BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Alberto Roncoroni DTSTART:20210716T020000Z DTEND:20210716T030000Z DTSTAMP:20260418T094829Z UID:2ndGAF/1 DESCRIPTION:Title: Q uantitative Studies of Alexadrov's Theorem\nby Alberto Roncoroni as pa rt of The 2nd Geometric Analysis Festival\n\n\nAbstract\nAlexandrov's soap bubbles Theorem states that the spheres are the only closed\, connected\, and embedded hypersurfaces with constant mean curvature in the Euclidean space. The theorem holds true also in the so-called space forms and for m ore general functions of the principal curvatures. \n\nIn the talk we will present the classical result by Alexandrov together with two proofs: the original one based on the\, nowadays called\, method of moving planes and another one based on integral inequalities. Then we will show a quantitati ve stability result for hypersurfaces with almost constant mean curvature. In particular\, we will consider hypersurfaces\, satisfying the so-called uniform touching ball condition\, whose mean curvature is close to a cons tant and we will quantitatively describe\, in terms of the oscillation of the mean curvature\, the closedness to a single ball.\n\nThis is based on a joint work with G. Ciraolo and L. Vezzoni.\n LOCATION:https://researchseminars.org/talk/2ndGAF/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Fabian Rupp DTSTART:20210716T010000Z DTEND:20210716T020000Z DTSTAMP:20260418T094829Z UID:2ndGAF/3 DESCRIPTION:Title: A Li-Yau inequality for the 1-dimensional Willmore energy\nby Fabian Ru pp as part of The 2nd Geometric Analysis Festival\n\n\nAbstract\nBy the cl assical Li--Yau inequality\, an immersion of a closed surface in $\\mathbb {R}^n$ with Willmore energy below $8\\pi$ has to be embedded. We discuss a nalogous results for curves in $\\mathbb{R}^2$\, involving Euler’s elast ic energy and other possible curvature functionals. Additionally\, we prov ide applications to associated gradient flows. This is based on a joint wo rk with Marius M\\"uller (Albert-Ludwigs-Universit\\"at Freiburg).\n LOCATION:https://researchseminars.org/talk/2ndGAF/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Jesse Madnick DTSTART:20210715T230000Z DTEND:20210716T000000Z DTSTAMP:20260418T094829Z UID:2ndGAF/5 DESCRIPTION:Title: T he Jacobi Spectrum of Null-Torsion Holomorphic Curves in the 6-Sphere\ nby Jesse Madnick as part of The 2nd Geometric Analysis Festival\n\n\nAbst ract\nMinimal surfaces are area-minimizing to first order\, but not necess arily to second-order. The extent to which a minimal surface is (or isn't ) area-minimizing to second-order is encoded by its Jacobi operator. Howev er\, for a given minimal surface\, computing the spectrum of the Jacobi op erator — i.e.\, the eigenvalues and their multiplicities — is generall y a non-trivial task. \n\\indent In this talk\, we will discuss a class of minimal surfaces in the round 6-sphere known as “null-torsion holomorph ic curves.” These surfaces are of interest to $G_2$ geometry\, and exis t in abundance. Indeed\, by a remarkable theorem of Bryant\, extended by Rowland\, every closed Riemann surface may be conformally embedded as a nu ll-torsion holomorphic curve in $S^6$. \n\\indent For null-torsion holomor phic curves of low genus\, we will compute the multiplicity of the first J acobi eigenvalue. Moreover\, for all genera\, we will give a simple lower bound for the nullity (the multiplicity of the zero eigenspace) in terms of the area and genus. We expect that these results will have implication s for the deformation theory of asymptotically conical associative 3-folds in euclidean $R^7$.\n LOCATION:https://researchseminars.org/talk/2ndGAF/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Min Chen DTSTART:20210716T000000Z DTEND:20210716T010000Z DTSTAMP:20260418T094829Z UID:2ndGAF/7 DESCRIPTION:Title: A lexandrov-Fenchel type inequalities in the sphere\nby Min Chen as part of The 2nd Geometric Analysis Festival\n\n\nAbstract\nIn this paper\, we attempt to use two types of flows to study the relations between quermassi ntegrals $\\mathcal{A}_k$\, which correspond to the Alexandrov-Fenchel ine qualities for closed convex $C^2$-hypersurfaces in $\\mathbb{S}_+^{n+1}.$\ n\nPlease\, submit your questions to speakers at https://forms.gle/F8z5Ljf NNwt3DD4i8\n LOCATION:https://researchseminars.org/talk/2ndGAF/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Demetre Kazaras DTSTART:20210715T150000Z DTEND:20210715T200000Z DTSTAMP:20260418T094829Z UID:2ndGAF/8 DESCRIPTION:Title: M ass of asymptotically Euclidean manifolds using spinors and 1-forms\nb y Demetre Kazaras as part of The 2nd Geometric Analysis Festival\n\n\nAbst ract\nThe total mass of an asymptotically Euclidean manifold is an invaria nt from mathematical General Relativity which has fascinated geometers for many decades. In these lectures\, we will discus the celebrated Positive Mass Theorem\, first describing in some detail the proof by Witten which u ses spinors. I will not assume any prior knowledge of spinors. We will the n focus on a contemporary approach using 1-forms which arise as the differ ential of solutions to a certain "spacetime harmonic" equation motivated b y recent work by Daniel Stern. This second part contains work by myself\, Hugh Bray\, Sven Hirsch\, Marcus Khuri\, and Yiyue Zhang.\n LOCATION:https://researchseminars.org/talk/2ndGAF/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Davi Maximo DTSTART:20210716T060000Z DTEND:20210716T080000Z DTSTAMP:20260418T094829Z UID:2ndGAF/13 DESCRIPTION:Title: On the geometry and topology of 3-manifolds with Positive Scalar Curvature \nby Davi Maximo as part of The 2nd Geometric Analysis Festival\n\n\nA bstract\nIn these talks\, we will discuss classical and recent results abo ut 3-manifolds with positive scalar curvature. We will describe their topo logy and show how they can be (singularly) foliated by surfaces of control led area\, diameter and genus.\n LOCATION:https://researchseminars.org/talk/2ndGAF/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Ao Sun DTSTART:20210715T200000Z DTEND:20210715T230000Z DTSTAMP:20260418T094829Z UID:2ndGAF/16 DESCRIPTION:Title: Uniqueness problem in geometric analysis and Lojasiewicz inequality\nb y Ao Sun as part of The 2nd Geometric Analysis Festival\n\n\nAbstract\nLoj asiewicz inequality is an inequality in real algebraic geometry. It was fi rst discovered by Leon Simon that Lojasiewicz inequality can be used to pr ove uniqueness of critical points in the problem of calculus of variation. In these lectures I will first introduce the Lojasiewicz inequality\; the n I will discuss the infinite dimensional Lojasiewicz inequality proved by Leon Simon in the setting of calculus of variations\; then I will discuss some applications of Lojasiewicz inequality to prove the uniqueness of so me geometric object\; finally\, I will discuss joint work with Jonathan Zh u on proving Lojasiewicz inequality finding an explicit power of the Lojas iewicz inequality near special self-shrinkers of mean curvature flow.\n LOCATION:https://researchseminars.org/talk/2ndGAF/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Otis Chodosh DTSTART:20210716T030000Z DTEND:20210716T060000Z DTSTAMP:20260418T094829Z UID:2ndGAF/19 DESCRIPTION:Title: Some new generic regularity results for minimal surfaces and mean curvatur e flows\nby Otis Chodosh as part of The 2nd Geometric Analysis Festiva l\n\n\nAbstract\nMinimal surfaces are critical points of the area function al while mean curvature flow is the gradient flow of the area functional. Singularities arise in both problems\, and a fundamental issue in geometri c analysis is to understand such singularities. I will present some recent work concerning the generic behavior of both problems\, in particular I w ill discuss the papers (with K. Choi\, C. Mantoulidis\, F. Schulze) arXiv: 2003.14344\, arXiv:2102.11978 as well as (with Y. Liokumovich\, L. Spolao r) arXiv:2007.11560.\n LOCATION:https://researchseminars.org/talk/2ndGAF/19/ END:VEVENT END:VCALENDAR