BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Federico Caucci (Florence) DTSTART:20200617T130000Z DTEND:20200617T140000Z DTSTAMP:20260422T212708Z UID:GeoSem/1 DESCRIPTION:Title: D erived invariance and the Albanese morphism\nby Federico Caucci (Flore nce) as part of Geometry Seminar - University of Florence\n\n\nAbstract\nI will give an overview on the derived invariance problem: how much of the geometry of a smooth complex projective variety is determined by its bound ed derived category? I will recall the main theorems and conjectures of th is area. Finally\, I will present the results of a joint work in progress with L. Lombardi and G. Pareschi\, involving the Albanese morphism.\n LOCATION:https://researchseminars.org/talk/GeoSem/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Marco Radeschi (University of Notre Dame) DTSTART:20200701T123000Z DTEND:20200701T133000Z DTSTAMP:20260422T212708Z UID:GeoSem/2 DESCRIPTION:Title: I nvariant Theory without groups\nby Marco Radeschi (University of Notre Dame) as part of Geometry Seminar - University of Florence\n\n\nAbstract\ nGiven an orthogonal representation of a Lie group G on a Euclidean vector space V\, Invariant Theory studies the algebra of G-invariant polynomials on V. This setting can be generalized by replacing the orbits of the repr esentation with a foliation by the fibers of a manifold submetry\nfrom the unit sphere S(V)\, and consider the algebra of polynomials that are const ant along these fibers (effectively producing an Invariant Theory\, but wi thout groups)\nIn this talk we will exhibit a surprisingly strong relation between the geometric information coming from the submetry and the algebr aic information coming from the corresponding algebra\, with several appli cations to classical Invariant Theory.\nThis talk is based on a joint work with Ricardo Mendes.\n LOCATION:https://researchseminars.org/talk/GeoSem/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Francesco Pediconi (Università di Firenze) DTSTART:20201015T123000Z DTEND:20201015T133000Z DTSTAMP:20260422T212708Z UID:GeoSem/3 DESCRIPTION:Title: O n cohomogeneity one Hermitian metrics\nby Francesco Pediconi (Universi tà di Firenze) as part of Geometry Seminar - University of Florence\n\nAb stract: TBA\n LOCATION:https://researchseminars.org/talk/GeoSem/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Romina Arroyo (Universidad Nacional de C\\'ordoba and CONICET) DTSTART:20201029T140000Z DTEND:20201029T150000Z DTSTAMP:20260422T212708Z UID:GeoSem/4 DESCRIPTION:Title: T he prescribed Ricci curvature problem for naturally reductive metrics on s imple Lie groups\nby Romina Arroyo (Universidad Nacional de C\\'ordoba and CONICET) as part of Geometry Seminar - University of Florence\n\n\nAb stract\nThe prescribed Ricci curvature problem consists in finding a Riema nnian metric $g$ and a real number $c>0$ satisfying\n\\[\n\\operatorname{R ic} (g) = c T\,\n\\]\nfor some fixed symmetric $(0\, 2)$-tensor field $T$ on a manifold $M\,$ where $\\operatorname{Ric} (g)$ denotes the Ricci curv ature of $g.$\n\nThe aim of this talk is to discuss this problem within th e class of left-invariant naturally reductive metrics when $M$ is a simple Lie group\, and present recently obtained results in this setting. \n\nTh is talk is based on joint works with Mark Gould (The University of Queensl and) Artem Pulemotov (The University of Queensland) and Wolfgang Ziller (U niversity of Pennsylvania).\n LOCATION:https://researchseminars.org/talk/GeoSem/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Sammy Sbiti (University of Pennsylvania) DTSTART:20201105T150000Z DTEND:20201105T160000Z DTSTAMP:20260422T212708Z UID:GeoSem/5 DESCRIPTION:Title: O n the Ricci flow of homogeneous metrics on spheres\nby Sammy Sbiti (Un iversity of Pennsylvania) as part of Geometry Seminar - University of Flor ence\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/GeoSem/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Daniele Angella (Università di Firenze) DTSTART:20201112T150000Z DTEND:20201112T160000Z DTSTAMP:20260422T212708Z UID:GeoSem/6 DESCRIPTION:Title: O n the Chern-Ricci flow on Inoue surfaces\nby Daniele Angella (Universi tà di Firenze) as part of Geometry Seminar - University of Florence\n\nAb stract: TBA\n LOCATION:https://researchseminars.org/talk/GeoSem/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Mario Garcia-Fernandez (Universidad Autónoma de Madrid) DTSTART:20201117T140000Z DTEND:20201117T150000Z DTSTAMP:20260422T212708Z UID:GeoSem/7 DESCRIPTION:Title: K ähler moduli spaces on non-Kähler Calabi-Yau manifolds\nby Mario Gar cia-Fernandez (Universidad Autónoma de Madrid) as part of Geometry Semina r - University of Florence\n\n\nAbstract\nModuli spaces of Calabi-Yau metr ics play a prominent role in geometry and mathematical physics. The intere st on these moduli spaces lies in their rich geometric structure\, related to mirror symmetry and enumerative geometry. In this talk I will explain how the Kähler metric on the “Kähler moduli space” of a Calabi-Yau m anifold can be obtained from symplectic reduction. I will then move on to show how a suitable choice of vector bundle allows us to extend this const ruction to non-Kähler Calabi-Yau manifolds\, by means of the Hull-Stromin ger moduli space. Based on joint work with Rubio (UAB) and Tipler (UBO) in arXiv:2004.11399\, and ongoing work with Raúl González Molina.\n LOCATION:https://researchseminars.org/talk/GeoSem/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Mehdi Lejmi (Bronx Community College of City University of New Yor k) DTSTART:20201126T150000Z DTEND:20201126T160000Z DTSTAMP:20260422T212708Z UID:GeoSem/8 DESCRIPTION:Title: C onformally Kähler Einstein-Maxwell metrics on blow-ups\nby Mehdi Lejm i (Bronx Community College of City University of New York) as part of Geom etry Seminar - University of Florence\n\n\nAbstract\nConformally Kähler H ermitian metrics of constant Riemannian scalar curvature and J-invariant R icci are called conformally Kähler Einstein Maxwell metrics. In this talk \, we discuss deformations and possible construction of such metrics on bl ow-ups. This is a joint work in progress with Abdellah Lahdili.\n LOCATION:https://researchseminars.org/talk/GeoSem/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Francesco Bei (Università di Roma La Sapienza) DTSTART:20201210T133000Z DTEND:20201210T143000Z DTSTAMP:20260422T212708Z UID:GeoSem/9 DESCRIPTION:Title: O n the spectral theory and analytic K-homology of complex spaces\nby Fr ancesco Bei (Università di Roma La Sapienza) as part of Geometry Seminar - University of Florence\n\n\nAbstract\nLet $(X\, h)$ be a compact and irr educible Hermitian complex space. In the last\nthirty years\, motivated am ong other things by the Cheeger-Goresky-MacPherson\nconjecture and the Rie mann-Roch theorem of Baum-Fulton-MacPherson\, the $L^2$-\ntheory of the Ho dge-de Rham operator $d + d^t$\, the Hodge-Dolbeault operator $\\overline\ \partial + \\overline\\partial^t$ and the associated Laplacians on $(X\, h )$ has been the subject of many investigations. In the first part of this talk we will report about some recent results concerning the existence of self-adjoint extensions of the Hodge-\nKodaira Laplacian with entirely dis crete spectrum. Then in the second part we will describe some applications to the K-homology of X. In particular assuming $\\dim(sing(X)) = 0$ we wi ll show how the operator $\\overline\\partial+\\overline\\partial^t$ induc es an analytic K-homology class in $K^{an}_{0}(X)$ and we will give a geom etric interpretation of this class in terms of a resolution of $X$.\n LOCATION:https://researchseminars.org/talk/GeoSem/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Giorgio Ottaviani (Università di Firenze) DTSTART:20201112T140000Z DTEND:20201112T150000Z DTSTAMP:20260422T212708Z UID:GeoSem/10 DESCRIPTION:Title: Singular t-ples of tensors and their geometry\nby Giorgio Ottaviani (U niversità di Firenze) as part of Geometry Seminar - University of Florenc e\n\n\nAbstract\nThere is a natural invariant metric on the space of tenso rs\, called Frobenius metric. In optimization setting one considers the (c omplex) critical points on the Segre variety of the distance function from a given tensor\, they are called singular t-ples\, among them there is th e best rank one approximation. Their number is the EDdegree of the Segre v ariety. The geometry of the critical points is appealing\, since they lie in a linear space called critical space\, which has dimension smaller than the number of critical points\, in other words the critical points are li nearly dependent\, unless the matrix case. We expose some properties of si ngular t-ples. In a following talk Emanuele Ventura will lecture about the asymptotic behaviour of EDdegree and other more advanced properties.\n\nA pplied Algebraic Geometry 2020-2021:\nhttp://web.math.unifi.it/gruppi/alge braic-geometry/AppliedAlgebraicGeometry20202021.html\n LOCATION:https://researchseminars.org/talk/GeoSem/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Giovanni Bazzoni (Università dell'Insubria) DTSTART:20201203T133000Z DTEND:20201203T143000Z DTSTAMP:20260422T212708Z UID:GeoSem/11 DESCRIPTION:Title: Homotopy Invariants and almost non-negative curvature\nby Giovanni Baz zoni (Università dell'Insubria) as part of Geometry Seminar - University of Florence\n\n\nAbstract\nAlmost non-negative sectional curvature (ANSC) is a curvature condition on a Riemannian manifold\, which encompasses both the almost flat and the non-negatively curved case. It was shown in a rem arkable paper by Kapovitch\, Petrunin and Tuschmann that\, modulo some tec hnical details\, a compact ANSC manifold is a fiber bundle over a nilmanif old\, and that the fiber satisfies a curvature condition only slightly mor e general than ANSC. In this talk\, based on joint work with G. Lupton and J. Oprea\, we will discuss such manifolds from the point of view of Ratio nal Homotopy Theory\, presenting various invariants of bundles of such typ e\, and proving a (rational) Bochner-type theorem.\n LOCATION:https://researchseminars.org/talk/GeoSem/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Francesco Pediconi (Università di Firenze) DTSTART:20210114T133000Z DTEND:20210114T143000Z DTSTAMP:20260422T212708Z UID:GeoSem/12 DESCRIPTION:Title: Hermitian curvature flow on locally homogeneous complex surfaces\nby F rancesco Pediconi (Università di Firenze) as part of Geometry Seminar - U niversity of Florence\n\n\nAbstract\nThe Hermitian curvature flow ("HCF" s hortly) is a strictly\nparabolic flow of Hermitian metrics\, introduced by Streets and Tian\,\nwhich evolves an initial Hermitian metric in the dire ction of its\nsecond Chern-Ricci curvature tensor with some first-order te rms in the\ntorsion. In this talk\, we study the long-time behavior of loc ally\nhomogeneous non-Kähler solutions to the HCF on compact complex\nsu rfaces and\, after a suitable normalization\, we compute the\nGromov-Hausd orff limit of those which are immortal. This is a joint\nwork with Mattia Pujia.\n\nSeminario PRIN2017 "Real and Complex Manifolds: Topology\, Geome try and Holomorphic Dynamics"\n LOCATION:https://researchseminars.org/talk/GeoSem/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Antonella Nannicini (Università di Firenze) DTSTART:20210128T133000Z DTEND:20210128T143000Z DTSTAMP:20260422T212708Z UID:GeoSem/13 DESCRIPTION:Title: Almost complex setting for Kodaira dimension\nby Antonella Nannicini ( Università di Firenze) as part of Geometry Seminar - University of Floren ce\n\n\nAbstract\nThe concept of Kodaira dimension has been recently exten ded from complex to almost complex\ncontext by H. Chen and W. Zhang. In th is talk\, first we describe similarities and differences between Kodaira d imension for complex and almost complex manifolds\, then we focus on compa ct 4-dimensional solvmanifolds without any integrable almost complex struc ture. We present recent results for Kodaira dimension of certain families of almost complex structures\, providing a twistorial description. Also we describe some aspects of the correspondence between Kodaira dimension and curvature. Results are based on joint works with A. Tomassini and A. Catt aneo.\n LOCATION:https://researchseminars.org/talk/GeoSem/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Lucas Kaufmann Sacchetto (National University of Singapore) DTSTART:20210204T133000Z DTEND:20210204T143000Z DTSTAMP:20260422T212708Z UID:GeoSem/14 DESCRIPTION:Title: Currents\, their intersection and applications\nby Lucas Kaufmann Sacc hetto (National University of Singapore) as part of Geometry Seminar - Uni versity of Florence\n\n\nAbstract\nPositive closed currents are central ob jects in pluripotential theory and modern complex analysis. They generaliz e both smooth differential forms and subvarieties. Given two currents it is of central importance to understand when a meaningful notion of interse ction (or wedge product) between them can be given. This is useful for ins tance in producing invariant measures for dynamical systems and in the stu dy of the complex Monge-Ampère equation with singular data.\n\nIn this ta lk I aim to overview some basic facts about currents in complex analysis ( including their definition) and recent approaches to their intersection th eory. I'll also mention some applications to geometry and to the dynamics of maps and foliations.\n LOCATION:https://researchseminars.org/talk/GeoSem/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Fabio Tonini (Università di Firenze) DTSTART:20210304T133000Z DTEND:20210304T143000Z DTSTAMP:20260422T212708Z UID:GeoSem/15 DESCRIPTION:Title: Fundamental groups in algebraic geometry\nby Fabio Tonini (Università di Firenze) as part of Geometry Seminar - University of Florence\n\n\nAbs tract\nI plan to introduce and discuss several notions of fundamental grou p in the context of algebraic geometry\, for example the Grothendieck-éta le fundamental group and the Nori fundamental group scheme\, following the parallel with the classical topological fundamental group and the theory of topological (Galois) coverings.\n LOCATION:https://researchseminars.org/talk/GeoSem/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Scott Wilson (Queens College and CUNY) DTSTART:20210414T133000Z DTEND:20210414T143000Z DTSTAMP:20260422T212708Z UID:GeoSem/16 DESCRIPTION:Title: Small Nijenhuis tensors on compact almost complex manifolds with no comple x structure\nby Scott Wilson (Queens College and CUNY) as part of Geom etry Seminar - University of Florence\n\n\nAbstract\nI will present severa l examples of compact almost complex manifolds with a $1$-parameter family of almost complex structures having arbitrarily small Nijenhuis tensors i n the $C^0$-norm. The $4$-dimensional examples possess no complex structur e\, while the $6$-dimensional examples do not possess left invariant compl ex structures\, and whether they possess complex structures appears to be unknown. This is joint work with Luis Fernandez and Tobias Shin.\n LOCATION:https://researchseminars.org/talk/GeoSem/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Ramiro Lafuente (The University of Queensland) DTSTART:20210211T080000Z DTEND:20210211T090000Z DTSTAMP:20260422T212708Z UID:GeoSem/17 DESCRIPTION:Title: On the signature of the Ricci curvature on nilmanifolds\nby Ramiro Laf uente (The University of Queensland) as part of Geometry Seminar - Univers ity of Florence\n\n\nAbstract\nIn this talk we will explain the solution t o the following problem: Given an arbitrary nilpotent Lie group\, determi ne all possible signatures of the Ricci curvature of left invariant metric s on it. The solution involves constructing invariant metrics with many ze ros in their Ricci curvature\, for which we use ideas from GIT\, and then an Implicit function theorem argument.\n LOCATION:https://researchseminars.org/talk/GeoSem/17/ END:VEVENT BEGIN:VEVENT SUMMARY:Uwe Semmelmann (Universität Stuttgart) DTSTART:20210225T133000Z DTEND:20210225T143000Z DTSTAMP:20260422T212708Z UID:GeoSem/18 DESCRIPTION:Title: Stability of Einstein metrics\nby Uwe Semmelmann (Universität Stuttga rt) as part of Geometry Seminar - University of Florence\n\n\nAbstract\nEi nstein metrics can be characterised as critical points of\nthe (normalised ) total scalar curvature functional. They are always\nsaddle points. Howev er\, there are Einstein metrics which are local\nmaxima of the functional restricted to metrics of fixed\nvolume and constant scalar curvature. Thes e are by definition stable\nEinstein metrics. Stability can equivalently b e characterised by\na spectral condition for the Lichnerowicz Laplacian on divergence- and\ntrace-free symmetric 2-tensors\, i.e. on so-called tt-te nsors:\nan Einstein metric is stable if twice the Einstein constant is a l ower\nbound for this operator. Stability is also related to Perelman's\n\\ nu entropy and dynamical stability with respect to the Ricci flow.\n\nIn m y talk I will discuss the stability condition. I will present a\nrecent re sult obtained with G. Weingart\, which completes the work\nof Koiso on the classification of stable compact symmetric spaces.\nMoreover\, I will des cribe an interesting relation between instability\nand the existence of ha rmonic forms. This is done in the case of nearly\nKähler\, Einstein-Sasa ki and nearly G_2 manifolds. If\ntime permits I will also explain the inst ability of the Berger space\nSO(5)/SO(3)\, which is a homology sphere. In this case\ninstability surprisingly is related to the existence of Killing tensors.\nThe latter results are contained in joint work with\nM. Wang an d C. Wang.\n LOCATION:https://researchseminars.org/talk/GeoSem/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Chengjian Yao (ShanghaiTech University) DTSTART:20210311T130000Z DTEND:20210311T140000Z DTSTAMP:20260422T212708Z UID:GeoSem/19 DESCRIPTION:Title: Einstein-Bogomol’nyi equation and Gravitating Vortex equations on Rieman n surfaces\nby Chengjian Yao (ShanghaiTech University) as part of Geom etry Seminar - University of Florence\n\n\nAbstract\nThe Einstein’s Fiel ds Equation coupled with an Abelian gauge field and a Higgs field possesse s a special type of solution\, mathematically known as Einstein-Bogomol’ nyi equation and physically known as Cosmic Strings. In this talk\, I will present some existence theorems for such equation and also its close comp anion Gravitating Cortex equations\, introduced from a moment map picture. This is based on the joint work with Garcia-Fernandez and Pingali.\n LOCATION:https://researchseminars.org/talk/GeoSem/19/ END:VEVENT BEGIN:VEVENT SUMMARY:Jorge Lauret (Universidad Nacional de Córdoba) DTSTART:20210408T123000Z DTEND:20210408T133000Z DTSTAMP:20260422T212708Z UID:GeoSem/20 DESCRIPTION:Title: On the stability of compact homogeneous Einstein manifolds\nby Jorge L auret (Universidad Nacional de Córdoba) as part of Geometry Seminar - Uni versity of Florence\n\n\nAbstract\nAfter some quick preliminaries on the g eneral stability theory of compact Einstein manifolds\, we will focus on t he homogeneous case and give a formula for the Lichnerowicz Laplacian of a G-invariant metric on a compact homogeneous space M=G/K\, restricted to t he subspace of G-invariant TT-tensors\, which was obtained via the moving bracket approach. \n\nAs an application\, we study the stability type of G-invariant Einstein metrics on M\, which are known to be the critical poi nts of the scalar curvature restricted to unit volume G-invariant metrics. The naturally reductive case presents some advantages. \n\nThis is joi nt work with Cynthia Will and Emilio Lauret.\n LOCATION:https://researchseminars.org/talk/GeoSem/20/ END:VEVENT BEGIN:VEVENT SUMMARY:Caterina Stoppato (Università di Firenze) DTSTART:20210325T133000Z DTEND:20210325T143000Z DTSTAMP:20260422T212708Z UID:GeoSem/21 DESCRIPTION:Title: Dual quaternions and slice functions: theory and applications\nby Cate rina Stoppato (Università di Firenze) as part of Geometry Seminar - Unive rsity of Florence\n\n\nAbstract\nThe talk will present some recent results in the theory of slice functions\nover alternative *-algebras\, introduce d by Ghiloni and Perotti in 2011 as\na generalization of the theory of qua ternionic slice regular functions\nlaunched by Gentili and Struppa in 2006 .\nThe talk will focus on the algebra of dual quaternions. For this algebr a\,\nan explicit classification of zero divisors is available. This makes it\npossible to study the zero sets of slice functions\, slice regular fun ctions\nand polynomials over this algebra in full detail.\nThis study can be applied to the open problem of factorizing motion\npolynomials over dua l quaternions. The polynomials in this class\,\nintroduced by Hegedüs\, S chicho\, and Schröcker in 2013\, correspond to\nrational rigid body motio ns in the Euclidean 3-space. Their factorizations\ncorrespond to linkages producing the same motions\, so their\nclassification is relevant to mecha nism science.\nThe main results presented have been proven jointly with Gr aziano\nGentili and Tomaso Trinci.\n LOCATION:https://researchseminars.org/talk/GeoSem/21/ END:VEVENT BEGIN:VEVENT SUMMARY:Xuemiao Chen DTSTART:20210422T123000Z DTEND:20210422T133000Z DTSTAMP:20260422T212708Z UID:GeoSem/22 DESCRIPTION:Title: Singularities of Hermitian-Yang-Mills connections\nby Xuemiao Chen as part of Geometry Seminar - University of Florence\n\n\nAbstract\nAfter int roducing some background about stable bundles and HYM connections\, I will explain both the analytic and algebraic sides when studying singularities of HYM connections. \n\nIt turns out that local algebraic invariants can be extracted to characterize the analytic side. In particular\, the analyt ic tangent cone is an algebraic invariant. (Based on joint works with Song Sun.)\n LOCATION:https://researchseminars.org/talk/GeoSem/22/ END:VEVENT BEGIN:VEVENT SUMMARY:Filippo Fagioli (Università di Roma La Sapienza) DTSTART:20210506T123000Z DTEND:20210506T133000Z DTSTAMP:20260422T212708Z UID:GeoSem/23 DESCRIPTION:Title: Pointwise push-forward formulae for flag bundles and their applications in positivity\nby Filippo Fagioli (Università di Roma La Sapienza) as p art of Geometry Seminar - University of Florence\n\n\nAbstract\nIn this ta lk\, after recalling some basics on flag bundles associated to holomorphic vector bundles\, I present a result that provides the pointwise\, Hermiti an version of a universal push-forward formula for flag bundles valid in c ohomology. As an application\, I explain how to use the above result to ob tain the positivity of several polynomials in the Chern forms of a Griffit hs positive vector bundle. This gives a partial confirmation of a conjectu re proposed by Griffiths in the late sixties\, which has raised interest i n the past as well as in recent years. This talk is based on a joint work with S. Diverio.\n LOCATION:https://researchseminars.org/talk/GeoSem/23/ END:VEVENT BEGIN:VEVENT SUMMARY:Francesca Salvatore (Università di Torino) DTSTART:20210513T123000Z DTEND:20210513T133000Z DTSTAMP:20260422T212708Z UID:GeoSem/24 DESCRIPTION:Title: Closed G2-structures on unimodular with non-trivial center Lie groups\ nby Francesca Salvatore (Università di Torino) as part of Geometry Semina r - University of Florence\n\n\nAbstract\nClosed $G_2$-structures arise as a natural generalization of torsion-free $G_2$-structures on seven-dimens ional smooth manifolds. In this talk\, I shall focus on Lie groups with no n-trivial\n\ncenter endowed with a left-invariant closed $G_2$-structure. After highlighting the relation\nwith six-dimensional geometry\, I shall p resent a classification result in the unimodular case\nas well as new comp act examples. Results about Laplacian solitons\, which correspond to\nself -similar solutions of the $G_2$-Laplacian flow introduced by Bryant\, are also included. This is joint work with A. Fino and A. Raffero.\n LOCATION:https://researchseminars.org/talk/GeoSem/24/ END:VEVENT BEGIN:VEVENT SUMMARY:Jonas Stelzig DTSTART:20211012T123000Z DTEND:20211012T133000Z DTSTAMP:20260422T212708Z UID:GeoSem/25 DESCRIPTION:Title: Linear combinations of cohomological invariants of compact complex manifol ds\nby Jonas Stelzig as part of Geometry Seminar - University of Flore nce\n\n\nAbstract\nWe will give answers to the following three questions a bout\nthe set of all compact complex manifolds of a given dimension:\n\n\n (i) Which linear relations between Hodge\, Betti and Chern numbers are\nun iversally satisfied?\n\n(ii) Which linear combinations of Hodge\, Betti an d Chern numbers are\nbimeromorphism invariants?\n\n(iii) Which linear comb inations of Hodge\, Betti and Chern numbers are\ntopological invariants?\n \n\nWe also present a strategy to answer the analogous questions when aske d\nabout `all' cohomological invariants (including e.g. the dimensions of\ nhigher pages of the Frölicher spectral sequence or Bott Chern and Aeppli \ncohomology). We carry this out to obtain answers in low dimensions\, wit h\nanswers in any dimension being reduced to specific construction problem s.\n LOCATION:https://researchseminars.org/talk/GeoSem/25/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexandra Otiman DTSTART:20211019T123000Z DTEND:20211019T133000Z DTSTAMP:20260422T212708Z UID:GeoSem/26 DESCRIPTION:Title: New constructions in non-Kähler toric geometry\nby Alexandra Otiman a s part of Geometry Seminar - University of Florence\n\n\nAbstract\nKato ma nifolds are compact complex manifolds containing a \nglobal spherical shel l. Their modern study has been widely carried out \nin complex dimension 2 and originates in the seminal work of Inoue\, \nKato\, Nakamura and Hirze bruch.\nIn this talk I plan to describe a special class of Kato manifolds in \narbitrary complex dimension\, whose construction arises from toric \n geometry. Using the toric language\, I will present several of their \nana lytic and geometric properties\, including existence of special \ncomplex submanifolds and partial results on their Dolbeault \ncohomology. Moreover \, since they are compact complex manifolds of \nnon-Kahler type\, I will investigate what special Hermitian metrics \nthey support.\n LOCATION:https://researchseminars.org/talk/GeoSem/26/ END:VEVENT BEGIN:VEVENT SUMMARY:Gao Chen DTSTART:20211026T123000Z DTEND:20211026T133000Z DTSTAMP:20260422T212708Z UID:GeoSem/27 DESCRIPTION:Title: The J-equation and deformed Hermitian-Yang-Mills equation\nby Gao Chen as part of Geometry Seminar - University of Florence\n\n\nAbstract\nThe d eformed Hermitian-Yang-Mills (dHYM) equation is the mirror equation for th e special Lagrangian equation. The ”small radius limit” of the dHYM eq uation is the J-equation\, which is closely related to the constant scalar curvature Kaehler (cscK) metrics. In this talk\, I will explain my recent result that the solvability of the J-equation is equivalent to a notion o f stability. I will also explain my similar result on the supercritical dH YM equation as well as the application of my results to the cscK problem.\ n LOCATION:https://researchseminars.org/talk/GeoSem/27/ END:VEVENT BEGIN:VEVENT SUMMARY:Miron Stanciu DTSTART:20211109T133000Z DTEND:20211109T143000Z DTSTAMP:20260422T212708Z UID:GeoSem/28 DESCRIPTION:Title: Vaisman's theorem for lcK spaces with singularities\nby Miron Stanciu as part of Geometry Seminar - University of Florence\n\n\nAbstract\nVaisma n’s theorem for locally conformally K\\" ahler (lcK) compact manifolds s tates that any lcK metric on a compact complex manifold which admits a K\\ " ahler metric is\, in fact\, globally conformally K\\" ahler. In this tal k\, I will show the steps we used to extend this result to compact complex spaces with singularities. This is a joint work with Ovidiu Preda.\n LOCATION:https://researchseminars.org/talk/GeoSem/28/ END:VEVENT BEGIN:VEVENT SUMMARY:Ruobing Zhang DTSTART:20211116T133000Z DTEND:20211116T143000Z DTSTAMP:20260422T212708Z UID:GeoSem/29 DESCRIPTION:Title: Collapsing geometry of hyperkaehler four-manifolds\nby Ruobing Zhang a s part of Geometry Seminar - University of Florence\n\n\nAbstract\nThis ta lk focuses on the recent resolution of the following three well-known conj ectures in the study of Ricci-flat four manifolds (joint with Song Sun). \ n\n(1) Any volume collapsed limit of unit-diameter hyperkaehler metrics on the K3 manifold is isometric to one of the following: the quotient of a f lat 3-torus by an involution\, a singular special Kaehler metric on the 2- sphere\, or the unit interval. \n(2) Any complete non-compact hyperkaehler 4-manifold with quadratically integrable curvature must have one of the f ollowing asymptotic model geometries: ALE\, ALF\, ALG\, ALH\, ALG* and ALH *.\n(3) Any gravitational instanton is holomorphic to an open dense subset of some compact algebraic surface.\n\nWith the above classification resul ts\, we obtain a rather complete picture of the collapsing geometry of hyp erkaehler four manifolds.\n LOCATION:https://researchseminars.org/talk/GeoSem/29/ END:VEVENT BEGIN:VEVENT SUMMARY:Anusha Krishnan DTSTART:20211207T133000Z DTEND:20211207T143000Z DTSTAMP:20260422T212708Z UID:GeoSem/30 DESCRIPTION:Title: Positive sectional curvature and Ricci flow\nby Anusha Krishnan as par t of Geometry Seminar - University of Florence\n\n\nAbstract\nThe preserva tion of positive curvature conditions under the Ricci flow has been an imp ortant ingredient in applications of the flow to solving problems in geome try and topology. Works by Hamilton and others established that certain po sitive curvature conditions are preserved under the flow\, culminating in Wilking's unified\, Lie algebraic approach to proving invariance of positi ve curvature conditions. Yet\, some questions remain. In this talk\, we de scribe sec > 0 initial metrics on S^4\, where the condition of sec > 0 is not preserved under the Ricci flow. Previously\, examples of such behaviou r were known for sec \\geq 0\, and for sec > 0 in dimension 6 and above. T his is joint work with Renato Bettiol.\n LOCATION:https://researchseminars.org/talk/GeoSem/30/ END:VEVENT BEGIN:VEVENT SUMMARY:Lucía Martín Merchán DTSTART:20211123T133000Z DTEND:20211123T143000Z DTSTAMP:20260422T212708Z UID:GeoSem/31 DESCRIPTION:Title: A compact non-formal closed G_2 manifold with b_1=1\nby Lucía Martí n Merchán as part of Geometry Seminar - University of Florence\n\n\nAbstr act\nA G_2 structure on a 7-dimensional Riemannian manifold determined by a certain type of 3-form φ. These are classified into 16 types according to PDEs involving φ\; for instance\, the G_2 structure is torsion-free if φ is parallel\, closed if φ is closed and cocalibrated if φ is co-cl osed.\nThis talk contributes to understanding topological properties of co mpact manifolds with a closed G_2 structure that cannot be endowed with an y torsion-free G_2 structure. Namely\, we construct such a manifold that i s non-formal and has first Betti number b_1=1. The starting point is a nil manifold (M\,φ) with a closed G_2 structure that admits an involution pre serving φ such that the quotient M/Z_2 is a non-formal orbifold with b_1 =1. Then we perform a resolution of these singularities obtaining a manifo ld endowed with a closed G_2 structure\; we finally prove that the resolut ion verifies the same topological properties and do not admit any torsion- free G_2 structure.\n LOCATION:https://researchseminars.org/talk/GeoSem/31/ END:VEVENT BEGIN:VEVENT SUMMARY:Ioannis Chrysikos DTSTART:20211130T133000Z DTEND:20211130T143000Z DTSTAMP:20260422T212708Z UID:GeoSem/32 DESCRIPTION:Title: Almost hypercomplex/quaternionic skew-Hermitian structures\nby Ioannis Chrysikos as part of Geometry Seminar - University of Florence\n\n\nAbstr act\nThis talk provides a short introduction to the differential geometry of 4n-dimensional manifolds admitting \na SO*(2n)-structure\, or a SO*(2 n)Sp(1)-structure\, where SO*(2n) denotes the quaternionic real form of SO (2n\, C). \nSuch G-structures form the symplectic analog of the well-know n almost hypercomplex/quaternionic Hermitian structures\, and we call the m almost hypercomplex/quaternionic skew-Hermitian structures\, respective ly. \nWe describe the basic data encoding such geometric structures\, an d then we focus on their intrinsic torsion and related 1st-order integrabi lity conditions. Some examples and classification examples will be also di scusssed.\nThis talk is based on a joint work with J. Gregorovič (UHK) an d H. Winther (Masaryk).\n LOCATION:https://researchseminars.org/talk/GeoSem/32/ END:VEVENT BEGIN:VEVENT SUMMARY:Valerio Melani DTSTART:20211214T133000Z DTEND:20211214T143000Z DTSTAMP:20260422T212708Z UID:GeoSem/33 DESCRIPTION:Title: Weinstein's "Poisson category" in derived geometry\nby Valerio Melani as part of Geometry Seminar - University of Florence\n\n\nAbstract\nMotiva ted by deformation quantization\, Weinstein initiated the study of\nthe "P oisson category". This should be a category whose objects are\nPoisson man ifolds\, and whose morphisms are coisotropic correspondences.\nUnfortunate ly\, in the general case there is no such category. In fact\,\ncomposition of morphisms by fiber products is not always available\, and\none needs t o put strong enough "clean intersection" hypothesis to make\nit possible. In this talk\, we present a realization of the Poisson\ncategory in the co ntext of derived (algebraic) geometry\, which is a\nhomotopical generaliza tion of "classical" algebraic geometry. The talk\nwill be based on joint w ork(s) with Rune Haugseng and Pavel Safronov.\n LOCATION:https://researchseminars.org/talk/GeoSem/33/ END:VEVENT BEGIN:VEVENT SUMMARY:Xi Sisi Shen DTSTART:20220224T150000Z DTEND:20220224T160000Z DTSTAMP:20260422T212708Z UID:GeoSem/34 DESCRIPTION:Title: Metrics of constant Chern scalar curvature and a Chern-Calabi flow\nby Xi Sisi Shen as part of Geometry Seminar - University of Florence\n\n\nAb stract\nWe discuss the existence problem of constant Chern scalar curvatur e metrics on a compact complex manifold. We prove a priori estimates for t hese metrics conditional on an upper bound on the entropy\, extending a re cent result by Chen-Cheng in the Kähler setting. In addition\, we show ho w these estimates can be used to prove a convergence result for a Hermitia n analogue of the Calabi flow on compact complex manifolds with vanishing first Bott-Chern class.\n LOCATION:https://researchseminars.org/talk/GeoSem/34/ END:VEVENT BEGIN:VEVENT SUMMARY:Bertrand Toën DTSTART:20220303T133000Z DTEND:20220303T143000Z DTSTAMP:20260422T212708Z UID:GeoSem/35 DESCRIPTION:Title: Integrability of singular foliations\nby Bertrand Toën as part of Geo metry Seminar - University of Florence\n\n\nAbstract\nIn this talk\, I wil l introduce derived foliations (in the\nalgebraic and complex analytic set tings)\,\na general notion of foliations for which leaves are allowed to b e\nsingular subvarieties. I will explain how\nthese can be globally integr ated by contructing a monodromy and a\nholonomy groupoid. When the derived foliation\nis algebraic I'll explain how a Riemann-Hilbert correspondence can be\nused in order to describe\n(part of) the holonomy using purely al gebraic constructions. Joint with\nG. Vezzosi.\n LOCATION:https://researchseminars.org/talk/GeoSem/35/ END:VEVENT BEGIN:VEVENT SUMMARY:Xiangwen Zhang DTSTART:20220310T163000Z DTEND:20220310T173000Z DTSTAMP:20260422T212708Z UID:GeoSem/36 DESCRIPTION:Title: A geometric flow for Type IIA superstrings\nby Xiangwen Zhang as part of Geometry Seminar - University of Florence\n\n\nAbstract\nThe equations of flux compactifications of Type IIA superstrings were written down by To masiello and Tseng-Yau.\nTo study these equations\, we introduce a natural geometric flow on symplectic Calabi-Yau 6-manifolds. In this talk\, we wi ll\ndiscuss the recent progress on the study of this Type IIA flow. This i s based on joint work with Fei\, Phong and Picard.\n LOCATION:https://researchseminars.org/talk/GeoSem/36/ END:VEVENT BEGIN:VEVENT SUMMARY:Arthur Renaudineau DTSTART:20220324T143000Z DTEND:20220324T153000Z DTSTAMP:20260422T212708Z UID:GeoSem/37 DESCRIPTION:Title: Topology of real algebraic varieties near the tropical limit\nby Arthu r Renaudineau as part of Geometry Seminar - University of Florence\n\n\nAb stract\nDescribing all the possible topologies of real projective hypersur faces of fixed degree and dimension is a very difficult problem\, going ba ck to Hilbert's sixteenth problem. We will show some progress on this prob lem when assuming that the variety is closed to some degeneration\, called tropical limit. We will recall some basics on real algebraic geometry and tropical geometry and then relate the Betti numbers of a real variety nea r the tropical limit to the dimension of some tropical homology groups (by the way of a spectral sequence). It is based on joint works with Kris Sha w and Johannes Rau and Kris Shaw.\n LOCATION:https://researchseminars.org/talk/GeoSem/37/ END:VEVENT BEGIN:VEVENT SUMMARY:Antonio Trusiani DTSTART:20220328T133000Z DTEND:20220328T143000Z DTSTAMP:20260422T212708Z UID:GeoSem/38 DESCRIPTION:Title: From Kähler-Einstein metrics with prescribed singularities to K-stability \nby Antonio Trusiani as part of Geometry Seminar - University of Flor ence\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/GeoSem/38/ END:VEVENT BEGIN:VEVENT SUMMARY:Andrea Loi DTSTART:20220407T123000Z DTEND:20220407T133000Z DTSTAMP:20260422T212708Z UID:GeoSem/39 DESCRIPTION:Title: Kaehler-Ricci soliton indotti da spazi di forme complessi\nby Andrea L oi as part of Geometry Seminar - University of Florence\n\n\nAbstract\nDop o aver ricordato i risultati principali sulle metriche di Kahler e Kaehl er-Einstein indotte da spazi di forme complessi finito e infinito dimen sionali verrà fornita un’idea della dimostrazione di un recente risulta to ottenuto in collaborazione con R. Mossa che mostra che un KRS indotto da uno spazio di forme complesso finito dimensionale è necessarimente ba nale\, cioè Kahler-Einstein.\n LOCATION:https://researchseminars.org/talk/GeoSem/39/ END:VEVENT BEGIN:VEVENT SUMMARY:Andrei Moroianu DTSTART:20220428T123000Z DTEND:20220428T133000Z DTSTAMP:20260422T212708Z UID:GeoSem/40 DESCRIPTION:Title: Conformal vector fields on lcK manifolds\nby Andrei Moroianu as part o f Geometry Seminar - University of Florence\n\n\nAbstract\nIt is well know n that on compact Kähler manifolds every conformal vector field is Killin g (Lichnerowicz) and every Killing vector field is holomorphic. In this ta lk I will extend these results to the locally conformally Kähler setting. More precisely\, I will show that any conformal vector field $\\xi$ on a compact lcK manifold is Killing with respect to the Gauduchon metric\, and if the Kähler cover of the manifold is neither flat\, nor hyperkähler\, then $\\xi$ is holomorphic. This is joint work with Mihaela Pilca.\n LOCATION:https://researchseminars.org/talk/GeoSem/40/ END:VEVENT BEGIN:VEVENT SUMMARY:Paul Schwahn DTSTART:20220505T123000Z DTEND:20220505T133000Z DTSTAMP:20260422T212708Z UID:GeoSem/41 DESCRIPTION:Title: Stability and rigidity of normal homogeneous Einstein manifolds\nby Pa ul Schwahn as part of Geometry Seminar - University of Florence\n\n\nAbstr act\nThe stability of an Einstein metric is decided by the (non-)existence of small eigenvalues of the Lichnerowicz Laplacian on tt-tensors. In the homogeneous setting\, harmonic analysis allows us to approach the computat ion of these eigenvalues. This easy on symmetric spaces\, but considerably more difficult in the non-symmetric case. I review the case of irreducibl e symmetric spaces of compact type\, prove the existence of a non-symmetri c stable Einstein metric of positive scalar curvature\, and give an outloo k on how to investigate the normal homogeneous case. Furthermore\, I explo re the rigidity and infinitesimal deformability of homogeneous Einstein me trics.\n LOCATION:https://researchseminars.org/talk/GeoSem/41/ END:VEVENT BEGIN:VEVENT SUMMARY:Jeff Viaclovsky DTSTART:20220512T160000Z DTEND:20220512T170000Z DTSTAMP:20260422T212708Z UID:GeoSem/42 DESCRIPTION:Title: Gravitational instantons\, rational surfaces\, and K3 surfaces\nby Jef f Viaclovsky as part of Geometry Seminar - University of Florence\n\n\nAbs tract\nI will describe some examples of complete non-compact\nRicci-flat m etrics in dimension 4\, which are called "gravitational\ninstantons." In m any cases\, these can be compactified complex\nanalytically to rational su rfaces. I will also discuss how these\ngravitational instantons can arise from sequences of degenerating\nRicci-flat metrics on the compact K3 surfa ce\, through a process called\n"bubbling".\n LOCATION:https://researchseminars.org/talk/GeoSem/42/ END:VEVENT BEGIN:VEVENT SUMMARY:Bruno Klingler DTSTART:20220601T123000Z DTEND:20220601T133000Z DTSTAMP:20260422T212708Z UID:GeoSem/43 DESCRIPTION:by Bruno Klingler as part of Geometry Seminar - University of Florence\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/GeoSem/43/ END:VEVENT END:VCALENDAR