I am an Assistant Professor at Notre Dame. I study problems in geometric analysis and geometric measure theory. Earlier, I was an NSF Fellow and CLE Moore instructor at MIT, under the sponsorshop of Tobias Colding; I was a PhD student at Stanford advised by Simon Brendle and coadvised by Brian White; I was an undergraduate at University of Edinburgh. My email is nedelen at nd dot edu. My office is 283 Hurley.

I am a coorganizer of our Geometry and Analysis seminar.

This spring 2024 I am teaching graduate differential geometry. Past teaching.

Papers

- Uniqueness of regular tangent cones for immersed stable hypersurfaces (joint with Paul Minter)
*submitted*(2024). - Improved regularity for minimizing capillary hypersurfaces (joint with Otis Chodosh and Chao Li)
*submitted*(2024). - The symmetric (log-)epiperimetric inequality and a decay-growth estimate (joint with Luca Spolaor and Bozhidar Velichkov)
*Calc. Var. PDE*, 63, 2 (2024). arxiv - A Liouville-type theorem for cylindrical cones (joint with Gabor Szekelyhidi)
*Comm. Pure. Appl. Math.*, to appear (2023). - A strong maximum principle for minimizers of the one-phase Bernoulli problem (joint with Luca Spolaor and Bozhidar Velichkov)
*Indiana Univ. Math. J.*, to appear (2022). - Degeneration of 7-dimensional minimal hypersurfaces which are stable or have bounded index
*Arch. Ration. Mech. Anal.*, to appear (2022). - A Bernstein-type theorem for minimal graphs over convex domains (joint with Zhehui Wang)
*Ann. Inst. H. Poincare Anal. Non Lineaire*, 39:749-760 (2021). arxiv - Regularity of free boundary minimal surfaces in locally polyhedral domains (joint with Chao Li)
*Comm. Pure. Appl. Math.*, 75:970-1031 (2021). arxiv - Mean convex mean curvature flow with free-boundary (joint with Robert Haslhofer, Mohammad Ivaki, and Jonathan Zhu)
*Comm. Pure. Appl. Math.*, 75:767-817 (2020). arxiv - Regularity of minimal surfaces near quadratic cones (joint with Luca Spolaor)
*Ann. of Math.*, 198:1013-1046 (2023). arxiv - A note on the singular set of area-minimizing hypersurfaces
*Calc. Var. PDE*59:1-18 (2020). arxiv - Effective Reifenberg theorems in Hilbert and Banach spaces (joint with Aaron Naber and Daniele Valtorta).
*Math. Ann.*372:1139-1218 (2018). arxiv - The singular set of minimal surfaces near polyhedral cones (joint with Maria Colombo and Luca Spolaor)
*J. Differ. Geom.*120:411-503 (2022). arixv - Quantitative stratification for some free-boundary problems (joint with Max Engelstein)
*Trans. Amer. Math. Soc.*, 371:2043-2072 (2019). arxiv - Quantitative Reifenberg theorem for measures (joint with Aaron Naber and Daniele Valtorta)
*submitted*(2016). - The free-boundary Brakke flow
*J. Reine Angew. Math.*, 758:95-137 (2020). arxiv - The PPW conjecture in curved spaces
*J. Funct. Anal.*, 272:849-865 (2017). arxiv - Convexity estimates for mean curvature flow with free boundary
*Adv. Math.*, 294:1-36 (2016). arxiv - Noncollapsing of Curve-Shortening Flow in Surfaces
*Int. Math. Res. Not.*2015:10143-10153 (2015). - Constant mean curvature, flux conservation, and symmetry (joint with Bruce Solomon)
*Pacific J. Math.*, 274:53-72 (2015). arxiv

Other:

- Notes on Naber-Valtorta's discrete/rectifiable-Reifenberg, and their proof of finite rectifiability of the singular set (also, a measure theoretic version).
- Notes on Brian White's classes on mean curvature flow, and minimal surfaces (see also Otis's page).
- Notes on free boundary varifolds.