Christos Mantoulidis

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


        Currently       CLE Moore Instructor     (2017-2020)

        Office          MIT Department of Mathematics, 77 Massachusetts Ave, 2-167, Cambridge, MA 02139

        Email           [first initial].[last name]@mit.edu

        Support       - 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. Choi 
                        Submitted
                        [arXiv] [Oberwolfach Report]

                      - Minimal hypersurfaces with arbitrarily large area / joint with O. Chodosh 
                        International Mathematics Research Notices, rnz128
                        [Journal] [arXiv]

                      - Capacity, quasi-local mass, singular fill-ins / joint with P. Miao, L.-F. Tam 
                        Journal 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. Chodosh
                        Annals of Mathematics, to appear
                        [Journal] [arXiv] [Oberwolfach Report]

                      - Positive scalar curvature with skeleton singularities / joint with C. Li
                        Mathematische Annalen, vol. 374 (2019), no. 1, 99-131
                        [MR3961306] [Journal] [arXiv]

                      - Allen-Cahn min-max on surfaces
                        Journal 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. Miao
                        Communications in Mathematical Physics, vol. 352 (2017), no. 2, 703-718
                        [MR3627410] [Journal] [arXiv]

                      - On the Bartnik mass of apparent horizons / joint with R. Schoen
                        Classical 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]
    

        Teaching        Massachusetts 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 R2
                        [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 Rn+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]