My Research
My research centers around mathematical characteristics of special holonomy manifolds and related geometries. These manifolds not only hold a central place in differential geometry, but also are interesting spaces on which to compactify superstring theories and M-Theory. I am particular interested in using techniques from geometric flows to study these manifolds and related structures.
Publications
A. Kennon, "Spin(7)-Manifolds and Multisymplectic Geometry", J. Math. Phys. vol. 62, 2021. Published Version
A. Kennon and J. D. Lotay, "Geometric Flows of G2-Structures on 3-Sasakian 7-Manifolds", Journal of Geometry and Physics, vol. 187, 2023. Published Version
A. Kennon, "Remarks on Exact G2-Structures on Compact Manifolds", Accepted by Differential Geometry and its Applications (2023) Submitted Version
A. Kennon, Closed G2-Structures from Extremally Ricci-Pinched Geometry, Submitted to Journal of Geometric Analysis (2023) Submitted Version
A. Kennon, G2-Manifolds and M-Theory Compactifications, Submitted to Reviews of Mathematical Physics (2023) Submitted Version
Talks
Some Remarks on Exact G2-Structures on Compact Manifolds (UCSB Differential Geometry Seminar, 02/04/2022)
On the Laplacian Flow and its Soliton Solutions (University of Wisconsin, Madison Geometry and Topology Seminar, 04/29/2022)
Spin(7)-Manifolds and Multisymplectic Geometry (NYU Geometry Festival Poster Session, 04/30/2022)
Geometric Flows of G2-Structures (University of California, Irvine Differential Geometry Seminar, 05/03/2022)
Soliton Solutions of the Laplacian Flow from the Perspective of Exact G2-Structures (FIU Geometry Seminar, 08/26/2022)
Geometric Flows of 3-Sasakian Structures (Simons Collaboration on Special Holonomy in Geometry, Analysis, and Physics Meeting at Stony Brook, 09/11/2022)
Applications of Geometric Flows to Questions in Nearly-Parallel G2-Geometry (UCSB Differential Geometry Seminar, 10/07/2022)
Nearly Parallel G2-Structures from the Perspective of Geometric Flows (University of Oregon Geometric Analysis Seminar, 11/07/2022)
On the Stability of 3-Sasakian Nearly Parallel G2-Structures (Rutgers Geometry and Topology Seminar, 12/13/2022)
Applications of Geometric Flows of G2-Structures to 3-Sasakian Geometry (University of Chicago Geometric Analysis Seminar, March 2023)
Nearly-Parallel G2-Structures from the Perspective of Geometric Flows (Workshop on Ricci Flow at the University of California, San Diego, May 2023)
Testing Curvature Pinching Conditions under the Laplacian Flow (University of Connecticut PDE and Differential Geometry Seminar, 09/25/2023)
Geometric Flows and Nearly-Parallel G2-Structures (Yale Geometric Analysis and Applications Seminar, 10/14/2023)
Testing Dynamical Stability of Nearly-Parallel G2-Structures (Brown Geometric Analysis Seminar, 11/07/2023)
Connections of Geometric Flows of G2-Structures to Complex and Sasakian Geometry (Rutgers Complex Analysis and Geometry Seminar, 11/10/2023)
Progress Towards Long-Time Existence and Convergence of Geometric Flows of G2-Structures (University of Maryland Informal Geometric Analysis Seminar, 11/14/2023)
Identifying Promising Initial Data for Geometric Flows of G2-Structures (Lehigh Geometric Analysis Seminar, 11/30/2023)
Testing Long-Time Existence Conjectures for Geometric Flows of G2-Structures (Rutgers Geometric Analysis Seminar, 12/05/2023)
Teaching Experience
Physics 6L. Fall 2017
Physics 1. Winter 2018
Physics 22. Spring 2018
Physics CS 140 Tensor Analysis for General Relativity. Spring 2018
Physics 110A Electricity and Magnetism. Summer B 2018
Physics 119A Statistical Physics. Summer B 2018
Physics 2. Spring 2020
Physics 103 Intermediate Mechanics. Summer A 2020
Physics 103 Intermediate Mechanics. Summer B 2020
Physics 119A Statistical Physics. Fall 2020
Physics 103 Intermediate Mechanics. Summer A 2021
Physics 2. Summer B 2021
Physics 100A Mathematical Methods of Physics. Summer A 2022
Physics 110A Electricity and Magnetism (Instructor of Record). Summer B 2022
Math 4B Ordinary Differential Equations. Fall 2022
Math 3B Calculus with Applications. Summer A 2023
Physics 104 Advanced Mechanics (Instructor of Record). Summer B 2023
UCSB Pillars Teaching Certificate. Conferred February 2022
UCSB Certificate in College and University Teaching. Will be awarded along with Ph.D. Thesis Linked Here.