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Posts by Collection
portfolio
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publications
Classification of Convex Ancient Solutions to Free Boundary Curve Shortening Flow in Convex Domains
Published in The Journal of Geometric Analysis, 2025
Joint with Theodora Bourni & Spencer Catron. We show that for each diameter of a closed convex region, there are exactly two ancient solutions to the free boundary curve shortening flow which backwards in time to said diameter.
Recommended citation: Theodora Bourni, Nathan Burns and Spencer Catron (2025). "Classification of Convex Ancient Solutions to Free Boundary Curve Shortening Flow in Convex Domains." The Journal of Geometric Analysis. 35(210).
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Stability of the Shrinking Semi-Circle Under the Free Boundary Curve Shortening Flow
Published in arXiv, 2026
Joint with Theodora Bourni and Mat Langford. We prove a sharp rate of convergence for free boundary curve shortening flows whose normalised flow converge to the unit semi-circle.
Recommended citation: Theodora Bourni, Nathan Burns and Mat Langford (2026). "Stability of the Shrinking Semi-Circle under the Free Boundary Curve Shortening Flow" arXiv:2603.06949.
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talks
Geometric Flows and Relativity Workshop
Published:
Title: Classification of Ancient Solutions to the Free Boundary Curve Shortening Flow in Convex Domains
SLMath - Graduate Student Seminar
Published:
Title: Ancient Solutions to Geometric Flows
MATRIX-MFO Tandem Workshop: Nonlinear Geometric Diffusion Equations
Published:
Title: Classification of Ancient Solutions to the Free Boundary Curve Shortening Flow in Convex Domains
ANU Geometric Analysis Seminar
Published:
Title: Classification of Ancient Solutions to the Free Boundary Curve Shortening Flow in Convex Domains
Rutgers Gauge Theory, Low-Dimensional Topology and Geometric Analysis Conference 2025
Published:
Title: Ancient Solutions to the Free Boundary Curve Shortening Flow
AMS Fall Central Meeting 2025: Special Session on Riemannian Geometry and Symmetry
Published:
Title: Stability of Ancient Rays
AMS Spring Southeastern Meeting 2026: Special Session on Geometric and Non-Smooth Analysis
Published:
Title: The Free Boundary Curve Shortening Flow and its Ancient Solutions
NCSU Geometric Analysis Seminar
Published:
Title: Stability in the Free Boundary Curve Shortening Flow
JHU Geometric Analysis Seminar
Published:
Title: Stability in the Free Boundary Curve Shortening Flow
teaching
Teaching Assistant at the University of Tennessee
Teaching Assistant, University of Tennessee, 2021
During my time as a graduate student at the University of Tennessee, I have been a teaching assistant for numerous courses.
Instructor of Record at the University of Tennessee
Instructor of Record, University of Tennessee, 2022
During my time as a graduate student at the University of Tennessee, I have been the instructor of record for numerous courses.