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:20260422T212830Z UID:PrincetonDG/1 DESCRIPTION:Title: Regularity of the free boundary for the two-phase Bernoulli problem\nby Guido De Philippis (Courant Institute) as part of Princeton differen tial geometry and geometric analysis seminar\n\nLecture held in Fine 314.\ n\nAbstract\nI will illustrate a recent result obtained in collaboration with L. Spolaor and B. Velichkov concerning the regularity of the free b oundaries in the two phase Bernoulli problems. The new main point is the a nalysis of the free boundary close to branch points\, where we show that i t is given by the union of two $C ^ 1$ graphs. This complete the analysis started by Alt Caffarelli Friedman in the 80’s.\n LOCATION:https://researchseminars.org/talk/PrincetonDG/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Guillermo Henry (Princeton University) DTSTART:20200422T190000Z DTEND:20200422T200000Z DTSTAMP:20260422T212830Z UID:PrincetonDG/2 DESCRIPTION:Title: Isoparametric functions and solutions of the Yamabe equation.\nby Guillermo Henry (Princeton University) as part of Princeton differential g eometry and geometric analysis seminar\n\nLecture held in Fine 314.\n\nAbs tract\nIn this talk we will discuss the relationship between isoparametric functions on closed Riemannian manifolds and solutions of the Yamabe equ ation. I will show some results on the existence and multiplicity of posit ive and nodal solutions of the Yamabe equation that have the property of b eing constant along the level sets of an isoparametric function.\n LOCATION:https://researchseminars.org/talk/PrincetonDG/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Nick Edelen (University of Notre Dame) DTSTART:20200429T190000Z DTEND:20200429T200000Z DTSTAMP:20260422T212830Z UID:PrincetonDG/3 DESCRIPTION:Title: Regularity of minimal surfaces near quadratic cones\nby Nick Edele n (University of Notre Dame) as part of Princeton differential geometry an d geometric analysis seminar\n\nLecture held in Fine 314.\n\nAbstract\nHar dt-Simon proved that every area-minimizing hypercone $C$ having only an is olated singularity fits into a foliation of $R^{n+1}$ by smooth\, area-min imizing hypersurfaces asymptotic to $C$. We prove that if a minimal hypers urface $M$ in the unit ball $B_1 \\subset R^{n+1}$ lies sufficiently 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 cone itse lf\, or some leaf of its associated foliation. In particular\, we show tha t singularities modeled on these cones determine the local structure not o nly of $M$\, but of any nearby minimal surface. Our result also implies th e Bernstein-type result of Simon-Solomon\, which characterizes area-minimi zing hypersurfaces in $R^{n+1}$ asymptotic to a quadratic cone as either t he cone itself\, or some leaf of the foliation. \n\nThis is joint work wit h Luca Spolaor\n LOCATION:https://researchseminars.org/talk/PrincetonDG/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Xavier Cabre (ICREA and Universitat Politecnica de Catalunya) DTSTART:20200506T190000Z DTEND:20200506T200000Z DTSTAMP:20260422T212830Z UID:PrincetonDG/4 DESCRIPTION:Title: Stable solutions to semilinear elliptic equations are smooth up to dim ension 9\nby Xavier Cabre (ICREA and Universitat Politecnica de Catalu nya) as part of Princeton differential geometry and geometric analysis sem inar\n\nLecture held in Fine 314.\n\nAbstract\nThe regularity of stable so lutions to semilinear elliptic PDEs has been studied since the 1970's. In dimensions 10 and higher\, there exist singular stable energy solutions. I n this talk I will describe a recent work in collaboration with Figalli\, Ros-Oton\, and Serra\, where we prove that stable solutions are smooth up to the optimal dimension 9. This answers to an open problem posed by Brezi s in the mid-nineties concerning the regularity of extremal solutions to G elfand-type problems.\n LOCATION:https://researchseminars.org/talk/PrincetonDG/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Ao Sun (MIT) DTSTART:20200513T210000Z DTEND:20200513T220000Z DTSTAMP:20260422T212830Z UID:PrincetonDG/5 DESCRIPTION:Title: Generalizations of mean curvature flow entropy\nby Ao Sun (MIT) as part of Princeton differential geometry and geometric analysis seminar\n\ nLecture held in Fine 314.\n\nAbstract\nMean curvature flow entropy was in troduced by Colding-Minicozzi\, and it is a very important quantity in the study of mean curvature flow and related geometric problem. In this talk\ , I will discuss two generalizations of mean curvature flow entropy: one i s a localized version of entropy\, another one is entropy in a closed mani fold. I will discuss how to use these generalizations to study the regular ity problem of mean curvature flow. In particular\, I will discuss how to use these generalizations of entropy rule out some pathological asymptotic behaviors.\n\nNote unusual time\n LOCATION:https://researchseminars.org/talk/PrincetonDG/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Eden Prywes (Princeton University) DTSTART:20200527T190000Z DTEND:20200527T200000Z DTSTAMP:20260422T212830Z UID:PrincetonDG/6 DESCRIPTION:Title: Characterization of Branched Covers with Simplicial Branch Sets\nb y Eden Prywes (Princeton University) as part of Princeton differential geo metry and geometric analysis seminar\n\nLecture held in Fine 314.\n\nAbstr act\nA branched covering $f \\colon \\mathbb R^n \\to \\mathbb R^n$ is an open and discrete map. Branched coverings are topological generalizations of quasiregular and holomorphic mappings. The branch set of $f$ is the se t where $f$ fails to be locally injective. It is well known that the imag e of the branch set of a PL branched covering between PL $n$-manifolds is a simplicial $(n-2)$-complex. I will discuss a recent result that the reve rse implication also holds. More precisely\, a branched covering with the image of the branch set contained in a simplicial $(n-2)$-complex is equiv alent 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 wi th Rami Luisto.\n LOCATION:https://researchseminars.org/talk/PrincetonDG/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Silvia Ghinassi (Institute for Advanced Study) DTSTART:20200603T190000Z DTEND:20200603T200000Z DTSTAMP:20260422T212830Z UID:PrincetonDG/7 DESCRIPTION:Title: Higher order Reifenberg theorems and the Analyst’s Traveling Salesma n Theorem\nby Silvia Ghinassi (Institute for Advanced Study) as part o f Princeton differential geometry and geometric analysis seminar\n\nLectur e held in Fine 314.\n\nAbstract\nWe provide geometric sufficient condition s for Reifenberg flat sets of any integer dimension in Euclidean space to be parametrized by a Lipschitz map with Hölder derivatives. The condition s use a Jones type square function and all statements are quantitative in that the Hölder and Lipschitz constants of the parametrizations depend on such a function. We use these results to prove sufficient conditions for higher order rectifiability of sets and measures. Key tools for the proof come from Guy David and Tatiana Toro’s parametrization of Reifenberg fla t sets in the Hölder and Lipschitz categories. If time allows\, we will d iscuss some related work in progress and an example that shows that the co nditions are not necessary.\n LOCATION:https://researchseminars.org/talk/PrincetonDG/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Jonathan Zhu (Princeton) DTSTART:20200611T210000Z DTEND:20200611T220000Z DTSTAMP:20260422T212830Z UID:PrincetonDG/8 DESCRIPTION:Title: Mean convex mean curvature flow with free boundary\nby Jonathan Zh u (Princeton) as part of Princeton differential geometry and geometric ana lysis seminar\n\nLecture held in Fine 314.\n\nAbstract\nIn the class of me an convex surfaces\, the mean curvature flow provides a useful geometric t ool\, owing its power to the regularity and structure theory established b y White and with subsequent developments by Haslhofer\, Kleiner and Hershk ovits. In joint work with Edelen\, Haslhofer and Ivaki\, we generalise thi s theory to the free boundary setting. We will discuss the analytic and ge ometric issues that arise in the passage to free boundary as well as furth er developments in progress.\n LOCATION:https://researchseminars.org/talk/PrincetonDG/8/ END:VEVENT END:VCALENDAR