Shane Rankin - Research

Research

My Advisor is Dr. Wee Liang Gan. My research interests revolve around understanding Symplectic and Poisson Geometry via interactions with Lie theory.

Papers/Preprints:

The Curvature of Left-invariant Magnetic Systems - joint with I. Terek, D. Weed - Submitted - arXiv
Algebroid Desingularizable Poisson Structures -Submitted - arXiv
The Hard Lefschetz Theorem on Kähler Lie Algebroids - Illinois Journal of Mathematics, Volume 70, Issue 1 - Journal - arXiv
Symplectic Hodge Theory on Lie Algebroids - Differential Geometry and its Applications, Volume 102, Feb. 2026 - Journal - arXiv

Talks Given:

External:

Symplectic Hodge Theory on Lie Algebroids- May 2025 - AMS Western Sectional Special Session on Recent Developments in Contact and Symplectic Geometry
Symplectic Hodge Theory on Lie Algebroids - March 2025 - Gone Fishing 2025
Symplectic Hodge Theory on Lie Algebroids - February 2025 - Claremont/McKenna Topology Seminar

Internal:

Shadows of Symplectic Geometry in some Poisson Manifolds - October 2025 - UCR Geometry/Topology Seminar
The Hard Lefschetz Theorem on Kähler Lie Algebroids - April 2025 - UCR Geometry/Topology Seminar
Introduction to Riemannian Hodge Theory - April 2025 - UCR Graduate Student Seminar
Introduction to J-Holomorphic Curves - November 2024 - UCR Pre-Symplectathon Seminar
Symplectic Hodge Theory on Lie Algebroids - May 2024 - UCR Graduate Student Seminar
Moment Maps in Algebraic Geometry - May 2024 - UCR Algebraic Geometry Course
Introduction To Symplectic Hodge Theory - April 2024 - UCR 2024 Incoming Student Welcome Day

Fellowships/Awards:

Conferences Attended: