^ **Friday** ^ ^^
| 09:00-09:30 | **Registration** ||
| 09:30-10:30 | **Building Algorithmic Polytopes** ||
| ::: | //David Bremner// ||
| ::: | Room: MA313 ||
| 10:30-11:00 | **Coffee and Helpdesk** ||
| ::: | Room: MA315 ||
| 11:00-12:00 | **Tut: basics (perl)** | **Tut: C++ code** |
| ::: | //Assarf/Kastner// | //Lorenz/Müller// |
| ::: | Room: MA313 | Room: MA315 |
| 12:00-14:00 | **Lunch** ||
| 14:00-15:00 | **Very ample and Koszul segmental fibrations** ||
| ::: | //Matthias Beck// ||
| ::: | Room: MA313 ||
| 15:00-15:30 | **Coffee and Helpdesk** ||
| ::: | Room: MA315 ||
| 15:30-16:30 | **Tut: topaz** | **Tut: tropical/atint** |
| ::: | //Michael Joswig// | //Simon Hampe// |
| ::: | Room: MA313 | Room: MA315 |
| 16:30-18:00 | **Helpdesk** ||
| ::: | Rooms: MA313 / MA315 / MA621 / ... ||
| ~19:00 | **Dinner** (self paid) ||
**David Bremner:** Building Algorithmic Polytopes -- [[http://www.cs.unb.ca/~bremner/research/talks/matching-14b.pdf|Slides]]
In this talk I will discuss ongoing work to develop a compiler from a
simple ALGOL-like pseudocode to polynomial sized linear programs.
These LPs can compute the output for any input (of a given size) to
the corresponding algorithm by a trivial encoding of the input into
the objective function. The talk will cover the structure of the
inequalities needed to simulate a simple bit-oriented register machine
supporting arithmetic and arrays, and a limited kind of integrality
guarantee needed to solve these systems as linear, rather than integer
linear programs. I'll also give an overview of the current compiler
implementation, and time permitting a demo.\\
This talk shares some background and motivation with my recent MDS
seminar on "Succinct linear programs for easy problems", but it should
be accessible to people that missed that, and mostly new to people
that saw the previous talk.
**Matthias Beck:** Very ample and Koszul segmental fibrations -- [[http://math.sfsu.edu/beck/papers/veryample.slides.pdf|Slides]]
A lattice polytope P ⊂ **R**n is the convex hull of finitely many
points in **Z**n. There is a natural hierarchy of structural
sophistication for lattice polytopes, with various concepts motivated from
toric geometry and commutative algebra. We will discuss three such concepts in
this hierarchy, occupying a point of origin (normality), the bottom (very
ampleness), and the top spot (Koszul property). More specifically, we explore
a simple construction for lattice polytopes with a twofold aim. On the one
hand, we derive an explicit series of very ample 3-dimensional polytopes with
arbitrarily large deviation from the normality property, measured via the
highest discrepancy degree between the corresponding Hilbert functions and
Hilbert polynomials. On the other hand, we describe a large class of Koszul
polytopes of arbitrary dimensions, containing many smooth polytopes and
extending the previously known class of Nakajima polytopes.\\
This is joint work with Jessica Delgado, Joseph Gubeladze, and Mateusz Michalek.