Gregory J. Parker

Publications (Geometric Analysis)

Non-Product Minimal Submanifolds with Cylindrical Tangent Cones
Rafe Mazzeo, Gregory J. Parker
expected Jan. 2025
| In Preparation

ℤ₂-Harmonic Spinors and 1-forms on Connect Sums and Torus Sums of 3-Manifolds
Siqi He, Gregory J. Parker
July 2024
arXiv: 2407.10922 | Submitted

Gluing ℤ₂-Harmonic Spinors and Seiberg--Witten Monopoles on 3-Manifolds
Gregory J. Parker
February 2024
arXiv: 2402.03682 | Submitted

Concentrating Dirac Operators and Generalized Seiberg--Witten Equations
Gregory J. Parker
July 2023
arXiv: 2307.00694 | To appear in Mathematical Research Letters

Deformations of ℤ₂-Harmonic Spinors on 3-Manifolds
Gregory J. Parker
January 2023
arXiv: 2301.06245 | Submitted

Concentrating Local Solutions of the Two-Spinor Seiberg--Witten Equations on 3-Manifolds
Gregory J. Parker
October 2022
arXiv: 2210.08148 | Submitted

Publications (Applied Mathematics and Physics)

A propagator-based multilevel Monte-Carlo scheme for kinetic neutrals in edge plasmas
Gregory J. Parker, Maxim V. Umansky, Benjamin D. Dudson
September 2025.
| Submitted

Machine Learning approach to modeling of neutral particles transport in plasma
Maxim V. Umansky,Gregory J. Parker, Roman Smirnov
September 2025.
| Submitted

Coupling Fluid Plasma and Kinetic Neutral Models using Correlated Monte Carlo Methods
Gregory J. Parker, Maxim V. Umansky, Benjamin D. Dudson
July 2024.
arXiv: 2407.10936 | Nuclear Materials and Energy 42(101889), 2025.

LIBS and ablation threshold analysis using a megahertz Yb fiber laser oscillator.
Gregory J. Parker, Daniel E. Parker, Bai Nie, Vadim Lozovoy and Marcos Dantus.
Spectrochimica Acta Part B: Atomic Spectroscopy. May 2015.
DOI

Energy scaling of Yb fiber oscillator producing clusters of femtosecond pulses
Bai Nie, Gregory J. Parker, Vadim Lozovoy and Marcos Dantus.
Optical Engineering 53(5):051505. May 2013.
DOI

Talks and Conferences (Mathematics)

Non-Product Minimal Submanifolds with Cylindrical Tangent Cones
Invited Seminar Talk
University of Oregon Geometry Seminar
University of Oregon, Eugene, OR, May 2025.

Non-Product Minimal Submanifolds with Cylindrical Tangent Cones
Invited Seminar Talk
UCSD Geometry and Analysis Seminar
University of California San Diego, La Jolla, CA May 2025.

Non-Product Minimal Submanifolds with Cylindrical Tangent Cones
Invited Seminar Talk
Cornell Analysis Seminar
Cornell University, Ithaca NY May 2025.

Non-Product Minimal Submanifolds with Cylindrical Tangent Cones
Invited Seminar Talk
Leheigh Geometry Seminar
Virtual, 21 Jan 2025.

Non-Product Minimal Submanifolds with Cylindrical Tangent Cones
Invited Seminar Talk
MSRI Program Seminar
MSRI, Berkeley CA. 27 Nov 2024.

Non-Product Minimal Submanifolds with Cylindrical Tangent Cones
Invited Seminar Talk
Stanford Geometry Seminar
Stanford University, Stanford CA. 22 Nov 2024.

The role of ℤ₂-Harmonic 1-forms in Counting Special Lagrangians
Invited Conference Talk
Geometry and Analysis of Special Structures on Manifolds
MSRI, Berkeley. 21 Nov 2024.

ℤ₂-Harmonic Spinors and 1-forms II (joint with Siqi He)
Invited Conference Talk
Qingtian Geometry and Topology Conference 2024
Qingtian, China. 5 June 2024.

ℤ₂-Harmonic Spinors and Flat SL(2,C) connections on 3-Manifolds
Invited Conference Talk (Virtual)
Rutgers Geometric Analysis Seminar
Rutgers University, New Brunswick, NJ, 15 May 2024.

A Fredholm Framework for Singular Deformation Problems
Invited Conference Talk (Virtual)
Simons Collaboration on Special Holonomy Annual Meeting
Duke University, Durham, NC, 14 May 2024.

ℤ₂-Harmonic Spinors as Limiting Objects in Geometry and Topology
Seminar Talk
Representation Theory and Mathematical Physics Seminar
Louisiana State University, Baton Rouge LA, 22 April 2024.

Gluing, Excision, and the Alternating Method
Seminar Talk
Rutgers Geometric Analysis Seminar (Virtual)
Rutgers University, New Brunswick, NJ, January 2024.

Compactness and Wall-Crossing Formulas in Gauge Theory
Seminar Talk
Stanford Topology Seminar
Stanford University, Stanford CA, September 2023.

Deformations of ℤ₂-Harmonic Spinors
Invited Conference Talk
ULB Summer School on Geometric Analysis
Université libre de Bruxelles, Brussels, Belgium, August 2023.

Deformations of ℤ₂-Harmonic Spinors
Seminar Talk
Stanford Geometry Seminar
Stanford University, Stanford CA, January 2023.

Concentrating Local Solutions of the Two-Spinor Seiberg--Witten Equations
Invited Conference Talk
New Four-Dimensional Gauge Theories Conference
MSRI, Berkeley CA, Oct 2022.

Gluing ℤ₂-Harmonic Spinors
Invited Conference and Colloquium Talk
Simons Collaboration on Special Holonomy Annual Meeting and SCGP Weekly Talk
Simons Center for Geometry and Physics, Stony Brook NY, September 2022.

Variations of the ℤ₂-Harmonic Dirac Operator
Seminar Talk
Rutgers Geometric Analysis Seminar
Rutgers University, New Brunswick NJ, May 2022.

Gluing ℤ₂-Harmonic Spinors
Seminar Talk
Low-Dimensional Topology, Gauge Theory, and Symplectic Geometry Seminar
Simons Center for Geometry and Physics, Stony Brook NY, April 2022.

Gluing ℤ₂-Harmonic Spinors
Invited Conference Talk
AMS Special Session on Gauge Theory, Geometric Analysis, and Low-Dimensional Topology
Tufts University, Medford MA, March 2022.

Talks and Conferences (Applied Mathematics and Physics)

A propagator-based multi-level Monte-Carlo scheme for kinetic neutrals in edge plasmas
Conference Invited Talk
Plasma Edge Theory (PET) 20.
KU Leuven, Leuven Belgium, 25 September 2025.

A propagator-based multi-level Monte-Carlo scheme for kinetic neutrals in edge plasmas
Seminar Talk
LLNL-FES EMU(S) Seminar.
Lawerence Livermore National Laboratory, Fusion Energy Sciences, EMU(S) seminar 18 September 2025.

Differentiable Monte-Carlo and Implicit Coupling Methods
Seminar Talk
Computation Seminar
Princeton Plasma Physics Laboratory, Princeton NJ, 1 August 2024.

Differentiable Monte-Carlo and Implicit Coupling
Poster
26th Plasma Surface Interaction Conference
Marseilles France, 15 May 2024.

Coupling Fluid Plasma and Kinetic Neutral Models using Differentiable Monte-Carlo Methods
Seminar Talk
UEDGE and Magnetic Fusion Theory Seminar
Lawrence Livermore National Laboratory, Livermoe CA, 29 Nov 2023.

Coupling Fluid Plasma and Kinetic Neutral Models using Correlated Monte-Carlo Methods
Poster
APS Fall Meeting
Denver, CO, 1 Nov 2023.

Teaching

Math 126: Partial Differential Equations
Berkeley, Fall 2025.
UC Berkeley's undergraduate PDE course for math and applied math majors
Course Notes coming soon

Math 53: Differential Equations with Linear Algebra, Fourier Methods, and Modern Applications
Stanford, Winter 2025.
Stanford's introductory ODE course for math,physics, engineering, etc. majors.
Course Notes

Math 172: Measure Theory and Fourier Analysis
Stanford, Fall 2024.
Second course of Stanford's advanced undergraduate analysis sequence.
Course Notes

Math 116: Complex Analysis
Stanford, Fall 2024.
Undergraduate complex analysis course for math majors.
Course Notes

Math 20: Calculus II
Stanford, Spring 2023.
Course head. Second course Stanford's undergraduate single-variable calculus sequence.