Dylan Galt

I am a 5th-year mathematics Ph.D. student at Stony Brook University, advised by Simon Donaldson. My research concerns calibrated submanifolds of, and gauge theory on, special holonomy manifolds, and involves a combination of adiabatic limit and gluing techniques. I am interested in moduli spaces of calibrated submanifolds, non-compactness phenomena arising from singular limits of sequences of smooth calibrated submanifolds, and more broadly in desingularizing singular minimal submanifolds with positive-dimensional singular strata. In addition, I am interested in various aspects of the Donaldson-Segal-Thomas program of gauge theory in higher dimensions, especially moduli spaces of G2- and Spin(7)-instantons. I have also done work in arithmetic geometry, studying Hecke operators on the cohomology of arithmetic groups.

I am currently on the job market for postdoctoral positions.

CV

Office: Math Tower 2-109

Address: Department of Mathematics, Stony Brook University, Stony Brook, NY 11794

E-mail: dylan.galt@stonybrook.edu

Publications

  1. D. Galt: An invariant for transverse coassociative 4-folds (2024)
  2. D. Galt and L. Ma: Dimensions reductions in instanton theory, submitted (2024)
  3. D. Galt and M. McConnell: Cohomology at infinity and the well-tempered complex, submitted (2023)
  4. D. Galt and M. McConnell: Computing Hecke operators for arithmetic subgroups of Sp4, Euro-Tbilisi Math. J. special volume on Cohomology, Geometry, Explicit Number Theory (2021), pp. 67-80

Research Interests: gauge theory, calibrated submanifolds, moduli spaces of instantons, special holonomy manifolds, gluing problems, cohomology of arithmetic groups

I am a co-founder and co-organizer of ENYGMMa (Empowering New York Gender Minority Mathematicians), an inter-university seminar series organized jointly by Stony Brook, Columbia, CUNY, and NYU. The seminars are held in rotation at these four universities and open to all to attend, being aimed broadly at gender minority graduate students and postdocs in mathematics. The goal of ENYGMMa is to promote representation and foster community among women and non-binary mathematicians in the New York area, increasing academic visibillity and cooperation, and combatting marginalization.

If you are interested in participating in ENYGMMa or helping organize and have questions, please feel free to email me! You can find details about previous and upcoming events on our website.

Dylan Galt

I am a 5th-year mathematics Ph.D. student at Stony Brook University, advised by Simon Donaldson. My research concerns calibrated submanifolds of, and gauge theory on, special holonomy manifolds, and involves a combination of singular perturbation, adiabatic limit, and gluing techniques. I am interested in moduli spaces of calibrated submanifolds, non-compactness phenomena arising from singular limits of sequences of smooth calibrated submanifolds, and more broadly in desingularizing singular minimal submanifolds with positive-dimensional singular strata. In addition, I am interested in various aspects of the Donaldson-Segal-Thomas program of gauge theory in higher dimensions, especially moduli spaces of G2- and Spin(7)-instantons. I have also done work in arithmetic geometry, studying Hecke operators on the cohomology of arithmetic groups.

I will be on the job market this fall for postdoctoral positions.

CV

Office: Math Tower 2-109

Address: Department of Mathematics, Stony Brook University, Stony Brook, NY 11794

E-mail: dylan.galt@stonybrook.edu

Publications

  1. D. Galt and L. Ma: Dimensions reductions in instanton theory, submitted (2024)
  2. D. Galt and M. McConnell: Cohomology at infinity and the well-tempered complex, submitted (2023)
  3. D. Galt and M. McConnell: Computing Hecke operators for arithmetic subgroups of Sp4, Euro-Tbilisi Math. J. special volume on Cohomology, Geometry, Explicit Number Theory (2021), pp. 67-80

Research Interests: gauge theory, calibrated submanifolds, moduli spaces of instantons, special holonomy manifolds, gluing and singular perturbation problems, cohomology of arithmetic groups

I am a co-founder and co-organizer of ENYGMMa (Empowering New York Gender Minority Mathematicians), an inter-university seminar series organized jointly by Stony Brook, Columbia, CUNY, and NYU. The seminars are held in rotation at these four universities and open to all to attend, being aimed broadly at gender minority graduate students and postdocs in mathematics. The goal of ENYGMMa is to promote representation and foster community among women and non-binary mathematicians in the New York area, increasing academic visibillity and cooperation, and combatting marginalization.

If you are interested in participating in ENYGMMa or helping organize and have questions, please feel free to email me! You can find details about previous and upcoming events on our website.