BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Giovanni Bazzoni (Università degli Studi dell'Insubria) DTSTART:20201020T150000Z DTEND:20201020T160000Z DTSTAMP:20260422T225722Z UID:DGSTO/1 DESCRIPTION:Title: Sy mmetric and skew-symmetric complex structures\nby Giovanni Bazzoni (Un iversità degli Studi dell'Insubria) as part of Differential Geometry Semi nar Torino\n\n\nAbstract\nIn this talk we study the geometry of a complex manifold $(M\,J)$ endowed with a closed\, non-degenerate 2-form $\\omega$ with respect to which $J$ is either symmetric or skew-symmetric. This lead s to\, respectively\, complex-symplectic and pseudo-Kähler structures. Co mplex symplectic structures are related to a number of other geometric str uctures\, such as (hyper)Kähler\, hypercomplex\, and hypersymplectic. We are interested in examples of manifolds which carry some of these structur es\, but no others. Joint work with M. Freibert\, A. Gil García\, A. Lato rre\, B. Meinke.\n LOCATION:https://researchseminars.org/talk/DGSTO/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Wayne Rossman (Kobe University) DTSTART:20201028T090000Z DTEND:20201028T100000Z DTSTAMP:20260422T225722Z UID:DGSTO/2 DESCRIPTION:Title: Da rboux flow and semi-discrete mKdV equation\nby Wayne Rossman (Kobe Uni versity) as part of Differential Geometry Seminar Torino\n\nAbstract: TBA\ n LOCATION:https://researchseminars.org/talk/DGSTO/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Tommaso Pacini (Università degli Studi di Torino) DTSTART:20201117T160000Z DTEND:20201117T170000Z DTSTAMP:20260422T225722Z UID:DGSTO/3 DESCRIPTION:Title: Fr om calibrated geometry to holomorphic invariants\nby Tommaso Pacini (U niversità degli Studi di Torino) as part of Differential Geometry Seminar Torino\n\n\nAbstract\nThe seminar will address questions such as: (i) How to use submanifolds to study the ambient space\, (ii) How to use ideas fr om calibrated geometry to build new holomorphic invariants\, (iii) How to calculate these invariants\, and why we might care.\nThis will be a non-te chnical survey of my recent research and of its context within classical c omplex analysis and the current theory of manifolds with special holonomy. \n LOCATION:https://researchseminars.org/talk/DGSTO/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Mason Pember (Politecnico di Torino) DTSTART:20201120T150000Z DTEND:20201120T154000Z DTSTAMP:20260422T225722Z UID:DGSTO/4 DESCRIPTION:Title: Sp herical curves in Lie sphere geometry\nby Mason Pember (Politecnico di Torino) as part of Differential Geometry Seminar Torino\n\n\nAbstract\nBl aschke showed that a surface with one family of spherical curvature lines can be parametrised via a certain flow of an initial curve on a sphere. I n this talk we characterise when this surface is additionally a Lie applic able surface\, by restricting the flow and the initial curve. It turns out that the initial curve must project to a constrained elastic curve in som e space form\, which leads us to a Lie geometric characterisation of such curves.\n\nThis talk will be held on the occasion of the PRIN seminar orga nised by the Politecnico di Torino PRIN unit.\n LOCATION:https://researchseminars.org/talk/DGSTO/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Andreas Vollmer (Politecnico di Torino) DTSTART:20201120T155000Z DTEND:20201120T163000Z DTSTAMP:20260422T225722Z UID:DGSTO/5 DESCRIPTION:Title: Tw o-dimensional superintegrable metrics with symmetries that preserve geodes ic curves\nby Andreas Vollmer (Politecnico di Torino) as part of Diffe rential Geometry Seminar Torino\n\n\nAbstract\nIn 1882\, Sophus Lie formul ated the task to describe two-dimensional metrics admitting non-trivial sy mmetries that preserve geodesics up to reparametrisation. Such symmetries are called projective. Lie's Problem has been resolved in recent years in terms of a classification up to diffeomorphisms (Bryant-Manno-Matveev 2008 \, Matveev 2012 and Manno-V 2020).\n\nThe talk will focus on a distinct su bclass of these metrics\, namely those that are superintegrable with quadr atic integrals of motion. Generally speaking a metric is superintegrable i f it admits a maximal amount of independent constants of motion.\nMatveev' s geometries are a particular example\, in which case the projective symme try is unique. It turns out that all of Matveev's geometries share the sam e geodesics up to reparametrisation (in other words\, they are projectivel y equivalent). The associated superintegrable systems are of non-degenerat e type meaning that they admit a four-parameter potential.\n\nThis talk wi ll be held on the occasion of the PRIN seminar organised by the Politecnic o di Torino PRIN unit.\n LOCATION:https://researchseminars.org/talk/DGSTO/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Jason Lotay (University of Oxford) DTSTART:20201201T160000Z DTEND:20201201T170000Z DTSTAMP:20260422T225722Z UID:DGSTO/6 DESCRIPTION:Title: Mi nimal Lagrangians and where to find them\nby Jason Lotay (University o f Oxford) as part of Differential Geometry Seminar Torino\n\n\nAbstract\nA classical problem going back to ancient Greece is to find the shortest cu rve in the plane enclosing a given area: the isoperimetric problem. A simi lar question is whether given a curve on a surface it can be deformed to a shortest one. Whilst the solutions to these classical problems are well-k nown\, natural generalisations in higher dimensions are mostly unsolved. I will explain how this leads us to the study of minimal Lagrangians and th e question of how to find them\, which will take us to the interface betwe en symplectic topology\, Riemannian geometry and analysis of nonlinear PDE s\, with links to theoretical physics.\n\nThis talk will be held on the oc casion of the PRIN seminar organised by the Università di Torino PRIN uni t.\n LOCATION:https://researchseminars.org/talk/DGSTO/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Thomas Ivey (College of Charleston) DTSTART:20201214T160000Z DTEND:20201214T170000Z DTSTAMP:20260422T225722Z UID:DGSTO/7 DESCRIPTION:Title: Ne w Integrable Curve Flows in the Pseudoconformal 3-Sphere\nby Thomas Iv ey (College of Charleston) as part of Differential Geometry Seminar Torino \n\n\nAbstract\nThe pseudoconformal 3-sphere $S^3$ is the projectivization of the null cone in $\\mathbb C^3$ with the standard pseudo-Hermitian inn er product. The Lie group $SU(2\,1)$ fixing this metric naturally acts on the sphere\, preserving a contact structure\, and can be identified with t he pseudoconformal frame bundle of $S^3$. By normalizing lifts to the fram e bundle\, we define scalar geometric invariants for Legendrian curves (L- curves) in $S^3$\, and for curves transverse to the contact planes (T-curv es).\nWe seek invariant geometric flows for these parametrized curves that induce integrable evolution systems for the invariants. While there is an infinite sequence of geometric flows for L-curves inducing the Boussinesq hierarchy\, for T-curves there is another infinite sequence of flows that induces a sequence of 3-component evolution systems for the invariants\, evidently a novel integrable bi-Hamiltonian hierarchy. This closely resem bles the NLS hierarchy\, itself realized by a sequence of curve flows in E uclidean 3-space\, including the vortex filament equation. We discuss som e common features of these hierarchies\, describe the geometry and dynamic s of travelling wave solutions (also arising as critical curves for Lagran gians derived from the conserved densities) and conclude with some open qu estions.\n LOCATION:https://researchseminars.org/talk/DGSTO/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Francesco Bonsante (Università degli Studi di Pavia) DTSTART:20210127T160000Z DTEND:20210127T170000Z DTSTAMP:20260422T225722Z UID:DGSTO/8 DESCRIPTION:Title: Mi nimizing immersions of surfaces in hyperbolic 3-manifolds\nby Francesc o Bonsante (Università degli Studi di Pavia) as part of Differential Geom etry Seminar Torino\n\n\nAbstract\nTrapani and Valle proposed to study the L^1 holomorphic energy of diffeomorphisms between Riemannian surfaces. Th is is defined as the L^1-norm of the (1\,0)-part of the differential of th e map. They proved that if the domain and the target are surfaces of negat ive curvature\, any homotopy class of diffeomorphisms contains a unique mi nimizer for the functional. In a recent work with Gabriele Mondello and Je an-Marc Schlenker we tried to generalize the functional in the setting wh ere the domain is a hyperbolic surface and the target a hyperbolic 3-manif old. The functional here is the L^1-Shatten energy\, which in fact coincid es with the L^1-holomorphic energy in the 2-dimensional case. More concret ely we considered the space of equivariant maps of the universal covering of a fixed surface of genus g into the hyperbolic space\, and studied map s which minimize the L^1-Shatten energy on fibers of the monodromy map. We proved that the space of such minimizing maps is naturally a complex mani fold of dimension 6g-6\, where g is the genus of the surface\, so that the monodromy map realize a holomorphic embedding onto some open subset of th e PSL_2(C)-character variety containing the Fuchsian locus.\n\nIn the talk I will describe the main results of this joint work.\n LOCATION:https://researchseminars.org/talk/DGSTO/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Ben Sharp (University of Leeds) DTSTART:20210209T160000Z DTEND:20210209T170000Z DTSTAMP:20260422T225722Z UID:DGSTO/9 DESCRIPTION:Title: Ł ojasiewicz-type inequalities for the H-functional near simple bubble trees \nby Ben Sharp (University of Leeds) as part of Differential Geometry Seminar Torino\n\n\nAbstract\nThe H-functional E is a natural variant of t he Dirichlet energy along maps u from a closed surface S into R^3. Critica l points of E include conformal parameterisations of constant mean curvatu re surfaces in R^3. The functional itself is unbounded from above and belo w on H^1(S\,R^3)\, but all critical points have H-energy E at least 4π/3\ , with equality attained if and only if we are parametrising a round spher e (so S itself must be a sphere) - this is the classical isoperimetric ine quality.\n\nHere we will address the simple question: can one approach the natural lower energy bound by critical points along fixed surfaces of hig her genus? In fact we prove more subtle quantitative estimates for any (al most-)critical point whose energy is close to 4π/3. Standard theory tells us that a sequence of (almost-)critical points on a fixed torus T\, whose energy approaches 4π/3\, must bubble-converge to a sphere: there is a sh rinking disc on the torus that gets mapped to a larger and larger region o f the round sphere\, and away from the disc our maps converge to a constan t. Thus the limiting object is really a map from a sphere to R^3\, and the challenge is to compare maps from a torus with the limiting map (i.e. a c hange of topology in the limit). In particular we can prove a gap theorem for the lowest energy level on a fixed surface and estimate the rates at w hich bubbling maps u are becoming spherical in terms of the size of dE[u] - these are commonly referred to as Łojasiewicz-type estimates. \n\nThis is a joint work with Andrea Malchiodi (SNS Pisa) and Melanie Rupflin (Oxfo rd).\n LOCATION:https://researchseminars.org/talk/DGSTO/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Vladimir Matveev (Universität Jena) DTSTART:20210223T160000Z DTEND:20210223T170000Z DTSTAMP:20260422T225722Z UID:DGSTO/10 DESCRIPTION:Title: N ijenhuis geometry\, multihamiltonian systems of hydrodynamic type and geod esic equivalence\nby Vladimir Matveev (Universität Jena) as part of D ifferential Geometry Seminar Torino\n\n\nAbstract\nWe connect two a priori unrelated topics\, theory of geodesically equivalent metrics in different ial geometry\, and theory of compatible infinite dimensional Poisson brack ets of hydrodynamic type in mathematical physics. \n\nNamely\, we prove t hat a pair of geodesically equivalent metrics such that one is flat produc es a pair of such brackets. We construct Casimirs for these brackets and t he corresponding commuting flows. \n\nThere are two ways to produce a larg e family of compatible Poisson structures from a pair of geodesically equi valent metrics one of which is flat. One of these families is $(n+1)(n+2) /2$ dimensional\; we describe it completely and show that it is maximal. A nother has dimension $\\le n+2$ and is\, in a certain sense\, polynomial. We show that a nontrivial polynomial family of compatible Poisson structur es of dimension $n+2$ is unique and comes from a pair of geodesically equi valent metrics.\n\nThe talk based on a series of joint publications with A . Bolsinov (Lboro) and A. Konyaev (Moscow)\; the most related one is https ://arxiv.org/abs/2009.07802\n LOCATION:https://researchseminars.org/talk/DGSTO/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Sebastien Picard (University of British Columbia) DTSTART:20210309T160000Z DTEND:20210309T170000Z DTSTAMP:20260422T225722Z UID:DGSTO/11 DESCRIPTION:Title: M etrics Through Non-Kahler Transitions\nby Sebastien Picard (University of British Columbia) as part of Differential Geometry Seminar Torino\n\n\ nAbstract\nIt was proposed by Clemens\, Friedman and Reid to connect Calab i-Yau threefolds of different topologies by an operation known as a conifo ld transition. However\, this process may produce a non-Kahler complex man ifold with trivial canonical bundle. We will consider conifold transitions from the point of view of differential geometry and discuss passing speci al metrics through a non-Kahler transition.\n\nThis is joint work with T.C . Collins and S.-T. Yau.\n LOCATION:https://researchseminars.org/talk/DGSTO/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Lorenzo Mazzieri (Università degli Studi di Trento) DTSTART:20210324T130000Z DTEND:20210324T140000Z DTSTAMP:20260422T225722Z UID:DGSTO/12 DESCRIPTION:Title: S errin-type theorems for domains with disconnected boundary\nby Lorenzo Mazzieri (Università degli Studi di Trento) as part of Differential Geom etry Seminar Torino\n\n\nAbstract\nWe prove new optimal symmetry results f or solutions to the torsion problem on domains with disconnected boundary. \nTime permitting\, we discuss their relations with the uniqueness theore m for the Schwarzschild-de Sitter static black hole in general relativity. \nThe results are obtained in collaboration with V. Agostiniani and S. Bo rghini.\n LOCATION:https://researchseminars.org/talk/DGSTO/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Yury Ustinovskiy (New York University) DTSTART:20210412T150000Z DTEND:20210412T160000Z DTSTAMP:20260422T225722Z UID:DGSTO/13 DESCRIPTION:Title: G ibbons-Hawking ansatz and Generalized Kahler solitons\nby Yury Ustinov skiy (New York University) as part of Differential Geometry Seminar Torino \n\n\nAbstract\nIn the last decades geometric flows have been proved to be a powerful tool in the classification and uniformization problems in geom etry and topology. Despite the wide range of applicability of the existing analytical methods\, we are still lacking efficient tools adapted to the study of general (non-Kahler) complex manifolds. In my talk I will discuss the pluriclosed flow - a modification of the Ricci flow - which was intro duced by Streets and Tian\, and shares many nice features of the Ricci flo w. The important open questions driving the ongoing research in complex ge ometry are the classification of compact non-Kahler surfaces\, and the Glo bal Spherical Shell conjecture. Our hope is that understanding the long-ti me behaviour and singularities of the pluriclosed flow well enough\, we ca n use it to approach these open questions.\n\nTo apply an analytic flow to any geometric problem\, we need to make the first necessary step - classi fy the stationary points of the flow\, and\, more generally\, its solitons (stationary points modulo diffeomorphisms). For the pluriclosed flow\, th is question reduces to a non-linear elliptic PDE for an Hermitian metric o n a given complex manifold. We will discuss this problem on compact/comple te complex surfaces\, and provide exhaustive classification under natural extra geometric assumptions. In the course of our classification we will d iscover a natural extension of the famous Gibbons-Hawking ansatz for hyper Kahler manifolds.\n LOCATION:https://researchseminars.org/talk/DGSTO/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Christos-Raent Onti (University of Cyprus) DTSTART:20210429T150000Z DTEND:20210429T160000Z DTSTAMP:20260422T225722Z UID:DGSTO/14 DESCRIPTION:Title: A class of Einstein submanifolds of Euclidean space\nby Christos-Raent Onti (University of Cyprus) as part of Differential Geometry Seminar Torin o\n\n\nAbstract\nThe knowledge on the subject of Euclidean Einstein subman ifolds\, except those with constant sectional curvature\, is quite limited . In fact\, as far as we know\, until now the only classification result a vailable under purely intrinsic assumptions is in the case of hypersurface s\, due to an observation by Cartan communicated by Thomas in 1937 and the work of Fialkow from 1938. In the talk\, I will discuss the characterizat ion of a class of Einstein manifolds isometrically immersed into Euclidean space as rotational submanifolds. The highlight is for submanifolds in co dimension two since in this case our assumptions are purely intrinsic. Thi s is a joint work with Marcos Dajczer (IMPA) and Theodoros Vlachos (Univer sity of Ioannina).\n LOCATION:https://researchseminars.org/talk/DGSTO/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Andrei Moroianu (Université Paris-Saclay) DTSTART:20210511T150000Z DTEND:20210511T160000Z DTSTAMP:20260422T225722Z UID:DGSTO/15 DESCRIPTION:Title: M etric connections with parallel torsion\nby Andrei Moroianu (Universit é Paris-Saclay) as part of Differential Geometry Seminar Torino\n\n\nAbst ract\nThe torsion of every metric connection on a Riemannian manifold has three components: one totally skew-symmetric\, one of vectorial type\, and one of twistorial type. In the first part of the talk I will explain the classification of complete simply connected Riemannian manifolds carrying a metric connection whose torsion is parallel\, has non-zero vectorial com ponent and vanishing twistorial component. In the second part I will desc ribe the case where the only non-vanishing component of the torsion is tot ally skew-symmetric. Although apparently simpler than the previous case\, the situation here is much more involved and a complete classification is currently not available. The talk is based on joint works with Mihaela Pil ca and Uwe Semmelmann.\n LOCATION:https://researchseminars.org/talk/DGSTO/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Giuseppe Tinaglia (King's College London) DTSTART:20210519T090000Z DTEND:20210519T100000Z DTSTAMP:20260422T225722Z UID:DGSTO/16 DESCRIPTION:Title: T he geometry of constant mean curvature surfaces in Euclidean space\nby Giuseppe Tinaglia (King's College London) as part of Differential Geometr y Seminar Torino\n\n\nAbstract\nI will begin by reviewing classical geomet ric properties of constant mean curvature surfaces\, H>0\, in R^3. I will then talk about several more recent results for surfaces embedded in R^3 w ith constant mean curvature\, such as curvature and radius estimates. I wi ll show applications of such estimates including a characterisation of the round sphere as the only simply-connected surface embedded in R^3 with co nstant mean curvature and area estimates for compact surfaces embedded in a flat torus with constant mean curvature and finite genus. I will also ta lk about the geometry of compact hyper surfaces embedded in a manifold wit h constant mean curvature and finite index.\n LOCATION:https://researchseminars.org/talk/DGSTO/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Nicolina Istrati (Philipps Universität Marburg) DTSTART:20210608T150000Z DTEND:20210608T160000Z DTSTAMP:20260422T225722Z UID:DGSTO/17 DESCRIPTION:Title: O n some variational problems in conformal geometry\nby Nicolina Istrati (Philipps Universität Marburg) as part of Differential Geometry Seminar Torino\n\n\nAbstract\nI will present several natural functionals defined o n a conformal class of almost Hermitian metrics on a compact manifold\, an d I will establish their Euler-Lagrange equations. I will show that the Ga uduchon metrics appear naturally as the unique extremal metrics of one suc h functional. Next\, a new class of metrics will be introduced\, also appe aring as extremal in complex dimension two. I will show that these new met rics\, while not Gauduchon in general\, give again unique representatives\ , up to constant multiples\, of conformal classes of almost Hermitian metr ics. This is joint work with D. Angella\, A. Otiman and N. Tardini.\n LOCATION:https://researchseminars.org/talk/DGSTO/17/ END:VEVENT BEGIN:VEVENT SUMMARY:Viviana del Barco (Universidade Estadual de Campinas) DTSTART:20210623T150000Z DTEND:20210623T160000Z DTSTAMP:20260422T225722Z UID:DGSTO/18 DESCRIPTION:Title: ( Purely) coclosed G$_2$-structures on 2-step nilmanifolds\nby Viviana d el Barco (Universidade Estadual de Campinas) as part of Differential Geome try Seminar Torino\n\n\nAbstract\nIn Riemannian geometry\, simply connecte d nilpotent Lie groups endowed with left-invariant metrics\, and their com pact quotients\, have been the source of valuable examples in the field. T his motivated several authors to study\, in particular\, left-invariant G$ _2$-structures on 7-dimensional nilpotent Lie groups. These structures cou ld also be induced to the associated compact quotients\, also known as nil manifolds.\n\nLeft-invariant torsion free G$_2$-structures\, that is\, def ined by a simultaneously closed and coclosed positive $3$-form\, do not ex ist on nilpotent Lie groups. But relaxations of this condition have been t he subject of study on nilmanifolds lately. One of them are coclosed G$_2$ -structures\, for which the defining $3$-form verifies $\\mathrm{d} \\star _{g_\\varphi}\\varphi=0$\, and more specifically\, purely coclosed structu res\, which are defined as those which are coclosed and satisfy $\\varphi\ \wedge \\mathrm{d} \\varphi=0$. \n\nIn this talk\, there will be presented recent classification results regarding left-invariant coclosed and purel y coclosed G$_2$-structures on 2-step nilpotent Lie groups. \n\nOur result s are twofold. On the one hand we give the isomorphism classes of 2-step n ilpotent Lie algebras admitting purely coclosed G$_2$-structures. The anal ogous result for coclosed structures was obtained by Bagaglini\, Fernánde z and Fino [Forum Math. 2018]. \n\nOn the other hand\, we focus on the que stion of which metrics on these Lie algebras can be induced by a coclosed or purely coclosed structure. We show that any left-invariant metric is in duced by a coclosed structure\, whereas every Lie algebra admitting purely coclosed structures admits metrics which are not induced by any such a st ructure. In the way of proving these results we obtain a method to constru ct purely coclosed G$_2$-structures. As a consequence\, we obtain new exam ples of compact nilmanifolds carrying purely coclosed G$_2$-structures. \n \nThis is joint work with Andrei Moroianu and Alberto Raffero.\n LOCATION:https://researchseminars.org/talk/DGSTO/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Joseph Cho (TU Wien) DTSTART:20211012T150000Z DTEND:20211012T160000Z DTSTAMP:20260422T225722Z UID:DGSTO/19 DESCRIPTION:Title: M onodromy of discrete Darboux transformations\nby Joseph Cho (TU Wien) as part of Differential Geometry Seminar Torino\n\n\nAbstract\nThe monodro my of Darboux transformations of smooth isothermic surfaces can be simplif ied via the gauge theoretic approach. In pursuit of the discrete analogue\ , we consider the discrete curve case. In particular\, using a quaternioni c approach\, we not only solve the monodromy of discrete Darboux transform ations\, but also obtain explicit parametrisations for closed discrete Dar boux transformations of a discrete circle.\n LOCATION:https://researchseminars.org/talk/DGSTO/19/ END:VEVENT BEGIN:VEVENT SUMMARY:Romina Arroyo (Universidad Nacional de Córdoba) DTSTART:20211102T160000Z DTEND:20211102T170000Z DTSTAMP:20260422T225722Z UID:DGSTO/20 DESCRIPTION:Title: O n the signature of the Ricci curvature on nilmanifolds\nby Romina Arro yo (Universidad Nacional de Córdoba) as part of Differential Geometry Sem inar Torino\n\n\nAbstract\nIn this talk I will present a joint work with R amiro Lafuente (The University of Queensland) in which we completely descr ibe all possible signatures for the Ricci curvature of left-invariant metr ics on nilmanifolds. To do that\, we use ideas from GIT to construct a met ric whose Ricci curvature has a signature with as many zeros as possible\, and then we apply an Implicit Function Theorem argument.\n LOCATION:https://researchseminars.org/talk/DGSTO/20/ END:VEVENT BEGIN:VEVENT SUMMARY:Katrin Leschke (University of Leicester) DTSTART:20211109T150000Z DTEND:20211109T160000Z DTSTAMP:20260422T225722Z UID:DGSTO/21 DESCRIPTION:Title: L inks between the integrable systems of a CMC surface\nby Katrin Leschk e (University of Leicester) as part of Differential Geometry Seminar Torin o\n\n\nAbstract\nA CMC surface in 3-space is constrained Willmore and isot hermic. It is well known that these 3 surface classes are each determined by a family of flat connections. In this talk we discuss links between the corresponding families of flat connections: we show that parallel section s of the associated family of flat connections of the harmonic Gauss map g ive algebraically the parallel sections of the other families. In particul ar\, we obtain links between transformations of CMC surfaces\, isothermic surfaces and constrained Willmore surfaces which are given by parallel sec tions\, such as the associated family\, the simple factor dressing and the Darboux transformation.\n LOCATION:https://researchseminars.org/talk/DGSTO/21/ END:VEVENT BEGIN:VEVENT SUMMARY:Marcin Sroka (Jagiellonian University) DTSTART:20211130T150000Z DTEND:20211130T160000Z DTSTAMP:20260422T225722Z UID:DGSTO/22 DESCRIPTION:Title: T he conjecture of Alesker and Verbitsky under hyperKähler assumption.\ nby Marcin Sroka (Jagiellonian University) as part of Differential Geometr y Seminar Torino\n\n\nAbstract\nI will discuss the advances towards provin g the so called\nquaternionic Calabi conjecture. I will focus on the recen t result in this\ndirection due to Dinew and myself. I will include the di scussion on the\nMonge-Ampère type equations in quaternionic geometry fro m the unifying\nperspective (in the spirit of Harvey-Lawson).\n LOCATION:https://researchseminars.org/talk/DGSTO/22/ END:VEVENT BEGIN:VEVENT SUMMARY:Alex Mramor (John Hopkins University) DTSTART:20211207T150000Z DTEND:20211207T160000Z DTSTAMP:20260422T225722Z UID:DGSTO/23 DESCRIPTION:Title: S ome new applications of the mean curvature flow to self shrinkers\nby Alex Mramor (John Hopkins University) as part of Differential Geometry Sem inar Torino\n\n\nAbstract\nThe mean curvature flow\, where one deforms a s ubmanifold by its mean curvature vector\, is known to in many cases develo p singularities. These are points where the curvature along the flow blows up\, or in some sense where the submanifold pinches. This makes the study of singularities vital to fully utilize the flow. Arguably the most basic local models for singularities are self shrinkers\, called such because t hey evolve by dilations. In this talk I’ll discuss some applications of the mean curvature flow to the study of self shrinkers in $\\mathbb{R}^{3} $ and $\\mathbb{R}^{4}$.\n LOCATION:https://researchseminars.org/talk/DGSTO/23/ END:VEVENT BEGIN:VEVENT SUMMARY:Pablo Mira (Universidad Politécnica de Cartagena) DTSTART:20220111T150000Z DTEND:20220111T160000Z DTSTAMP:20260422T225722Z UID:DGSTO/24 DESCRIPTION:Title: T he Bernstein problem for Weingarten surfaces\nby Pablo Mira (Universid ad Politécnica de Cartagena) as part of Differential Geometry Seminar Tor ino\n\n\nAbstract\nA surface in Euclidean $3$-space is an elliptic Weingar ten surface if its principal curvatures are related by a smooth\, symmetri c\, elliptic equation $W(k_1\,k_2)=0$. A well known open problem\, propose d for instance by Rosenberg and Sa Earp in 1994\, is to solve the Bernstei n problem for this class of surfaces\, that is: are planes the only entire elliptic Weingarten graphs? Up to now\, it is only known that the answer is positive if the Weingarten equation is uniformly elliptic\, i.e.\, if t he derivatives of $W$ with respect to $k_1$ and $k_2$ lie between two posi tive constants (for example\, minimal or CMC surfaces are uniformly ellipt ic with this terminology). This result follows from a deep theorem by L. S imon on entire graphs with quasiconformal Gauss map. In this talk we pres ent two theorems. In the first one\, we extend the solution to the Bernste in problem in the uniformly elliptic case to multigraphs\, proving that pl anes are the only complete uniformly elliptic Weingarten surfaces whose Ga uss map image lies in an open hemisphere. In the second one\, we will solv e in the affirmative the Bernstein problem for Weingarten graphs for a lar ge class of non-uniformly elliptic Weingarten equations. This is a joint w ork with Isabel Fernández and José A. Gálvez.\n LOCATION:https://researchseminars.org/talk/DGSTO/24/ END:VEVENT BEGIN:VEVENT SUMMARY:Mario Schulz (Westfälische Wilhelms-Universität Münster) DTSTART:20220125T140000Z DTEND:20220125T150000Z DTSTAMP:20260422T225722Z UID:DGSTO/25 DESCRIPTION:Title: N oncompact self-shrinkers for mean curvature flow\nby Mario Schulz (Wes tfälische Wilhelms-Universität Münster) as part of Differential Geometr y Seminar Torino\n\n\nAbstract\nIn his lecture notes on mean curvature flo w\, Ilmanen conjectured the existence of noncompact self-shrinkers with ar bitrary genus. We employ min-max techniques to give a rigorous existence p roof for these surfaces. Conjecturally\, the self-shrinkers that we obtain have precisely one (asymptotically conical) end. We confirm this for larg e genus via a precise analysis of the limiting object of sequences of such self-shrinkers for which the genus tends to infinity.\n\nJoint work with Reto Buzano and Huy The Nguyen.\n LOCATION:https://researchseminars.org/talk/DGSTO/25/ END:VEVENT BEGIN:VEVENT SUMMARY:Miguel Domínguez-Vázquez (University of Santiago de Compostela) DTSTART:20220208T150000Z DTEND:20220208T160000Z DTSTAMP:20260422T225722Z UID:DGSTO/26 DESCRIPTION:Title: I nhomogeneous isoparametric hypersurfaces in symmetric spaces of noncompact type\nby Miguel Domínguez-Vázquez (University of Santiago de Compos tela) as part of Differential Geometry Seminar Torino\n\n\nAbstract\nA hyp ersurface of a Riemannian manifold is called isoparametric if its nearby p arallel hypersurfaces have constant mean curvature. Homogeneous hypersurfa ces\, that is\, codimension one orbits of isometric actions\, constitute a fundamental class of examples. The problem of determining which spaces w ith a large isometry group admit inhomogeneous isoparametric hypersurfaces has a long history that traces back to Élie Cartan.\n\nIn this talk\, I will report on a joint work with Víctor Sanmartín-López where we constr uct the first examples of inhomogeneous isoparametric hypersurfaces in eve ry symmetric space of noncompact type and rank at least three.\n LOCATION:https://researchseminars.org/talk/DGSTO/26/ END:VEVENT BEGIN:VEVENT SUMMARY:Xi Sisi Shen (Columbia University) DTSTART:20220222T150000Z DTEND:20220222T160000Z DTSTAMP:20260422T225722Z UID:DGSTO/27 DESCRIPTION:Title: M etrics of constant Chern scalar curvature and a Chern-Calabi flow\nby Xi Sisi Shen (Columbia University) as part of Differential Geometry Semina r Torino\n\n\nAbstract\nWe discuss the existence problem of constant Chern scalar curvature metrics on a compact complex manifold. We prove a priori estimates for these metrics conditional on an upper bound on the entropy\ , extending a recent result by Chen-Cheng in the Kähler setting. In addit ion\, we show how these estimates can be used to prove a convergence resul t for a Hermitian analogue of the Calabi flow on compact complex manifolds with vanishing first Bott-Chern class.\n LOCATION:https://researchseminars.org/talk/DGSTO/27/ END:VEVENT BEGIN:VEVENT SUMMARY:Mattia Fogagnolo (Centro De Giorgi - SNS) DTSTART:20220322T150000Z DTEND:20220322T160000Z DTSTAMP:20260422T225722Z UID:DGSTO/28 DESCRIPTION:Title: N ew integral estimates in substatic manifolds and the Alexandrov Theorem\nby Mattia Fogagnolo (Centro De Giorgi - SNS) as part of Differential Ge ometry Seminar Torino\n\n\nAbstract\nThe classical Alexandrov Theorem in t he Euclidean space asserts that any bounded set with a smooth boundary of constant mean curvature is a ball.\nThis result can be more quantitatively expressed by showing that an integral deficit from being of constant mea n curvature dominates suitable analytic quantities that vanish exactly whe n the domain is a ball. In this talk\, we provide generalizations of this in the context of substatic manifolds with boundary\, that constitute a va st generalization of the family of manifolds with nonnegative Ricci curvat ure\, and that are of particular importance in General Relativity. Our app roach is based on the discovery of a vector field with nonnegative diverge nce involving the solution to a torsion-like boundary value problem introd uced by Li-Xia in a related earlier work.\nThe talk is based on a joint wo rk with A. Pinamonti (Trento).\n LOCATION:https://researchseminars.org/talk/DGSTO/28/ END:VEVENT BEGIN:VEVENT SUMMARY:Theodora Bourni (University of Tennessee Knoxville) DTSTART:20220405T140000Z DTEND:20220405T150000Z DTSTAMP:20260422T225722Z UID:DGSTO/30 DESCRIPTION:Title: C onvex ancient solutions to free boundary curve shortening flow\nby The odora Bourni (University of Tennessee Knoxville) as part of Differential G eometry Seminar Torino\n\n\nAbstract\nIn this talk we construct and classi fy convex ancient curve shortening flows in the disc with free boundary on the circle. This work is joint with Mat Langford.\n LOCATION:https://researchseminars.org/talk/DGSTO/30/ END:VEVENT BEGIN:VEVENT SUMMARY:James Stanfield (University of Queensland) DTSTART:20220419T080000Z DTEND:20220419T090000Z DTSTAMP:20260422T225722Z UID:DGSTO/32 DESCRIPTION:Title: C ompact Gauduchon-Flat Hermitian manifolds\nby James Stanfield (Univers ity of Queensland) as part of Differential Geometry Seminar Torino\n\n\nAb stract\nOn a non-Kähler Hermitian manifold\, the complex structure is not parallel with respect to the Levi-Civita connection. Instead\, it is natu ral to consider non-symmetric connections compatible with both metric and complex structures. In the 90's\, Gauduchon identified a canonical one-par ameter family of such Hermitian connections which includes the Chern and B ismut connections. In this talk we will discuss some recent progress in un derstanding the geometry of these so-called Gauduchon connections\, detail ing a proof of a conjecture of Yang and Zheng. Namely that other than the Chern or Bismut cases\, compact Hermitian manifolds with flat Gauduchon co nnections are Kähler.\n LOCATION:https://researchseminars.org/talk/DGSTO/32/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexey Bolsinov (Loughborough University) DTSTART:20220531T140000Z DTEND:20220531T150000Z DTSTAMP:20260422T225722Z UID:DGSTO/33 DESCRIPTION:Title: O n integrability of geodesic flows on 3-dimensional manifolds\nby Alexe y Bolsinov (Loughborough University) as part of Differential Geometry Semi nar Torino\n\n\nAbstract\nThe goal of the talk is to discuss the behaviour of geodesics on 3-manifolds $M$ with $SL(2\,\\mathbb R)$ geometry\, one of the eight natural geometries according to Thurston\, appearing on three -dimensional manifolds. It has been known that the corresponding geodesi c flows cannot be integrable\, however\, this particular case has not been studied in detail. The situation turned out quite interesting: we have observed (joint work with Alexander Veselov and Yiru Ye) that the phase space $T^*M$ contains to two open domains\, complementary to each other an d having common boundary\, with integrable and chaotic behaviour of geode sics. In the integrable domain\, we have integrability in the class of re al-analytic integrals\, whereas in the chaotic domain the geodesic flow h as positive topological entropy. As a specific example\, we study in more detail the geodesic flow on the modular 3-manifold $M=SL(2\,\\R)/ SL(2\, \\mathbb Z)$ homeomorphic to the complement of a trefoil knot $\\mathcal K $ in 3-sphere.\n\nI will try to talk about these results in the context of a more general problem on topological obstructions to integrability of ge odesic flows on smooth manifolds following papers by V. V. Kozlov\, I. A. Taimanov and L. Butler.\n LOCATION:https://researchseminars.org/talk/DGSTO/33/ END:VEVENT BEGIN:VEVENT SUMMARY:Marco Pozzetta (Università di Napoli) DTSTART:20220503T140000Z DTEND:20220503T150000Z DTSTAMP:20260422T225722Z UID:DGSTO/34 DESCRIPTION:by Marco Pozzetta (Università di Napoli) as part of Different ial Geometry Seminar Torino\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/DGSTO/34/ END:VEVENT BEGIN:VEVENT SUMMARY:Thomas Ivey DTSTART:20221012T120000Z DTEND:20221012T130000Z DTSTAMP:20260422T225722Z UID:DGSTO/35 DESCRIPTION:Title: C onstructing Solitons for an Isometric Flow on G_2 Structures\nby Thom as Ivey as part of Differential Geometry Seminar Torino\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/DGSTO/35/ END:VEVENT BEGIN:VEVENT SUMMARY:Fernanda Roing DTSTART:20221018T140000Z DTEND:20221018T150000Z DTSTAMP:20260422T225722Z UID:DGSTO/36 DESCRIPTION:Title: M ean curvature flow of graphs in generalized Robertson–Walker spacetimes with perpendicular Neumann boundary condition\nby Fernanda Roing as pa rt of Differential Geometry Seminar Torino\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/DGSTO/36/ END:VEVENT BEGIN:VEVENT SUMMARY:Vladimir Slesar (University Politehnica of Bucarest) DTSTART:20221122T133000Z DTEND:20221122T143000Z DTSTAMP:20260422T225722Z UID:DGSTO/37 DESCRIPTION:Title: V aisman manifolds\, transverse Kähler-Ricci flow and Einstein-Weyl structu res\nby Vladimir Slesar (University Politehnica of Bucarest) as part o f Differential Geometry Seminar Torino\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/DGSTO/37/ END:VEVENT BEGIN:VEVENT SUMMARY:Giuseppe Pipoli (Università degli Studi dell'Aquila) DTSTART:20221213T133000Z DTEND:20221213T143000Z DTSTAMP:20260422T225722Z UID:DGSTO/38 DESCRIPTION:by Giuseppe Pipoli (Università degli Studi dell'Aquila) as pa rt of Differential Geometry Seminar Torino\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/DGSTO/38/ END:VEVENT BEGIN:VEVENT SUMMARY:Fridrich Valach DTSTART:20230207T133000Z DTEND:20230207T143000Z DTSTAMP:20260422T225722Z UID:DGSTO/39 DESCRIPTION:Title: C ourant algebroids and supergravity\nby Fridrich Valach as part of Diff erential Geometry Seminar Torino\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/DGSTO/39/ END:VEVENT BEGIN:VEVENT SUMMARY:Alvaro Pampano DTSTART:20230210T133000Z DTEND:20230210T143000Z DTSTAMP:20260422T225722Z UID:DGSTO/40 DESCRIPTION:Title: E xistence and Properties of Closed Free p-Elastic Curves\nby Alvaro Pam pano as part of Differential Geometry Seminar Torino\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/DGSTO/40/ END:VEVENT BEGIN:VEVENT SUMMARY:Semyon Alesker DTSTART:20230314T133000Z DTEND:20230314T143000Z DTSTAMP:20260422T225722Z UID:DGSTO/41 DESCRIPTION:Title: O ctonionic Calabi-Yau theorem\nby Semyon Alesker as part of Differentia l Geometry Seminar Torino\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/DGSTO/41/ END:VEVENT BEGIN:VEVENT SUMMARY:Allan Freitas (Universidade Federal de Paraíba) DTSTART:20230328T123000Z DTEND:20230328T133000Z DTSTAMP:20260422T225722Z UID:DGSTO/42 DESCRIPTION:Title: I ntegral identities and rigidity problems for Riemannian manifolds\nby Allan Freitas (Universidade Federal de Paraíba) as part of Differential G eometry Seminar Torino\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/DGSTO/42/ END:VEVENT BEGIN:VEVENT SUMMARY:Alejandro Gil-Garcia (Universität Hamburg) DTSTART:20230517T090000Z DTEND:20230517T100000Z DTSTAMP:20260422T225722Z UID:DGSTO/43 DESCRIPTION:by Alejandro Gil-Garcia (Universität Hamburg) as part of Diff erential Geometry Seminar Torino\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/DGSTO/43/ END:VEVENT END:VCALENDAR