BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Guido De Philippis (Courant Institute) DTSTART:20200408T190000Z DTEND:20200408T200000Z DTSTAMP:20260404T094653Z UID:PrincetonDG/1 DESCRIPTION:Title: Regularity of the free boundary for the two-phase Bernoulli pro blem\nby Guido De Philippis (Courant Institute) as part of Princeton d ifferential geometry and geometric analysis seminar\n\nLecture held in Fin e 314.\n\nAbstract\nI will illustrate a recent result obtained in collabo ration with L. Spolaor and B. Velichkov concerning the regularity of the free boundaries in the two phase Bernoulli problems. The new main point i s the analysis of the free boundary close to branch points\, where we show that it is given by the union of two $C ^ 1$ graphs. This complete the an alysis started by Alt Caffarelli Friedman in the 80’s.\n LOCATION:https://stable.researchseminars.org/talk/PrincetonDG/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Guillermo Henry (Princeton University) DTSTART:20200422T190000Z DTEND:20200422T200000Z DTSTAMP:20260404T094653Z UID:PrincetonDG/2 DESCRIPTION:Title: Isoparametric functions and solutions of the Yamabe equation.\nby Guillermo Henry (Princeton University) as part of Princeton differe ntial geometry and geometric analysis seminar\n\nLecture held in Fine 314. \n\nAbstract\nIn this talk we will discuss the relationship between isopar ametric functions on closed Riemannian manifolds and solutions of the Yam abe equation. I will show some results on the existence and multiplicity o f positive and nodal solutions of the Yamabe equation that have the proper ty of being constant along the level sets of an isoparametric function.\n LOCATION:https://stable.researchseminars.org/talk/PrincetonDG/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Nick Edelen (University of Notre Dame) DTSTART:20200429T190000Z DTEND:20200429T200000Z DTSTAMP:20260404T094653Z UID:PrincetonDG/3 DESCRIPTION:Title: Regularity of minimal surfaces near quadratic cones\nby Nic k Edelen (University of Notre Dame) as part of Princeton differential geom etry and geometric analysis seminar\n\nLecture held in Fine 314.\n\nAbstra ct\nHardt-Simon proved that every area-minimizing hypercone $C$ having onl y an isolated singularity fits into a foliation of $R^{n+1}$ by smooth\, a rea-minimizing hypersurfaces asymptotic to $C$. We prove that if a minimal hypersurface $M$ in the unit ball $B_1 \\subset R^{n+1}$ lies sufficientl y close to a minimizing quadratic cone (for example\, the Simons' cone)\, then $M \\cap B_{1/2}$ is a $C^{1\,\\alpha}$ perturbation of either the co ne itself\, or some leaf of its associated foliation. In particular\, we s how that singularities modeled on these cones determine the local structur e not only of $M$\, but of any nearby minimal surface. Our result also imp lies the Bernstein-type result of Simon-Solomon\, which characterizes area -minimizing hypersurfaces in $R^{n+1}$ asymptotic to a quadratic cone as e ither the cone itself\, or some leaf of the foliation. \n\nThis is joint w ork with Luca Spolaor\n LOCATION:https://stable.researchseminars.org/talk/PrincetonDG/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Xavier Cabre (ICREA and Universitat Politecnica de Catalunya) DTSTART:20200506T190000Z DTEND:20200506T200000Z DTSTAMP:20260404T094653Z UID:PrincetonDG/4 DESCRIPTION:Title: Stable solutions to semilinear elliptic equations are smooth up to dimension 9\nby Xavier Cabre (ICREA and Universitat Politecnica de Catalunya) as part of Princeton differential geometry and geometric analy sis seminar\n\nLecture held in Fine 314.\n\nAbstract\nThe regularity of st able solutions to semilinear elliptic PDEs has been studied since the 1970 's. In dimensions 10 and higher\, there exist singular stable energy solut ions. In this talk I will describe a recent work in collaboration with Fig alli\, Ros-Oton\, and Serra\, where we prove that stable solutions are smo oth up to the optimal dimension 9. This answers to an open problem posed b y Brezis in the mid-nineties concerning the regularity of extremal solutio ns to Gelfand-type problems.\n LOCATION:https://stable.researchseminars.org/talk/PrincetonDG/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Ao Sun (MIT) DTSTART:20200513T210000Z DTEND:20200513T220000Z DTSTAMP:20260404T094653Z UID:PrincetonDG/5 DESCRIPTION:Title: Generalizations of mean curvature flow entropy\nby Ao Sun ( MIT) as part of Princeton differential geometry and geometric analysis sem inar\n\nLecture held in Fine 314.\n\nAbstract\nMean curvature flow entropy was introduced by Colding-Minicozzi\, and it is a very important quantity in the study of mean curvature flow and related geometric problem. In thi s talk\, I will discuss two generalizations of mean curvature flow entropy : one is a localized version of entropy\, another one is entropy in a clos ed manifold. I will discuss how to use these generalizations to study the regularity problem of mean curvature flow. In particular\, I will discuss how to use these generalizations of entropy rule out some pathological asy mptotic behaviors.\n\nNote unusual time\n LOCATION:https://stable.researchseminars.org/talk/PrincetonDG/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Eden Prywes (Princeton University) DTSTART:20200527T190000Z DTEND:20200527T200000Z DTSTAMP:20260404T094653Z UID:PrincetonDG/6 DESCRIPTION:Title: Characterization of Branched Covers with Simplicial Branch Sets \nby Eden Prywes (Princeton University) as part of Princeton different ial geometry and geometric analysis seminar\n\nLecture held in Fine 314.\n \nAbstract\nA branched covering $f \\colon \\mathbb R^n \\to \\mathbb R^n$ is an open and discrete map. Branched coverings are topological generali zations of quasiregular and holomorphic mappings. The branch set of $f$ is the set where $f$ fails to be locally injective. It is well known that t he image of the branch set of a PL branched covering between PL $n$-manifo lds is a simplicial $(n-2)$-complex. I will discuss a recent result that t he reverse implication also holds. More precisely\, a branched covering wi th the image of the branch set contained in a simplicial $(n-2)$-complex i s equivalent up to homeomorphism to a PL mapping. This result is classical for $n=2$ and was shown by Martio and Srebro for $n = 3$. This is joint work with Rami Luisto.\n LOCATION:https://stable.researchseminars.org/talk/PrincetonDG/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Silvia Ghinassi (Institute for Advanced Study) DTSTART:20200603T190000Z DTEND:20200603T200000Z DTSTAMP:20260404T094653Z UID:PrincetonDG/7 DESCRIPTION:Title: Higher order Reifenberg theorems and the Analyst’s Traveling Salesman Theorem\nby Silvia Ghinassi (Institute for Advanced Study) as part of Princeton differential geometry and geometric analysis seminar\n\ nLecture held in Fine 314.\n\nAbstract\nWe provide geometric sufficient co nditions for Reifenberg flat sets of any integer dimension in Euclidean sp ace to be parametrized by a Lipschitz map with Hölder derivatives. The co nditions use a Jones type square function and all statements are quantitat ive in that the Hölder and Lipschitz constants of the parametrizations de pend on such a function. We use these results to prove sufficient conditio ns for higher order rectifiability of sets and measures. Key tools for the proof come from Guy David and Tatiana Toro’s parametrization of Reifenb erg flat sets in the Hölder and Lipschitz categories. If time allows\, we will discuss some related work in progress and an example that shows that the conditions are not necessary.\n LOCATION:https://stable.researchseminars.org/talk/PrincetonDG/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Jonathan Zhu (Princeton) DTSTART:20200611T210000Z DTEND:20200611T220000Z DTSTAMP:20260404T094653Z UID:PrincetonDG/8 DESCRIPTION:Title: Mean convex mean curvature flow with free boundary\nby Jona than Zhu (Princeton) as part of Princeton differential geometry and geomet ric analysis seminar\n\nLecture held in Fine 314.\n\nAbstract\nIn the clas s of mean convex surfaces\, the mean curvature flow provides a useful geom etric tool\, owing its power to the regularity and structure theory establ ished by White and with subsequent developments by Haslhofer\, Kleiner and Hershkovits. In joint work with Edelen\, Haslhofer and Ivaki\, we general ise this theory to the free boundary setting. We will discuss the analytic and geometric issues that arise in the passage to free boundary as well a s further developments in progress.\n LOCATION:https://stable.researchseminars.org/talk/PrincetonDG/8/ END:VEVENT END:VCALENDAR