Research
Pre-prints/In-preparation/Publications
Pin(2)-Equivariance Property of the Rarita-Schwinger-Seiberg-Witten equations (publication version in The Journal of Geometric Analysis 33, Article number: 336 (2023). Arxiv)
An abelian gauge-theoretic variant of the Seiberg-Witten equations for multiple spinors (An important technical mistake in the set-up of this variant of generalization to Seiberg-Witten equations was pointed out to the author by Clifford Taubes and Thomas Walpuski. In particular, the equations are not elliptic as claimed. As a result, any statement about (or uses) regularity and transversality of the moduli space has to be disregarded. However, the moduli space is still compact. Arxiv)
The Seiberg-Witten equations for multiple spinors on 4-manifolds with definite intersection forms (The proof of the theorem in the notes relies on the results stated in our other posting arXiv:2301.09693. Specifically, one of the ingredients needed is transversality. Clifford Taubes and Thomas Walpuski pointed out to us that due to a technicality in our set-up, the system of equations that we consider is not elliptic. Hence, we should not expect transversality in this setup. Arxiv)
(with Ahmad Reza Saeedi Sadegh) The Seiberg-Witten equations for 3/2-spinors: a compactness theorem (Arxiv)
(with Ali Daemi) Plane Floer Homology and knot invariants. Expected Spring 2024
Doctoral Thesis
Master Thesis
A survey on algebraic K-Theory. The Pennsylvania State University, 2016
Undergraduate publication
(with James S. Cook, W. Spencer Leslie, Bailu Zhang) Laplace equations for real semisimple associate algebras of dimension 2, 3, or 4 (publication version in Topics from the 8th Annual UNCG Regional Mathematics and Statistic Conference, Springer (2013))
Talks
Knot invariants from Plane Floer homology. 1188th Regional AMS meeting, SUNY at Buffalo, NY, Fall 2023
An abelian gauge-theoretic variant of the Seiberg-Witten equations for multiple-spinors. SGGTC seminar, Columbia University, Fall 2022
Rarita-Schwinger operators in gauge theory. Conference on analysis of Dirac type and Higher Spin operators: Honoring John Ryan, Chapman University, Fall 2022
A generalization of the Hermitian-Yang-Mills equation and its relationshop to the moduli space of multiple-spinor Seiberg-Witten equations on Kahler surface, Geometry and Topology seminar, Washington University in St. Louis, Fall 2022
Finite dimensional approximation and Pin(2)-equivariant properties for the Rarita-Schwinger-Sieberg-Witten equations. Gauge Theory Virtual Seminar, Fall 2021
3/2-spinors on 4-manifolds and finite dimensional approximation. Lightning talk for Tech Topology Summer School, Summer 2021
Higher rank Seiberg-Witten equations. Symmetry and Geometry on the Southern Great Plains Conference, University of Oklahoma, Spring 2020
U(n) Seiberg-Witten Equations. Preliminary Report. 1152nd Regional AMS Meeting, University of Florida
U(n) Seiberg-Witten Equations and transversality. Topology Seminar at University of Arkansas, Fall 2019
Clifford bundles, spin structures and Dirac operators. Topology Seminar at University of Arkansas, Spring 2018
Workshops
Workshop at University of Miami: Gauge theory and low dimensional topology, Spring 2023
New 4-dimensional gauge theory workshop, MSRI, Fall 2022
MSRI Summer School in Gauge Theory in Geometry and Topology, 2021
Tech Topology Summer School, 2021
Conferences Attended
Yau's 70th Birthday Conference. Harvard University, Spring 2019
The Pacific Northwest Geometry Seminar. University of Washington, Spring 2019
AMS Regional meeting. University of Florida, Fall 2019
Symmetry and Geometry on the Southern Great Plains Conference. University of Oklahoma, Spring 2020
Conference on analysis of Dirac type and Higher Spin operators: Honoring John Ryan, Chapman University, Fall 2022
Instantons and Foams, MIT, May 2023
AMS regional meeting. SUNY at Buffalo, Fall 2023