Contact Info
Combinatorics & Optimization
University of Waterloo
Waterloo, Ontario
Canada N2L 3G1
Phone: 519-888-4567, ext 33038
PDF files require Adobe Acrobat Reader.
Title: Positivity Problems for Linear Recurrences
Speaker: | Steve Melczer |
Affliliation: | University of Waterloo |
Zoom: | Contact Emma Watson |
Abstract:
Although sequences satisfying linear recurrence relations have been studied for centuries, and appear as some of the first examples of combinatorial sequences encountered in an introductory combinatorics class, there are natural examples of simply stated problems related to their basic behaviour whose decidability is unknown. In this talk we survey some open computability and complexity questions related to the positivity of linearly recurrent sequences, before examining a new approach to proving positivity using rigorous numerical methods for functions satisfying linear differential equations. As a consequence, we give the first proof (to our knowledge) of solution uniqueness in genus one for an influential model of Canham which predicts the shape of biomembranes. Joint work with Marc Mezzarobba.
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Combinatorics & Optimization
University of Waterloo
Waterloo, Ontario
Canada N2L 3G1
Phone: 519-888-4567, ext 33038
PDF files require Adobe Acrobat Reader.
The University of Waterloo acknowledges that much of our work takes place on the traditional territory of the Neutral, Anishinaabeg and Haudenosaunee peoples. Our main campus is situated on the Haldimand Tract, the land granted to the Six Nations that includes six miles on each side of the Grand River. Our active work toward reconciliation takes place across our campuses through research, learning, teaching, and community building, and is centralized within our Office of Indigenous Relations.