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Jul 7, 2026, 9:00 - 11:00 AM

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Dissertation Defense for Justin Thorpe

Jul 20, 2026, 1:00 - 2:30 PM

 

Candidate:  Justin Thorpe

Degree Program:  PhD, Mathematical Sciences

Date of Defense:   Monday, July 20, 2026

Time:  1:00pm

Location of Defense
Zoom

Defense Title:  Periodic Orbits in the Setting of Combinatorial Dynamics

Defense Abstract:
This dissertation develops a theoretical framework for the generation of valid combinatorial multivector fields (CMVF) found within Conley-Morse-Forman theory. A CMVF is the setting of an abstract combinatorial dynamical system that can be linked to a finite phase space discretization to compute topological regions of interest for the underlying dynamical system. We introduce notions of flow accumulation and define dynamical transition spaces to generalize the existing approach in the literature of linking the abstract theory and the actual flow, which allows us to address practical limitations and provide connection to other facets of the theory. We demonstrate this new approach by examining two differential equations.

 

Committee Members
Thomas Wanner, Chair
Evelyn Sander
Daniel Anderson
Ernest Barreto

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