Marcus Aichmayr (Dissertation Defense): Computing Circuits and Sign Vectors with Applications to Linear Inequality and Reaction Networks

@Institut für Mathematik
  • Datum: 01.07.2026
  • Zeit: 09:30 Uhr
  • Ort: Raum 3321

Zoom-Link for online participation: 
https://uni-kassel.zoom-x.de/j/62311257535?pwd=4LpNlJrb4Y7DXHfWhAMuaA9b8nGl87.1

Meeting-ID: 623 1125 7535 
Kenncode: 407277 

 

Abstract

To study linear inequality systems, we generalize fundamental results of Rockafellar using circuits of a subspace. This leads to a circuit-based framework for both constructing solutions as a conformal sum and certifying unsolvability when no solution exists. As we state results as general as possible, the resulting algorithm works over arbitrary ordered fields, in particular real algebraic numbers.

Extending circuits to sign vectors leads naturally to oriented matroids, which can be viewed as abstractions of real subspaces. As an application, we investigate conditions for the uniqueness and unique existence of complex-balanced equilibria in generalized mass-action kinetics.

All methods developed in this thesis are implemented in four open-source SageMath packages, designed to support generality, exact computation, and computational efficiency.

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