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:20260422T185859Z UID:BIRS-21w5504/1 DESCRIPTION:Title: Type II smoothing in Mean curvature flow\nby Panagiota Daskalopou los (Columbia University) as part of BIRS workshop: New Directions in Geom etric Flows\n\n\nAbstract\nIn 1994 Velázquez constructed a smooth \\( O( 4)\\times O(4)\\) invariant Mean Curvature Flow that forms a type-II singu larity at the origin in space-time. Stolarski very recently showed that the mean curvature on this solution is uniformly bounded. Earlier\, Velá zquez also provided formal asymptotic expansions for a possible smooth con tinuation of the solution after the singularity. \nJointly with S. Angenen t and N. Sesum we establish the short time existence of Velázquez' form al continuation\, and we verify that the mean curvature is also uniformly bounded on the continuation.\n LOCATION:https://researchseminars.org/talk/BIRS-21w5504/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Paula Burkhardt-Guim (NYU Courant) DTSTART:20211108T173000Z DTEND:20211108T183000Z DTSTAMP:20260422T185859Z UID:BIRS-21w5504/2 DESCRIPTION:Title: Pointwise lower scalar curvature bounds for C^0 metrics via regulariz ing Ricci flow\nby Paula Burkhardt-Guim (NYU Courant) as part of BIRS workshop: New Directions in Geometric Flows\n\n\nAbstract\nWe propose a cl ass of local definitions of weak lower scalar curvature bounds that is wel l defined for C^0 metrics. We show the following: that our definitions 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 from C^0 initial data.\n LOCATION:https://researchseminars.org/talk/BIRS-21w5504/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Yi Lai (Stanford University) DTSTART:20211108T210000Z DTEND:20211108T220000Z DTSTAMP:20260422T185859Z UID:BIRS-21w5504/3 DESCRIPTION:Title: Steady gradient Ricci solitons with positive curvature operators\ nby Yi Lai (Stanford University) as part of BIRS workshop: New Directions in Geometric Flows\n\n\nAbstract\nWe find a family of 3d steady gradient R icci solitons that are flying wings. This verifies a conjecture by Hamilto n. For a 3d flying wing\, we show that the scalar curvature does not vanis h at infinity. The 3d flying wings are collapsed. For dimension n ≥ 4\, we find a family of Z2 × O(n − 1)-symmetric but non-rotationally symmet ric n-dimensional steady gradient solitons with positive curvature operato rs. We show that these solitons are non-collapsed.\n LOCATION:https://researchseminars.org/talk/BIRS-21w5504/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Alec Payne (Duke University) DTSTART:20211108T223000Z DTEND:20211108T230000Z DTSTAMP:20260422T185859Z 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 Geometric Fl ows\n\n\nAbstract\nMean curvature flow can be continued through singularit ies via Brakke flow or level set flow. Brakke flow is defined with an ineq uality which makes it tantamount to a subsolution to smooth mean curvature flow. On the other hand\, level set flow is like a supersolution\, since it may attain positive measure. In this talk\, we will discuss these weak solutions and will relate uniqueness problems for weak solutions to multip licity problems in mean curvature flow. In particular\, we discuss how Bra kke flows with only generic singularities achieve equality in the inequali ty defining the Brakke flow. This uses an analysis of worldlines in the Br akke flow\, analogous to the theory of singular Ricci flows.\n LOCATION:https://researchseminars.org/talk/BIRS-21w5504/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Brian Harvie (National Taiwan University) DTSTART:20211108T230000Z DTEND:20211108T233000Z DTSTAMP:20260422T185859Z UID:BIRS-21w5504/5 DESCRIPTION:Title: The Inverse Mean Curvature Flow and Minimal Surfaces\nby Brian Ha rvie (National Taiwan University) as part of BIRS workshop: New Directions in Geometric Flows\n\n\nAbstract\nIn this talk\, I will discuss the relat ionship between Inverse Mean Curvature Flow (IMCF)\, an expanding extrinsi c geometric flow\, and minimal surfaces. A natural question about the IMCF of a closed hypersurface in Euclidean space is whether a finite-time sing ularity forms. When one does form\, I will show how classical minimal surf aces may be used to characterize the flow behavior near the singular time: specifically\, they allow one to establish a uniform bound on total curva ture and hence a limit surface without rescaling the flow surfaces at the extinction. This singular profile contrasts sharply with the singular prof iles of other extrinsic flows.\nWhen one does not form and the evolution c ontinues for all time\, there is a connection to previous work by Meeks an d Yau on the embedded Plateau problem. In particular\, via a comparison pr inciple arising from embedded global solutions of IMCF\, I will show that global area-minimizers for Jordan curves confined to star-shaped or certai n rotationally symmetric mean-convex surfaces in $R^3$ are embedded. Furth ermore\, such curves admit only a finite number of stable minimal disks wi th areas smaller than any fixed number.\n LOCATION:https://researchseminars.org/talk/BIRS-21w5504/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Jian Song (Rutgers University) DTSTART:20211108T233000Z DTEND:20211109T003000Z DTSTAMP:20260422T185859Z UID:BIRS-21w5504/6 DESCRIPTION:Title: Long time solutions of the Kahler-Ricci flow\nby Jian Song (Rutge rs University) as part of BIRS workshop: New Directions in Geometric Flows \n\n\nAbstract\nThe Kahler-Ricci flow admits a long-time solution if and o nly if the canonical bundle of the underlying Kahler manifold is nef. We p rove that if the canonical bundle is semi-ample\, the diameter is uniforml y bounded for long-time solutions of the normalized Kahler-Ricci flow. Our diameter estimate combined with the scalar curvature estimate for long-ti me solutions of the Kahler-Ricci flow are natural extensions of Perelman's diameter and scalar curvature estimates for short-time solutions on Fano manifolds.\n LOCATION:https://researchseminars.org/talk/BIRS-21w5504/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Otis Chodosh (Stanford University) DTSTART:20211109T160000Z DTEND:20211109T170000Z DTSTAMP:20260422T185859Z UID:BIRS-21w5504/7 DESCRIPTION:Title: Generic mean curvature flow of low entropy initial data\nby Otis Chodosh (Stanford University) as part of BIRS workshop: New Directions in Geometric Flows\n\n\nAbstract\nI will describe recent work with Choi\, Man toulidis\, Schulze concerning generic behavior of MCF. I will compare two potential approaches to this problem and describe one of them (based on en tropy drop near non-generic singularities) in detail.\n LOCATION:https://researchseminars.org/talk/BIRS-21w5504/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Or Hershkovits (Hebrew University) DTSTART:20211109T173000Z DTEND:20211109T183000Z DTSTAMP:20260422T185859Z UID:BIRS-21w5504/8 DESCRIPTION:Title: Noncollapsed translators in R^4\nby Or Hershkovits (Hebrew Univer sity) as part of BIRS workshop: New Directions in Geometric Flows\n\n\nAbs tract\nTranslating solution to the mean curvature flow form\, together wit h self-shrinking solutions\, the most important class of singularity model s of the flow. When a translator arises as a blow-up of a mean convex mean curvature flow\, it also naturally satisfies a noncollapsing condition.\n In this talk\, I will report on a recent work with Kyeongsu Choi and Rober t Haslhofer\, in which we show that every mean convex\, noncollapsed\, tra nslator in $R^4$ is a member of a one parameter family of translators\, wh ich was earlier constructed by Hoffman\, Ilmanen\, Martin and White.\n LOCATION:https://researchseminars.org/talk/BIRS-21w5504/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Jonathan Zhu (Princeton University) DTSTART:20211109T223000Z DTEND:20211109T233000Z DTSTAMP:20260422T185859Z UID:BIRS-21w5504/9 DESCRIPTION:Title: Explicit Lojasiewicz inequalities for shrinking solitons\nby Jona than Zhu (Princeton University) as part of BIRS workshop: New Directions i n Geometric Flows\n\n\nAbstract\nŁojasiewicz inequalities are a popular t ool for studying the stability of geometric structures. For mean curvature flow\, Schulze used Simon’s reduction to the classical Łojasiewicz ine quality to study compact tangent flows. For round cylinders\, Colding and Minicozzi instead used a direct method to prove Łojasiewicz inequalities. We’ll discuss similarly explicit Łojasiewicz inequalities and applicat ions for other shrinking cylinders and products of spheres.\n LOCATION:https://researchseminars.org/talk/BIRS-21w5504/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Maxwell Stolarski (Arizona State University) DTSTART:20211109T233000Z DTEND:20211110T003000Z DTSTAMP:20260422T185859Z UID:BIRS-21w5504/10 DESCRIPTION:Title: Mean Curvature Flow Singularities with Bounded Mean Curvature\nb y Maxwell Stolarski (Arizona State University) as part of BIRS workshop: N ew Directions in Geometric Flows\n\n\nAbstract\nIn 1984\, Huisken showed t hat the second fundamental form always blows up at a finite-time singulari ty for the mean curvature flow. Naturally\, one might then ask if the mean curvature must also blow up at a finite-time singularity. We'll discuss w ork that shows the answer is "no" in general\, that is\, there exist mean curvature flow solutions that become singular with uniformly bounded mean curvature.\n LOCATION:https://researchseminars.org/talk/BIRS-21w5504/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Bruce Kleiner (New York University) DTSTART:20211110T160000Z DTEND:20211110T170000Z DTSTAMP:20260422T185859Z UID:BIRS-21w5504/11 DESCRIPTION:Title: Ricci flow through singularities\, and applications\nby Bruce Kl einer (New York University) as part of BIRS workshop: New Directions in Ge ometric Flows\n\n\nAbstract\nThe talk will survey Ricci flow through singu larities in dimension three\, and some applications to topology\; the lect ure is intended for nonexperts. This is joint work with Richard Bamler a nd John Lott.\n LOCATION:https://researchseminars.org/talk/BIRS-21w5504/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Mario Garcia-Fernandez (Universidad Autonoma de Madrid) DTSTART:20211110T173000Z DTEND:20211110T183000Z DTSTAMP:20260422T185859Z UID:BIRS-21w5504/12 DESCRIPTION:Title: Non-Kähler Calabi-Yau geometry and pluriclosed flow\nby Mario G arcia-Fernandez (Universidad Autonoma de Madrid) as part of BIRS workshop: New Directions in Geometric Flows\n\n\nAbstract\nIn this talk I will over view joint work with J. Jordan and J. Streets\, in arXiv:2106.13716\, abou t Hermitian\, pluriclosed metrics with vanishing Bismut-Ricci form. These metrics give a natural extension of Calabi-Yau metrics to the setting of c omplex\, non-Kähler manifolds\, and arise independently in mathematical p hysics. We reinterpret this condition in terms of the Hermitian-Einstein e quation on an associated holomorphic Courant algebroid\, and thus refer to solutions as Bismut Hermitian-Einstein. This implies Mumford-Takemoto slo pe stability obstructions\, and using these we exhibit infinitely many top ologically distinct complex manifolds in every dimension with vanishing fi rst Chern class which do not admit Bismut Hermitian-Einstein metrics. This reformulation also leads to a new description of pluriclosed flow\, as in troduced by Streets and Tian\, implying new global existence results. In p articular\, on all complex non-Kähler surfaces of nonnegative Kodaira dim ension. On complex manifolds which admit Bismut-flat metrics we show globa l existence and convergence of pluriclosed flow to a Bismut-flat metric.\n LOCATION:https://researchseminars.org/talk/BIRS-21w5504/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Felix Schulze (University of Warwick) DTSTART:20211111T160000Z DTEND:20211111T170000Z DTSTAMP:20260422T185859Z UID:BIRS-21w5504/13 DESCRIPTION:Title: A relative entropy and a unique continuation result for Ricci expand ers\nby Felix Schulze (University of Warwick) as part of BIRS workshop : New Directions in Geometric Flows\n\n\nAbstract\nWe prove an optimal rel ative integral convergence rate for two expanding gradient Ricci solitons coming out of the same cone. As a consequence\, we obtain a unique continu ation result at infinity and we prove that a relative entropy for two such self-similar solutions to the Ricci flow is well-defined. This is joint w ork with Alix Deruelle.\n LOCATION:https://researchseminars.org/talk/BIRS-21w5504/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Keaton Naff (MIT) DTSTART:20211111T173000Z DTEND:20211111T183000Z DTSTAMP:20260422T185859Z 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 Flows\n\n \nAbstract\nIn both Ricci flow and mean curvature flow\, there have recent ly been significant advances in our understanding of ancient solutions whi ch model singularity formation. One of the crucial tools to this advance h as been the development of local symmetry improvement results\, as first i ntroduced in mean curvature flow by Brendle and Choi\, and later to the Ri cci flow by Brendle. In this talk\, we would like to discuss how the techn ique can be adapted to higher codimension mean curvature flow\, exhibiting how both rotational symmetry and flatness improve along the flow.\n LOCATION:https://researchseminars.org/talk/BIRS-21w5504/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Zhichao Wang (University of British Columbia) DTSTART:20211111T223000Z DTEND:20211111T230000Z DTSTAMP:20260422T185859Z UID:BIRS-21w5504/15 DESCRIPTION:Title: Uryson width of three dimensional mean convex domains with non-negat ive Ricci curvature\nby Zhichao Wang (University of British Columbia) as part of BIRS workshop: New Directions in Geometric Flows\n\n\nAbstract\ nIn this joint work with B. Zhu\, we prove that for every three dimensiona l manifold with non-negative Ricci curvature and strictly mean convex boun dary\, there exists a Morse function so that each connected component of i ts level sets has a uniform diameter bound\, which depends only on the low er bound of mean curvature. This gives an upper bound of Uryson 1-width fo r those three manifolds with boundary. Our proof uses mean curvature flow with free boundary proved by Edelen-Haslhofer-Ivaki-Zhu.\n LOCATION:https://researchseminars.org/talk/BIRS-21w5504/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Lu Wang (Yale University) DTSTART:20211111T230000Z DTEND:20211112T000000Z DTSTAMP:20260422T185859Z UID:BIRS-21w5504/16 DESCRIPTION:Title: Closed hypersurfaces of low entropy are isotopically trivial\nby Lu Wang (Yale University) as part of BIRS workshop: New Directions in Geo metric Flows\n\n\nAbstract\nWe show that any closed connected hypersurface with sufficient low entropy is smoothly isotopic to the standard round sp here.\n LOCATION:https://researchseminars.org/talk/BIRS-21w5504/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Natasa Sesum (Rutgers University) DTSTART:20211112T160000Z DTEND:20211112T170000Z DTSTAMP:20260422T185859Z UID:BIRS-21w5504/17 DESCRIPTION:Title: Survey of recent classification results of ancient solutions\nby Natasa Sesum (Rutgers University) as part of BIRS workshop: New Direction s in Geometric Flows\n\n\nAbstract\nWe will discuss recent results and pro gress made on classifying ancient solutions in geometric flows. We will al so mention very nice applications of these results that play an important role in singularity analysis of mean curvature flow and Ricci flow.\n LOCATION:https://researchseminars.org/talk/BIRS-21w5504/17/ END:VEVENT BEGIN:VEVENT SUMMARY:Ronan Conlon (University of Texas at Dallas) DTSTART:20211112T173000Z DTEND:20211112T183000Z DTSTAMP:20260422T185859Z UID:BIRS-21w5504/18 DESCRIPTION:Title: Steady gradient Kahler-Ricci solitons\nby Ronan Conlon (Universi ty of Texas at Dallas) as part of BIRS workshop: New Directions in Geometr ic Flows\n\n\nAbstract\nSteady gradient Kähler-Ricci solitons are fixed p oints of the Kähler-Ricci flow evolving only by the action of biholomorph isms generated by a real holomorphic vector field. We show that there is a unique steady gradient Kähler-Ricci soliton in each Kähler class of a c repant resolution of a Calabi-Yau cone. To do this\, we solve a complex Mo nge-Ampere equation via a continuity method. Our construction is based on an ansatz due to Cao in the 90’s which was utilized by Biquard-MacBeth i n 2017. This is joint work with Alix Deruelle.\n LOCATION:https://researchseminars.org/talk/BIRS-21w5504/18/ END:VEVENT END:VCALENDAR