# Harrison Pugh

## Stony Brook University

Department of Mathematics

### Education:

Stony Brook University. PhD in Mathematics, 2018.

Cambridge University. Part III of the Mathematical Tripos (MASt.) 2011.

Harvard College. Bachelors in Mathematics (A.B. with High Honors) 2009.

### Awards & Fellowships:

Graduate Council Fellowship, 2012-2016.

IMPA Fellowship, 2010.

High Honors from Harvard College.

National Merit Scholarship.

### Papers in Preparation:

- Elliptic Measures and The Plateau Problem in the Presence of Gravity
- Smooth Structures on a Quasiconformal 4-Manifold

### Preprints & Submissions:

- Pugh, H. Reifenberg's Isoperimetric Inequality Revisited, submitted July 2017
- Pugh, H. Differential Forms are Dual to a Differential Coalgebra (2016), preprint
- Pugh, H. A Localized Besicovitch-Federer Projection Theorem, preprint

### Publications:

- Harrison, J. & Pugh, H. General Methods of Elliptic Minimization, Calc. Var. and PDEs (2017) 56: 123
- Harrison, J. & Pugh, H. Plateau's Problem. Open Problems in Mathematics, Nash, Rassias (Eds.) (2016), 273-302
- Harrison, J. & Pugh, H. Solutions to the Reifenberg Plateau problem with cohomological spanning conditions. Calc. Var. and PDEs (2016) 55, no. 4, Paper No. 87, 37 pp.
- Harrison, J. & Pugh, H. Existence and soap film regularity of solutions to Plateau’s problem, Advances in the Calculus of Variations (2016) Volume 9, Issue 4, pp. 357-394
- Harrison, J. & Pugh, H. Topological aspects of differential chains. J. Geom. Anal. 22 (2012), no. 3, 685–690

### Seminars & Invited Talks:

- Calculus of Variations and Nonlinear Partial Differential Equations Conference, Berkeley, May 2017 (hour lecture)
- Calculus of Variations, Optimal Transportation, and Geometric Measure Theory Conference, Lyon, Summer 2016
- AMS Spring Eastern Sectional Meeting, Stony Brook, Spring 2016 (invited talk)
- Geometric Measure Theory Seminar, Max Planck Institute, Potsdam, Summer 2014 (hour lecture)
- Graduate Student Seminars, Stony Brook, 2012, 2013, 2015

### Other Activities:

- Rock Climbing
- Ashtanga Yoga