Christos MantoulidisWelcome to my website! Skip to: [Papers] [Teaching] [Notes/Theses] [Pictures]

CurrentlyCLE Moore Instructor (2017-2020)OfficeMIT Department of Mathematics, 77 Massachusetts Ave, 2-167, Cambridge, MA 02139Support- NSF Grant DMS-1905165 (2019-2022) - AMS/Simons Travel Grant (2019-2021)

Interests- Differential Geometry - Partial Differential Equations - Mathematical General Relativity - Geometric Measure Theory - Geometric Flows

Papers- Ancient gradient flows of elliptic functionals and Morse index / joint with K. ChoiSubmitted[arXiv] [Oberwolfach Report] - Minimal hypersurfaces with arbitrarily large area / joint with O. ChodoshInternational Mathematics Research Notices, rnz128 [Journal] [arXiv] - Capacity, quasi-local mass, singular fill-ins / joint with P. Miao, L.-F. TamJournal für die reine und angewandte Mathematik, to appear [arXiv] - Minimal surfaces and the Allen-Cahn equation on 3-manifolds: index, multiplicity, and curvature estimates / joint with O. ChodoshAnnals of Mathematics, to appear [Journal] [arXiv] [Oberwolfach Report] - Positive scalar curvature with skeleton singularities / joint with C. LiMathematische Annalen, vol. 374 (2019), no. 1, 99-131 [MR3961306] [Journal] [arXiv] - Allen-Cahn min-max on surfacesJournal of Differential Geometry, to appear [arXiv] - Mean curvature deficit and a quasi-local mass / joint with P. Miao Nonlinear analysis in geometry and applied mathematics, 99-107,Harvard University Center of Mathematical Sciences and Appications (CMSA)Series in Mathematics, vol. 1. Int. Press, Somerville, MA, 2017 [MR3729087] - Total mean curvature, scalar curvature, and a variational analog of Brown-York mass / joint with P. MiaoCommunications in Mathematical Physics, vol. 352 (2017), no. 2, 703-718 [MR3627410] [Journal] [arXiv] - On the Bartnik mass of apparent horizons / joint with R. SchoenClassical and Quantum Gravity, vol. 32 (2015), no. 20, 205002 * Appeared on IOPselect 2015, a special edition of journal articles, on the basis of substantial advances, a high degree of novelty, and/or impact on future research. [MR3406373] [Journal] [arXiv] [Known Misprints] [CQG+ Insight Piece]

TeachingMassachusetts Institute of Technology- 18.965 / Geometry of Manifolds I (graduate course) - 18.994 / Seminar in Geometry (communication intensive course) - 18.02 / Multivariable Calculus [##]Stanford University[**] - Math 51 / Linear Algebra and Differential Calculus of Several Variables [##] - Math 53 / Ordinary Differential Equations with Linear Algebra [##] [**] = Awarded the Centennial Teaching Award by Stanford University. [##] = teaching assistant

Notes/Theses- Geometric variational problems in mathematical physics Ph.D. thesis. Advisor: Richard Schoen. [PDF] [Known Misprints] - A note on the Morse index of 2k-ended phase transitions in R^{2}[arXiv] - Richard Schoen's lectures on minimal submanifolds / joint with D. Cheng, C. Li [PDF] - T. H. Colding and W. P. Minicozzi's blowup uniqueness and Łojasiewicz inequalities [PDF] - Yi Wang's lectures on harmonic analysis and isoperimetric inequalities / joint with D. Cheng, O. Chodosh, N. Edelen, C. Henderson, P. Hintz [PDF] - Richard Bamler's lectures on Ricci flow / joint with O. Chodosh [PDF] - Brian White's lectures on minimal surfaces / joint with O. Chodosh [PDF] - Regularity of hypersurfaces in R^{n+1}moving by mean curvature flow Undergraduate honors thesis. Advisor: Leon Simon. Exposition follows Klaus Ecker's Regularity Theory for Mean Curvature Flow,Progress in Nonlinear Differential Equations and their Applications, 57. Birkhäuser Boston, Inc., Boston, MA, 2004 [PDF]

Pictures- Lecturing at the Institute for Advanced Study [Image] - Lecturing at Stony Brook's Mass in General Relativity workshop [Image] - At Oberwolfach [Image]