[Turkmath:712] MSGSU seminar, Thursday, October 22, 16:00

[Mohan Ravichandran]

Dear All,

    Zafeirakis Zaferakopuoulos from Galatasaray university will talk
this Thursday at the Mimar Sinan math department's weekly seminar.


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"Polyhedral Omega: A new linear Diophantine system solver."

Polyhedral Omega is a new algorithm for solving linear Diophantine
systems (LDS), i.e., for computing a multivariate rational function
representation of the set of all non-negative integer solutions to a
system of linear equations and inequalities. Polyhedral Omega combines
methods from partition analysis with methods from polyhedral geometry.
In particular, we combine MacMahon’s iterative approach based on the
Omega operator and explicit formulas for its evaluation with geometric
tools such as Brion decomposition and Barvinok’s short rational
function representations. In this way, we connect two branches of
research that have so far remained separate, unified by the concept of
symbolic cones which we introduce. The resulting LDS solver Polyhedral
Omega is significantly faster than previous solvers based on partition
analysis and it is competitive with state-of-the-art LDS solvers based
on geometric methods. Most importantly, this synthesis of ideas makes
Polyhedral Omega by far the simplest algorithm for solving linear
Diophantine systems available to date. This is joint work with Felix
Breuer.
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Time : 16:00
Date : Thursday, October 22
Place : 106, Bomonti campus