BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Panagiota Daskalopoulos (Columbia University) DTSTART:20211108T160000Z DTEND:20211108T170000Z DTSTAMP:20260404T042256Z UID:BIRS-21w5504/1 DESCRIPTION:Title: Type II smoothing in Mean curvature flow\nby Panagiota Das kalopoulos (Columbia University) as part of BIRS workshop: New Directions in Geometric Flows\n\n\nAbstract\nIn 1994 Velázquez constructed a smooth \\( O(4)\\times O(4)\\) invariant Mean Curvature Flow that forms a type-I I singularity at the origin in space-time. Stolarski very recently showe d that the mean curvature on this solution is uniformly bounded. Earlier\ , Velázquez also provided formal asymptotic expansions for a possible smo oth continuation of the solution after the singularity. \nJointly with S. Angenent and N. Sesum we establish the short time existence of Velázque z' formal continuation\, and we verify that the mean curvature is also uni formly bounded on the continuation.\n LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5504/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Paula Burkhardt-Guim (NYU Courant) DTSTART:20211108T173000Z DTEND:20211108T183000Z DTSTAMP:20260404T042256Z UID:BIRS-21w5504/2 DESCRIPTION:Title: Pointwise lower scalar curvature bounds for C^0 metrics via re gularizing Ricci flow\nby Paula Burkhardt-Guim (NYU Courant) as part o f BIRS workshop: New Directions in Geometric Flows\n\n\nAbstract\nWe propo se a class of local definitions of weak lower scalar curvature bounds that is well defined for C^0 metrics. We show the following: that our definiti ons are stable under greater-than-second-order perturbation of the metric\ , that there exists a reasonable notion of a Ricci flow starting from C^0 initial data which is smooth for positive times\, and that the weak lower scalar curvature bounds are preserved under evolution by the Ricci flow fr om C^0 initial data.\n LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5504/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Yi Lai (Stanford University) DTSTART:20211108T210000Z DTEND:20211108T220000Z DTSTAMP:20260404T042256Z UID:BIRS-21w5504/3 DESCRIPTION:Title: Steady gradient Ricci solitons with positive curvature operato rs\nby Yi Lai (Stanford University) as part of BIRS workshop: New Dire ctions in Geometric Flows\n\n\nAbstract\nWe find a family of 3d steady gra dient Ricci solitons that are flying wings. This verifies a conjecture by Hamilton. For a 3d flying wing\, we show that the scalar curvature does no t vanish at infinity. The 3d flying wings are collapsed. For dimension n ≥ 4\, we find a family of Z2 × O(n − 1)-symmetric but non-rotationall y symmetric n-dimensional steady gradient solitons with positive curvature operators. We show that these solitons are non-collapsed.\n LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5504/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Alec Payne (Duke University) DTSTART:20211108T223000Z DTEND:20211108T230000Z DTSTAMP:20260404T042256Z UID:BIRS-21w5504/4 DESCRIPTION:Title: Mass Drop and Multiplicity in Mean Curvature Flow\nby Alec Payne (Duke University) as part of BIRS workshop: New Directions in Geome tric Flows\n\n\nAbstract\nMean curvature flow can be continued through sin gularities via Brakke flow or level set flow. Brakke flow is defined with an inequality which makes it tantamount to a subsolution to smooth mean cu rvature flow. On the other hand\, level set flow is like a supersolution\, since it may attain positive measure. In this talk\, we will discuss thes e weak solutions and will relate uniqueness problems for weak solutions to multiplicity problems in mean curvature flow. In particular\, we discuss how Brakke flows with only generic singularities achieve equality in the i nequality defining the Brakke flow. This uses an analysis of worldlines in the Brakke flow\, analogous to the theory of singular Ricci flows.\n LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5504/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Brian Harvie (National Taiwan University) DTSTART:20211108T230000Z DTEND:20211108T233000Z DTSTAMP:20260404T042256Z UID:BIRS-21w5504/5 DESCRIPTION:Title: The Inverse Mean Curvature Flow and Minimal Surfaces\nby B rian Harvie (National Taiwan University) as part of BIRS workshop: New Dir ections in Geometric Flows\n\n\nAbstract\nIn this talk\, I will discuss th e relationship between Inverse Mean Curvature Flow (IMCF)\, an expanding e xtrinsic geometric flow\, and minimal surfaces. A natural question about t he IMCF of a closed hypersurface in Euclidean space is whether a finite-ti me singularity forms. When one does form\, I will show how classical minim al surfaces may be used to characterize the flow behavior near the singula r time: specifically\, they allow one to establish a uniform bound on tota l curvature and hence a limit surface without rescaling the flow surfaces at the extinction. This singular profile contrasts sharply with the singul ar profiles of other extrinsic flows.\nWhen one does not form and the evol ution continues for all time\, there is a connection to previous work by M eeks and Yau on the embedded Plateau problem. In particular\, via a compar ison principle arising from embedded global solutions of IMCF\, I will sho w that global area-minimizers for Jordan curves confined to star-shaped or certain rotationally symmetric mean-convex surfaces in $R^3$ are embedded . Furthermore\, such curves admit only a finite number of stable minimal d isks with areas smaller than any fixed number.\n LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5504/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Jian Song (Rutgers University) DTSTART:20211108T233000Z DTEND:20211109T003000Z DTSTAMP:20260404T042256Z UID:BIRS-21w5504/6 DESCRIPTION:Title: Long time solutions of the Kahler-Ricci flow\nby Jian Song (Rutgers University) as part of BIRS workshop: New Directions in Geometri c Flows\n\n\nAbstract\nThe Kahler-Ricci flow admits a long-time solution i f and only if the canonical bundle of the underlying Kahler manifold is ne f. We prove that if the canonical bundle is semi-ample\, the diameter is u niformly bounded for long-time solutions of the normalized Kahler-Ricci fl ow. Our diameter estimate combined with the scalar curvature estimate for long-time solutions of the Kahler-Ricci flow are natural extensions of Per elman's diameter and scalar curvature estimates for short-time solutions o n Fano manifolds.\n LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5504/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Otis Chodosh (Stanford University) DTSTART:20211109T160000Z DTEND:20211109T170000Z DTSTAMP:20260404T042256Z UID:BIRS-21w5504/7 DESCRIPTION:Title: Generic mean curvature flow of low entropy initial data\nb y Otis Chodosh (Stanford University) as part of BIRS workshop: New Directi ons in Geometric Flows\n\n\nAbstract\nI will describe recent work with Cho i\, Mantoulidis\, Schulze concerning generic behavior of MCF. I will compa re two potential approaches to this problem and describe one of them (base d on entropy drop near non-generic singularities) in detail.\n LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5504/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Or Hershkovits (Hebrew University) DTSTART:20211109T173000Z DTEND:20211109T183000Z DTSTAMP:20260404T042256Z UID:BIRS-21w5504/8 DESCRIPTION:Title: Noncollapsed translators in R^4\nby Or Hershkovits (Hebrew University) as part of BIRS workshop: New Directions in Geometric Flows\n \n\nAbstract\nTranslating solution to the mean curvature flow form\, toget her with self-shrinking solutions\, the most important class of singularit y models of the flow. When a translator arises as a blow-up of a mean conv ex mean curvature flow\, it also naturally satisfies a noncollapsing condi tion.\nIn this talk\, I will report on a recent work with Kyeongsu Choi an d Robert Haslhofer\, in which we show that every mean convex\, noncollapse d\, translator in $R^4$ is a member of a one parameter family of translato rs\, which was earlier constructed by Hoffman\, Ilmanen\, Martin and White .\n LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5504/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Jonathan Zhu (Princeton University) DTSTART:20211109T223000Z DTEND:20211109T233000Z DTSTAMP:20260404T042256Z UID:BIRS-21w5504/9 DESCRIPTION:Title: Explicit Lojasiewicz inequalities for shrinking solitons\n by Jonathan Zhu (Princeton University) as part of BIRS workshop: New Direc tions in Geometric Flows\n\n\nAbstract\nŁojasiewicz inequalities are a po pular tool for studying the stability of geometric structures. For mean cu rvature flow\, Schulze used Simon’s reduction to the classical Łojasiew icz inequality to study compact tangent flows. For round cylinders\, Coldi ng and Minicozzi instead used a direct method to prove Łojasiewicz inequa lities. We’ll discuss similarly explicit Łojasiewicz inequalities and a pplications for other shrinking cylinders and products of spheres.\n LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5504/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Maxwell Stolarski (Arizona State University) DTSTART:20211109T233000Z DTEND:20211110T003000Z DTSTAMP:20260404T042256Z UID:BIRS-21w5504/10 DESCRIPTION:Title: Mean Curvature Flow Singularities with Bounded Mean Curvature \nby Maxwell Stolarski (Arizona State University) as part of BIRS work shop: New Directions in Geometric Flows\n\n\nAbstract\nIn 1984\, Huisken s howed that the second fundamental form always blows up at a finite-time si ngularity for the mean curvature flow. Naturally\, one might then ask if t he mean curvature must also blow up at a finite-time singularity. We'll di scuss work that shows the answer is "no" in general\, that is\, there exis t mean curvature flow solutions that become singular with uniformly bounde d mean curvature.\n LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5504/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Bruce Kleiner (New York University) DTSTART:20211110T160000Z DTEND:20211110T170000Z DTSTAMP:20260404T042256Z UID:BIRS-21w5504/11 DESCRIPTION:Title: Ricci flow through singularities\, and applications\nby B ruce Kleiner (New York University) as part of BIRS workshop: New Direction s in Geometric Flows\n\n\nAbstract\nThe talk will survey Ricci flow throug h singularities in dimension three\, and some applications to topology\; t he lecture is intended for nonexperts. This is joint work with Richard B amler and John Lott.\n LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5504/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Mario Garcia-Fernandez (Universidad Autonoma de Madrid) DTSTART:20211110T173000Z DTEND:20211110T183000Z DTSTAMP:20260404T042256Z UID:BIRS-21w5504/12 DESCRIPTION:Title: Non-Kähler Calabi-Yau geometry and pluriclosed flow\nby Mario Garcia-Fernandez (Universidad Autonoma de Madrid) as part of BIRS wo rkshop: New Directions in Geometric Flows\n\n\nAbstract\nIn this talk I wi ll overview joint work with J. Jordan and J. Streets\, in arXiv:2106.13716 \, about Hermitian\, pluriclosed metrics with vanishing Bismut-Ricci form. These metrics give a natural extension of Calabi-Yau metrics to the setti ng of complex\, non-Kähler manifolds\, and arise independently in mathema tical physics. We reinterpret this condition in terms of the Hermitian-Ein stein equation on an associated holomorphic Courant algebroid\, and thus r efer to solutions as Bismut Hermitian-Einstein. This implies Mumford-Takem oto slope stability obstructions\, and using these we exhibit infinitely m any topologically distinct complex manifolds in every dimension with vanis hing first Chern class which do not admit Bismut Hermitian-Einstein metric s. This reformulation also leads to a new description of pluriclosed flow\ , as introduced by Streets and Tian\, implying new global existence result s. In particular\, on all complex non-Kähler surfaces of nonnegative Koda ira dimension. On complex manifolds which admit Bismut-flat metrics we sho w global existence and convergence of pluriclosed flow to a Bismut-flat me tric.\n LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5504/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Felix Schulze (University of Warwick) DTSTART:20211111T160000Z DTEND:20211111T170000Z DTSTAMP:20260404T042256Z UID:BIRS-21w5504/13 DESCRIPTION:Title: A relative entropy and a unique continuation result for Ricci expanders\nby Felix Schulze (University of Warwick) as part of BIRS w orkshop: New Directions in Geometric Flows\n\n\nAbstract\nWe prove an opti mal relative integral convergence rate for two expanding gradient Ricci so litons coming out of the same cone. As a consequence\, we obtain a unique continuation result at infinity and we prove that a relative entropy for t wo such self-similar solutions to the Ricci flow is well-defined. This is joint work with Alix Deruelle.\n LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5504/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Keaton Naff (MIT) DTSTART:20211111T173000Z DTEND:20211111T183000Z DTSTAMP:20260404T042256Z UID:BIRS-21w5504/14 DESCRIPTION:Title: A neck improvement theorem in higher codimension MCF\nby Keaton Naff (MIT) as part of BIRS workshop: New Directions in Geometric Fl ows\n\n\nAbstract\nIn both Ricci flow and mean curvature flow\, there have recently been significant advances in our understanding of ancient soluti ons which model singularity formation. One of the crucial tools to this ad vance has been the development of local symmetry improvement results\, as first introduced in mean curvature flow by Brendle and Choi\, and later to the Ricci flow by Brendle. In this talk\, we would like to discuss how th e technique can be adapted to higher codimension mean curvature flow\, exh ibiting how both rotational symmetry and flatness improve along the flow.\ n LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5504/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Zhichao Wang (University of British Columbia) DTSTART:20211111T223000Z DTEND:20211111T230000Z DTSTAMP:20260404T042256Z UID:BIRS-21w5504/15 DESCRIPTION:Title: Uryson width of three dimensional mean convex domains with no n-negative Ricci curvature\nby Zhichao Wang (University of British Col umbia) as part of BIRS workshop: New Directions in Geometric Flows\n\n\nAb stract\nIn this joint work with B. Zhu\, we prove that for every three dim ensional manifold with non-negative Ricci curvature and strictly mean conv ex boundary\, there exists a Morse function so that each connected compone nt of its level sets has a uniform diameter bound\, which depends only on the lower bound of mean curvature. This gives an upper bound of Uryson 1-w idth for those three manifolds with boundary. Our proof uses mean curvatur e flow with free boundary proved by Edelen-Haslhofer-Ivaki-Zhu.\n LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5504/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Lu Wang (Yale University) DTSTART:20211111T230000Z DTEND:20211112T000000Z DTSTAMP:20260404T042256Z UID:BIRS-21w5504/16 DESCRIPTION:Title: Closed hypersurfaces of low entropy are isotopically trivial< /a>\nby Lu Wang (Yale University) as part of BIRS workshop: New Directions in Geometric Flows\n\n\nAbstract\nWe show that any closed connected hyper surface with sufficient low entropy is smoothly isotopic to the standard r ound sphere.\n LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5504/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Natasa Sesum (Rutgers University) DTSTART:20211112T160000Z DTEND:20211112T170000Z DTSTAMP:20260404T042256Z UID:BIRS-21w5504/17 DESCRIPTION:Title: Survey of recent classification results of ancient solutions< /a>\nby Natasa Sesum (Rutgers University) as part of BIRS workshop: New Di rections in Geometric Flows\n\n\nAbstract\nWe will discuss recent results and progress made on classifying ancient solutions in geometric flows. We will also mention very nice applications of these results that play an imp ortant role in singularity analysis of mean curvature flow and Ricci flow. \n LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5504/17/ END:VEVENT BEGIN:VEVENT SUMMARY:Ronan Conlon (University of Texas at Dallas) DTSTART:20211112T173000Z DTEND:20211112T183000Z DTSTAMP:20260404T042256Z UID:BIRS-21w5504/18 DESCRIPTION:Title: Steady gradient Kahler-Ricci solitons\nby Ronan Conlon (U niversity of Texas at Dallas) as part of BIRS workshop: New Directions in Geometric Flows\n\n\nAbstract\nSteady gradient Kähler-Ricci solitons are fixed points of the Kähler-Ricci flow evolving only by the action of biho lomorphisms generated by a real holomorphic vector field. We show that the re is a unique steady gradient Kähler-Ricci soliton in each Kähler class of a crepant resolution of a Calabi-Yau cone. To do this\, we solve a com plex Monge-Ampere equation via a continuity method. Our construction is ba sed on an ansatz due to Cao in the 90’s which was utilized by Biquard-Ma cBeth in 2017. This is joint work with Alix Deruelle.\n LOCATION:https://stable.researchseminars.org/talk/BIRS-21w5504/18/ END:VEVENT END:VCALENDAR