points is quadratically generated, as conjectured by Lesieutre and Park. The talk is based on recent work with Mara Belotti and will focus on computational aspects of the project.
General introduction to polymake, perl, and the datatypes.
We will talk about development tools for polymake and Oscar.jl, that are also useful in general, like: gdb, git, Yggdrasil, BinaryBuilder, screen, tmux, etc.
We give an overview of performing linear programming using Oscar.jl and implement the Conti-Traverso method which uses Groebner bases to solve certain integer linear programs. oscar_demo_for_participants.ipynb
We present some of the theory behind computing Markov basis, go over some of the implementations details and see some examples of how to compute Markov bases in polymake.
We present a new functionality in polymake which exploits tropical geometry to analyze phylogenetic data.
We show how to handle secondary fans in POLYMAKE and how to compute regular subdivisions with MPTOPCOM.
The developer meeting takes place on February 2nd and 4th. If you want to participate in the developer meeting as well, please let us know by email. Developers can find more information here.
Please contact us with any questions about the workshop. To email us, please use LASTNAME@math.tu-berlin.de.