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",  Differential Geometry and its Applications, vol. 93, 2024. Published Version 

• A. Kennon, Closed G2-Structures from Extremally Ricci-Pinched Geometry (Submitted)  Submitted Version 

• A. Kennon, Dimensional Reduction of Geometric Flows of Spin(7)-Structures (Forthcoming) Outline

• A,Kennon, The Laplacian Flow of G2-Structures on Complete Non-Compact 7-Manifolds (Forthcoming) Outline   

• A. Kennon, G2-Manifolds and M-Theory Compactifications  (Accepted) 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. Awarded along with Ph.D. Degree. CCUT Thesis Linked Here.