Research

Pre-prints/In-preparation/Publications

1. 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)

2. (with Ahmad Reza Haj Saeedi Sadegh) The Seiberg-Witten equations for 3/2-spinors: a compactness theorem (arXiv. Submitted to journal)

3. (with Ahmad Reza Haj Saeedi Sadegh) A Fueter operator for 3/2-spinors (arXiv. Submitted to journal)

4. (with William L. Blair) Existence of solutions to the Seiberg-Witten vortex equations with exponential decay on the plane (arXiv. Submitted to journal)

5. Spectral invariant and equivariant monopole Floer homology for rational homology three-spheres (arXiv)

6.  (with Ali Daemi) Equivariant Plane Floer Homology and knot invariants. Expected Summer 2024

Doctoral Thesis

Finite dimensional approximation and Pin(2)-equivariant property of Rarita-Schwinger-Seiberg-Witten equations,  University of Arkansas, 2022

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

1. Knot invariants from Equivariant Plane Floer homology. Groups, Geometry, and Topology seminar, University of Illinois, Urbana-Champaign, Spring 2024

2.  Knot invariants from Plane Floer homology. 1188th Regional AMS meeting, SUNY at Buffalo, NY, Fall 2023

3.  An abelian gauge-theoretic variant of the Seiberg-Witten equations for multiple-spinors. SGGTC seminar, Columbia University, Fall 2022

4.  Rarita-Schwinger operators in gauge theory. Conference on analysis of Dirac type and Higher Spin operators: Honoring John Ryan, Chapman University, Fall 2022

5. 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

6. Finite dimensional approximation and Pin(2)-equivariant properties for the Rarita-Schwinger-Sieberg-Witten equations. Gauge Theory Virtual Seminar, Fall 2021

7. 3/2-spinors on 4-manifolds and finite dimensional approximation. Lightning talk for Tech Topology Summer School, Summer 2021

8. Higher rank Seiberg-Witten equations. Symmetry and Geometry on the Southern Great Plains Conference, University of Oklahoma, Spring 2020

9. U(n) Seiberg-Witten Equations. Preliminary Report. 1152nd Regional AMS Meeting, University of Florida

10. U(n) Seiberg-Witten Equations and transversality. Topology Seminar at University of Arkansas, Fall 2019

11. Clifford bundles, spin structures and Dirac operators. Topology Seminar at University of Arkansas, Spring 2018

Workshops

1. Workshop in gauge theory and low dimensional topology, University of Miami, Spring 2024

2. Workshop at University of Miami: Gauge theory and low dimensional topology, Spring 2023

3. New 4-dimensional gauge theory workshop, MSRI, Fall 2022

4. MSRI Summer School in Gauge Theory in Geometry and Topology, 2021

5. Tech Topology Summer School, 2021

Conferences Attended

1. Yau's 70th Birthday Conference. Harvard University, Spring 2019

2. The Pacific Northwest Geometry Seminar. University of Washington, Spring 2019

3. AMS Regional meeting. University of Florida, Fall 2019

4. Symmetry and Geometry on the Southern Great Plains Conference. University of Oklahoma, Spring 2020

5.  Conference on analysis of Dirac type and Higher Spin operators: Honoring John Ryan, Chapman University, Fall 2022

6. Instantons and Foams, MIT, May 2023

7. AMS regional meeting. SUNY at Buffalo, Fall 2023

8. The St. Louis Topology Conference. Washington University in St. Louis, Spring 2024