Riemannian Geometry, Partial Differential Equations & Spectral Theory

Ancient mean curvature flows and their spacetime tracks (w/ F. Chini), 14 pages. [arXiv]

Non-existence for self-translating solitons, 15 pages. [arXiv]

Non-compact families of complete, properly immersed minimal surfaces with fixed topology, via desingularization (w/ S. Kleene), 45 pages. [arXiv]

Closed Self-Shrinking Surfaces in R^3 Via the Torus, 26 pages. [arXiv]

Bi-Halfspace and Convex Hull Theorems for Translating Solitons (w/ F. Chini), Int. Math. Res. Not. (to appear), 21 pages. [arXiv]

Mean Curvature Self-Shrinkers of High Genus: Non-Compact Examples (w/ N. Kapouleas, S. Kleene), J. Reine Angew. Math. 739 (2018), 1--39. [Publication] [arXiv]

Rigidity of conformal functionals on spheres (w/ B. Ørsted), Int. Math. Res. Not. 2014 (2014), 6302--6339. [Publication] [arXiv]

Self-shrinkers with a rotational symmetry (w/ S. Kleene), Trans. Amer. Math. Soc. 366 (2014), no. 8, 3943--3963. [Publication] [arXiv]

Mean Curvature Flow Self-Shrinkers with Genus and Asymptotically Conical Ends (doctoral dissertation), MIT (2012), 124 pages [Publication]

Extremal metrics for spectral functions of Dirac operators in even and odd dimensions, Adv. Math. 229 (2012), no. 2, 1001--1046. [Publication] [arXiv]

Dimensional asymptotics of determinants on 𝕊^{n}, and proof of Bär-Schopka's conjecture, Math. Ann. 343 (2009), no. 1, 35--51.
[Publication] [arXiv]

Mathematical Physics - Theory of Quantum Computing

The distribution of quantum fidelities (w/ L. Pedersen & K. Mølmer), Phys. Lett. A 372 (2008), 7028--7032. [Publication]

Fidelity of quantum operations (w/ L. Pedersen & K. Mølmer), Phys. Lett. A 367 (2007), no. 1-2, 47--51. [Publication]