BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Rui Loja Fernandes (University of Illinois at Urbana-Champaign) DTSTART:20200512T160000Z DTEND:20200512T170000Z DTSTAMP:20260315T011557Z UID:Geolis/1 DESCRIPTION:Title: N on-commutative integrable systems and their singularities\nby Rui Loja Fernandes (University of Illinois at Urbana-Champaign) as part of Geometr ia em Lisboa (IST)\n\n\nAbstract\nThe theory of singularities of non-commu tative integrable systems (a.k.a isotropic fibrations)\, in contrast with the well-known theory for the commutative case (a.k.a. Lagrangian fibratio ns)\, is nonexistent. In this talk I will describe a few first steps towar d such a theory.\n LOCATION:https://researchseminars.org/talk/Geolis/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Michael Singer (University College London) DTSTART:20200519T153000Z DTEND:20200519T163000Z DTSTAMP:20260315T011557Z UID:Geolis/2 DESCRIPTION:Title: A construction of $D_k$ asymptotically locally flat gravitational instanton s from Atiyah-Hitchin and Taub-NUT geometries\nby Michael Singer (Univ ersity College London) as part of Geometria em Lisboa (IST)\n\n\nAbstract\ nComplete hyperKaehler 4-manifolds with cubic volume growth (and suitable decay of the curvature)\, also known as ALF gravitational instantons\, are known to come in two families\, according to the `fundamental group at in finity’. This group must be a finite subgroup of $SU(2)$ and the only po ssibilities compatible with cubic volume growth are the cyclic groups ($A_ k$) and binary dihedral groups ($D_k$).\n\nThis talk will be about the con struction of $D_k$ ALF gravitational instantons by a gluing construction i n which the ingredients are the moduli space of centred charge-2 monopoles ($D_0$) and a particularly symmetric\, but singular\, $A_k$ ALF gravitati onal instanton. This construction was suggested in a paper of Sen (1997). It is also closely related to a construction due to Foscolo\, in which hyp erKaehler metrics are constructed on the $K3$ manifold that are `nearly’ collapsed to a 3-dimensional space.\n\nThis is joint work with Bernd Schr oers.\n LOCATION:https://researchseminars.org/talk/Geolis/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Xavier Roulleau (Université d’Aix-Marseille) DTSTART:20200526T160000Z DTEND:20200526T170000Z DTSTAMP:20260315T011557Z UID:Geolis/3 DESCRIPTION:Title: O n a special configuration of 12 conics and a related K3 surface\nby X avier Roulleau (Université d’Aix-Marseille) as part of Geometria em Lis boa (IST)\n\n\nAbstract\nA generalized Kummer surface $X$ obtained as the quotient of an abelian surface by a symplectic automorphism of order 3 con tains a $9{\\mathbf A}_{2}$-configuration of $(-2)$-curves (ie smooth rati onal curves). Such a configuration plays the role of the $16$ disjoint $(- 2)$-curves for the usual Kummer surfaces.
\nIn this talk we will explai n how construct $9$ other such $9{\\mathbf A}_{2}$-configurations on the g eneralized Kummer surface associated to the double cover of the plane bran ched over the sextic dual curve of a cubic curve.
\nThe new $9{\\mathb f A}_{2}$-configurations are obtained by taking the pullback of a certain configuration of $12$ conics which are in special position with respect to the branch curve\, plus some singular quartic curves. We will then explai n how construct some automorphisms of the K3 surface sending one configura tion to another.
\n(Joint work with David Kohel and Alessandra Sarti). \n LOCATION:https://researchseminars.org/talk/Geolis/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Steve Zelditch (Northwestern University) DTSTART:20200602T160000Z DTEND:20200602T170000Z DTSTAMP:20260315T011557Z UID:Geolis/4 DESCRIPTION:Title: P robabilistic aspects of toric Kähler geometry\nby Steve Zelditch (Nor thwestern University) as part of Geometria em Lisboa (IST)\n\n\nAbstract\n Let $(M\, \\omega\, L)$ be a polarized toric Kahler manifold with polytope $P$. Associated to this data is a family $\\mu_k^x$ of probability measur es on $P$ parametrized by $x \\in P.$ They generalize the multi-nomial mea sures on the simplex\, where $M = \\mathbb{CP}^n$ and $\\omega$ is the Fub ini-Study measure. As is well-known\, these measures satisfy a law of larg e numbers\, a central limit theorem\, a large deviations principle and ent ropy asymptotics. The measure of maximal entropy in this family correspond s to the center of mass $x$ of $P$. All of these results generalize to any toric Kahler manifold\, except the center of mass result\, which holds fo r Fano toric Kahler-Einstein manifolds.\n\nJoint work with Peng Zhou and P ierre Flurin.\n LOCATION:https://researchseminars.org/talk/Geolis/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Alessia Mandini (IST and Universidade Federal Fluminense) DTSTART:20200616T160000Z DTEND:20200616T170000Z DTSTAMP:20260315T011557Z UID:Geolis/5 DESCRIPTION:Title: Q uasi-parabolic Higgs bundles and null hyperpolygon spaces\nby Alessia Mandini (IST and Universidade Federal Fluminense) as part of Geometria em Lisboa (IST)\n\n\nAbstract\nHyperpolygons spaces are a family of hyperkäh ler manifolds\, that can be obtained from coadjoint orbits by hyperkähler reduction. Jointly with L. Godinho\, we showed that these space are isomo rphic to certain families of parabolic Higgs bundles\, when a suitable con dition between the parabolic weights and the spectra of the coadjoint orbi ts is satisfied.\n\nIn analogy to this construction\, we introduce two mod uli spaces: the moduli spaces of quasi-parabolic $SL(2\,\\mathbb{C})$-Higg s bundles over $\\mathbb{CP}^1$ on one hand and the null hyperpolygon spac es on the other\, and establish an isomorphism between them.\nFinally we d escribe the fixed loci of natural involutions defined on these spaces and relate them to the moduli space of null hyperpolygons in the Minkowski $3$ -space.\n\nThis is based in joint works with Leonor Godinho.\n LOCATION:https://researchseminars.org/talk/Geolis/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Mario Garcia-Fernandez (ICMAT and Universidad Autónoma de Madrid) DTSTART:20200623T160000Z DTEND:20200623T170000Z DTSTAMP:20260315T011557Z UID:Geolis/6 DESCRIPTION:Title: G auge theory for string algebroids\nby Mario Garcia-Fernandez (ICMAT an d Universidad Autónoma de Madrid) as part of Geometria em Lisboa (IST)\n\ n\nAbstract\nIn this talk I will overview recent joint work with Roberto R ubio and Carl Tipler in arXiv:2004.11399. We introduce a moment map pictur e for string algebroids\, a special class of holomorphic Courant algebroid s introduced in arXiv:1807.10329. An interesting feature of our constructi on is that the Hamiltonian gauge action is described by means of Morita eq uivalences\, as suggested by higher gauge theory. The zero locus of the mo ment map is given by the solutions of the Calabi system\, a coupled system of equations which provides a unifying framework for the classical Calabi problem and the Hull-Strominger system. Our main results are concerned wi th the geometry of the moduli space of solutions. Assuming a technical con dition\, we prove that the moduli space carries a pseudo-Kähler metric wi th Kähler potential given by the 'dilaton functional'\, a topological for mula for the metric\, and an infinitesimal Donaldson-Uhlenbeck-Yau type th eorem. Finally\, we relate our topological formula to a physical predictio n for the gravitino mass in order to obtain a new conjectural obstruction for the Hull-Strominger system.\n LOCATION:https://researchseminars.org/talk/Geolis/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Tara Holm (Cornell University) DTSTART:20200630T160000Z DTEND:20200630T170000Z DTSTAMP:20260315T011557Z UID:Geolis/7 DESCRIPTION:Title: S ymplectic embeddings and infinite staircases\nby Tara Holm (Cornell Un iversity) as part of Geometria em Lisboa (IST)\n\n\nAbstract\nMcDuff and S chlenk determined when a four-dimensional symplectic ellipsoid can be symp lectically embedded into a four-dimensional ball. They found that if the e llipsoid is close to round\, the answer is given by an infinite staircase determined by Fibonacci numbers\, while if the ellipsoid is sufficiently s tretched\, all obstructions vanish except for the volume obstruction. Infi nite staircases have also been found when embedding ellipsoids into polydi sks (Frenkel - Muller\, Usher) and into the ellipsoid E(2\,3) (Cristofaro- Gardiner - Kleinman). We will describe a general approach to the question of when embedding ellipsoids into a toric target has an infinite staircase \, where we provide the first obstruction to the existence of a staircase. We use this obstruction to explore infinite staircases for toric symplect ic manifolds\, identifying three new infinite staircases\, and culminating in the conjecture that these are the only toric examples. We will describ e further work-in-progress on ellipsoid embedding functions with more gene ral targets. I will not assume any prior acquaintance with infinite stairc ases and will motivate the talk with plentiful examples and pictures. This talk is based on a number of collaborations with Dan Cristofaro-Gardiner\ , Alessia Mandini\, and Ana Rita Pires\; Maria Bertozzi\, Emily Maw\, Dusa McDuff\, Grace Mwakyoma\, Ana Rita Pires\, Morgan Weiler\; and Nicki Magi ll.\n LOCATION:https://researchseminars.org/talk/Geolis/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Kai Cieliebak (Augsburg University) DTSTART:20200609T160000Z DTEND:20200609T170000Z DTSTAMP:20260315T011557Z UID:Geolis/8 DESCRIPTION:Title: P artial orders on contactomorphism groups and their Lie algebras\nby Ka i Cieliebak (Augsburg University) as part of Geometria em Lisboa (IST)\n\n \nAbstract\nEliashberg\, Kim and Polterovich constructed nontrivial partia l orders on contactomorphism groups of certain contact manifolds. After re calling their results\, the subject of this talk will be the remnants of t hese partial orders on the orbits of the coadjoint action on their Lie alg ebras.\n LOCATION:https://researchseminars.org/talk/Geolis/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Tian-Jun Li (University of Minnesota) DTSTART:20200714T160000Z DTEND:20200714T170000Z DTSTAMP:20260315T011557Z UID:Geolis/9 DESCRIPTION:Title: S ymplectic rational G-surfaces and the plane Cremona group\nby Tian-Jun Li (University of Minnesota) as part of Geometria em Lisboa (IST)\n\n\nAb stract\nWe give characterizations of a finite group $G$ acting symplectica lly on a rational surface ($\\mathbb{CP}^2$ blown up at two or more points ). In particular\, we obtain a symplectic version of the dichotomy of $G$- conic bundles versus $G$-del Pezzo surfaces for the corresponding $G$-rati onal surfaces\, analogous to the one in algebraic geometry. The connection with the symplectic mapping class group will be mentioned.\n\n\nThis is a joint work with Weimin Chen and Weiwei Wu (and partly with Jun Li).\n LOCATION:https://researchseminars.org/talk/Geolis/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Rahul Pandharipande (ETH Zürich) DTSTART:20200707T160000Z DTEND:20200707T170000Z DTSTAMP:20260315T011557Z UID:Geolis/10 DESCRIPTION:Title: Moduli spaces of differentials on curves\nby Rahul Pandharipande (ETH Zürich) as part of Geometria em Lisboa (IST)\n\n\nAbstract\nThe moduli of $(C\,f)$ where $C$ is a curve and $f$ is a rational function leads to the well-developed theory of Hurwitz spaces. The study of the moduli of $(C\, \\omega)$  where $C$ is a curve and $\\omega$ is a meromorphic different ial is a younger subject. I will discuss recent developments in the study of the moduli spaces of holomorphic/meromorphic differentials on curves. M any of the basic questions about cycle classes and integrals have now been solved (through the work of many people) -- but there are also several in teresting open directions.\n LOCATION:https://researchseminars.org/talk/Geolis/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Colin Guillarmou (Laboratoire de Mathématiques d'Orsay\, Universi té Paris-Sud) DTSTART:20200721T160000Z DTEND:20200721T170000Z DTSTAMP:20260315T011557Z UID:Geolis/11 DESCRIPTION:Title: On the marked length spectrum and geodesic stretch in negative curvature\nby Colin Guillarmou (Laboratoire de Mathématiques d'Orsay\, Universit é Paris-Sud) as part of Geometria em Lisboa (IST)\n\n\nAbstract\nI will r eview a couple of recent of results proved with T. Lefeuvre and G. Knieper on the local rigidity of the marked length spectrum of negatively curved metrics.\n LOCATION:https://researchseminars.org/talk/Geolis/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Mark Gross (Department of Pure Mathematics and Mathematical Statis tics\, University of Cambridge) DTSTART:20200728T160000Z DTEND:20200728T170000Z DTSTAMP:20260315T011557Z UID:Geolis/12 DESCRIPTION:Title: Intrinsic Mirror Symmetry\nby Mark Gross (Department of Pure Mathemati cs and Mathematical Statistics\, University of Cambridge) as part of Geome tria em Lisboa (IST)\n\n\nAbstract\nI will talk about joint work with Bern d Siebert\, proposing a general mirror construction for log Calabi-Yau pai rs\, i.e.\, a pair $(X\,D)$ with $D$ a "maximally degenerate" boundary div isor and $K_X+D=0$\, and for maximally unipotent degenerations of Calabi - Yau manifolds. We accomplish this by constructing the coordinate ring or homogeneous coordinate ring respectively in the two cases\, using certain kinds of Gromov-Witten invariants we call "punctured invariants"\, develop ed jointly with Abramovich and Chen.\n LOCATION:https://researchseminars.org/talk/Geolis/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Robert Berman (Chalmers University of Technology) DTSTART:20200915T100000Z DTEND:20200915T110000Z DTSTAMP:20260315T011557Z UID:Geolis/13 DESCRIPTION:Title: Kähler-Einstein metrics\, Archimedean Zeta functions and phase transition s\nby Robert Berman (Chalmers University of Technology) as part of Geo metria em Lisboa (IST)\n\n\nAbstract\nWhile the existence of a unique Käh ler-Einstein metrics on a canonically polarized manifold $X$ was establish ed already in the seventies there are very few explicit formulas available (even in the case of complex curves!). In this talk I will give a non-tec hnical introduction to a probabilistic approach to Kähler-Einstein metric s\, which\, in particular\, yields canonical approximations of the Kähler -Einstein metric on $X$. The approximating metrics in question are express ed as explicit period integrals and the conjectural extension to the case of a Fano variety leads to some intriguing connections with Zeta functions and the theory of phase transitions in statistical mechanics.\n LOCATION:https://researchseminars.org/talk/Geolis/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Gonçalo Oliveira (Universidade Federal Fluminense\, Brazil) DTSTART:20200929T160000Z DTEND:20200929T170000Z DTSTAMP:20260315T011557Z UID:Geolis/14 DESCRIPTION:Title: $G_2$-monopoles (a summary)\nby Gonçalo Oliveira (Universidade Federa l Fluminense\, Brazil) as part of Geometria em Lisboa (IST)\n\n\nAbstract\ nThis talk is aimed at reviewing what is known about $G_2$-monopoles and m otivate their study. After this\, I will mention some recent results obtai ned in collaboration with Ákos Nagy and Daniel Fadel which investigate th e asymptotic behavior of $G_2$-monopoles. Time permitting\, I will mention a few possible future directions regarding the use of monopoles in $G_2$- geometry.\n LOCATION:https://researchseminars.org/talk/Geolis/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Éveline Legendre (Université Paul Sabatier) DTSTART:20201006T160000Z DTEND:20201006T170000Z DTSTAMP:20260315T011557Z UID:Geolis/15 DESCRIPTION:Title: Localizing the Donaldson-Futaki invariant\nby Éveline Legendre (Unive rsité Paul Sabatier) as part of Geometria em Lisboa (IST)\n\n\nAbstract\n We will see how to represent the Donaldson-Futaki invariant as an intersec tion of equivariant closed forms. We will use it to express this invariant as the intersection on some specific subvarieties of the central fibre of the test configuration. As an application we provide a proof that for Kä hler orbifolds the Donaldson-Futaki invariant is the Futaki invariant of t he central fiber.\n LOCATION:https://researchseminars.org/talk/Geolis/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Sílvia Anjos (Instituto Superior Técnico and CAMGSD) DTSTART:20201117T170000Z DTEND:20201117T180000Z DTSTAMP:20260315T011557Z UID:Geolis/16 DESCRIPTION:Title: Loops in the fundamental group of $\\mathrm{Symp}(M\,\\omega)$ which are n ot represented by circle actions\nby Sílvia Anjos (Instituto Superior Técnico and CAMGSD) as part of Geometria em Lisboa (IST)\n\n\nAbstract\n It was observed by J. Kędra that there are many symplectic 4-manifolds $( M\, \\omega)$\, where $M$ is neither rational nor ruled\, that admit no ci rcle action and $\\pi_1 (\\mathrm{Ham}( M))$ is nontrivial. In the case $M ={\\mathbb C\\mathbb P}^2\\#\\\,k\\overline{\\mathbb C\\mathbb P}\\\,\\!^2 $\, with $k \\leq 4$\, it follows from the work of several authors that th e full rational homotopy of $\\mathrm{Symp}(M\,\\omega)$\, and in particul ar their fundamental group\, is generated by circle actions on the manifol d. In this talk we study loops in the fundamental group of $\\mathrm{Symp} _h({\\mathbb C\\mathbb P}^2\\#\\\,5\\overline{\\mathbb C\\mathbb P}\\\,\\! ^2) $ of symplectomorphisms that act trivially on homology\, and show that \, for some particular symplectic forms\, there are loops which cannot be realized by circle actions. Our work depends on Delzant classification of toric symplectic manifolds and Karshon's classification of Hamiltonian cir cle actions\n\nThis talk is based in joint work with Miguel Barata\, Marti n Pinsonnault and Ana Alexandra Reis.\n LOCATION:https://researchseminars.org/talk/Geolis/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Nick Sheridan (University of Edinburgh) DTSTART:20200908T160000Z DTEND:20200908T170000Z DTSTAMP:20260315T011557Z UID:Geolis/17 DESCRIPTION:Title: Lagrangian cobordism and Chow groups\nby Nick Sheridan (University of Edinburgh) as part of Geometria em Lisboa (IST)\n\n\nAbstract\nHomological mirror symmetry predicts an equivalence of categories\, between the Fukay a category of one space and the derived category of another. We can "decat egorify" by taking the Grothendieck group of these categories\, to get an isomorphism of abelian groups. The first of these abelian groups is relate d\, by work of Biran-Cornea\, to the Lagrangian cobordism group\; the seco nd is related\, via the Chern character\, to the Chow group. I will define the Lagrangian cobordism and Chow groups (which is much easier than defin ing the categories). Then I will describe joint work with Ivan Smith in wh ich we try to compare them directly\, and find some interesting analogies. \n LOCATION:https://researchseminars.org/talk/Geolis/17/ END:VEVENT BEGIN:VEVENT SUMMARY:Ana Rita Pires (University of Edinburgh) DTSTART:20200202T170000Z DTEND:20200202T180000Z DTSTAMP:20260315T011557Z UID:Geolis/18 DESCRIPTION:Title: Many more infinite staircases in symplectic embedding functions\nby An a Rita Pires (University of Edinburgh) as part of Geometria em Lisboa (IST )\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/Geolis/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Yang Li (Institute for Advanced Study) DTSTART:20200922T160000Z DTEND:20200922T170000Z DTSTAMP:20260315T011557Z UID:Geolis/19 DESCRIPTION:Title: Weak SYZ conjecture for hypersurfaces in the Fermat family\nby Yang Li (Institute for Advanced Study) as part of Geometria em Lisboa (IST)\n\n\n Abstract\nThe SYZ conjecture predicts that for polarised Calabi-Yau manifo lds undergoing the large complex structure limit\, there should be a speci al Lagrangian torus fibration. A weak version asks if this fibration can b e found in the generic region. I will discuss my recent work proving this weak SYZ conjecture for the degenerating hypersurfaces in the Fermat famil y. Although these examples are quite special\, this is the first construct ion of generic SYZ fibrations that works uniformly in all complex dimensio ns.\n LOCATION:https://researchseminars.org/talk/Geolis/19/ END:VEVENT BEGIN:VEVENT SUMMARY:Xiuxiong Chen (Stony Brook University) DTSTART:20201013T160000Z DTEND:20201013T170000Z DTSTAMP:20260315T011557Z UID:Geolis/20 DESCRIPTION:Title: On the space of Kähler metrics\nby Xiuxiong Chen (Stony Brook Univers ity) as part of Geometria em Lisboa (IST)\n\n\nAbstract\nInspired by the c elebrated $C^0\, C^2$ and $C^3$ a priori estimate of Calabi\, Yau and othe rs on Kähler Einstein metrics\, we will present an expository report of a priori estimates on the constant scalar curvature Kähler metrics. With t his estimate\, we prove the Donaldson conjecture on geodesic stability and the properness conjecture on Mabuchi energy functional.\n\nThis is a join t work with Cheng JingRui.\n LOCATION:https://researchseminars.org/talk/Geolis/20/ END:VEVENT BEGIN:VEVENT SUMMARY:Leonardo Macarini (Instituto Superior Técnico and CAMGSD) DTSTART:20201124T170000Z DTEND:20201124T180000Z DTSTAMP:20260315T011557Z UID:Geolis/21 DESCRIPTION:Title: Dynamical implications of convexity beyond dynamical convexity\nby Leo nardo Macarini (Instituto Superior Técnico and CAMGSD) as part of Geometr ia em Lisboa (IST)\n\n\nAbstract\nWe will show sharp dynamical implication s of convexity on symmetric spheres that do not follow from dynamical conv exity. It allows us to furnish new examples of dynamically convex contact forms that are not equivalent to convex ones via contactomorphisms that pr eserve the symmetry. Moreover\, these examples are $C^1$-stable in the sen se that they are actually not equivalent to convex ones via contactomorphi sms that are $C^1$-close to those preserving the symmetry. Other applicati ons are the multiplicity of symmetric non-hyperbolic closed Reeb orbits un der suitable pinching conditions and the existence of symmetric elliptic p eriodic Reeb orbits. \n\nThis is ongoing joint work with Miguel Abreu.\n LOCATION:https://researchseminars.org/talk/Geolis/21/ END:VEVENT BEGIN:VEVENT SUMMARY:Tristan C. Collins (MIT) DTSTART:20201020T160000Z DTEND:20201020T170000Z DTSTAMP:20260315T011557Z UID:Geolis/22 DESCRIPTION:Title: SYZ mirror symmetry for del Pezzo surfaces and rational elliptic surfaces< /a>\nby Tristan C. Collins (MIT) as part of Geometria em Lisboa (IST)\n\n\ nAbstract\nI will discuss some aspects of SYZ mirror symmetry for pairs $( X\,D)$ where $X$ is a del Pezzo surface or a rational elliptic surface and $D$ is an anti-canonical divisor.  In particular I will explain the exis tence of special Lagrangian fibrations\, mirror symmetry for (suitably int erpreted) Hodge numbers and\, if time permits\, I will describe a proof of SYZ mirror symmetry conjecture for del Pezzo surfaces.  \n\nThis is join t work with Adam Jacob and Yu-Shen Lin.\n LOCATION:https://researchseminars.org/talk/Geolis/22/ END:VEVENT BEGIN:VEVENT SUMMARY:Andrew Lobb (Durham University) DTSTART:20201103T170000Z DTEND:20201103T180000Z DTSTAMP:20260315T011557Z UID:Geolis/23 DESCRIPTION:Title: The rectangular peg problem\nby Andrew Lobb (Durham University) as par t of Geometria em Lisboa (IST)\n\n\nAbstract\nFor any smooth Jordan curve and rectangle in the plane\, we show that there exist four points on the J ordan curve forming the vertices of a rectangle similar to the given one.\ nJoint work with Josh Greene.\n LOCATION:https://researchseminars.org/talk/Geolis/23/ END:VEVENT BEGIN:VEVENT SUMMARY:Yaron Ostrover (Tel Aviv University) DTSTART:20201027T170000Z DTEND:20201027T180000Z DTSTAMP:20260315T011557Z UID:Geolis/24 DESCRIPTION:Title: On symplectic inner and outer radii of some convex domains\nby Yaron O strover (Tel Aviv University) as part of Geometria em Lisboa (IST)\n\n\nAb stract\nSymplectic embedding problems are at the heart of the study of sym plectic topology. In this talk we discuss how to use integrable systems to compute the symplectic inner and outer radii of certain convex domains.\n \nThe talk is based on a joint work with Vinicius Ramos.\n LOCATION:https://researchseminars.org/talk/Geolis/24/ END:VEVENT BEGIN:VEVENT SUMMARY:Simon K. Donaldson (Simons Center for Geometry and Physics Stony B rook and Imperial College London) DTSTART:20201215T170000Z DTEND:20201215T180000Z DTSTAMP:20260315T011557Z UID:Geolis/25 DESCRIPTION:Title: Co-associative fibrations of $G_{2}$-manifolds and deformations of singula r sets\nby Simon K. Donaldson (Simons Center for Geometry and Physics Stony Brook and Imperial College London) as part of Geometria em Lisboa (I ST)\n\n\nAbstract\nThe first part of the talk will review background mater ial on the differential geometry of $7$-dimensional manifolds with the exc eptional holonomy group $G_{2}$. There are now many thousands of examples of deformation classes of such manifolds and there are good reasons for th inking that many of these have fibrations with general fibre diffeomorphic to a $K3$ surface and some singular fibres: higher dimensional analogues of Lefschetz fibrations in algebraic geometry. In the second part of the t alk we will discuss some questions which arise in the analysis of these fi brations and their "adiabatic limits". The key difficulties involve the si ngular fibres. This brings up a PDE problem\, analogous to a free boundary problem\, and similar problems have arisen in a number of areas of differ ential geometry over the past few years\, such as in Taubes' work on gauge theory. We will outline some techniques for handling these questions.\n LOCATION:https://researchseminars.org/talk/Geolis/25/ END:VEVENT BEGIN:VEVENT SUMMARY:Leonor Godinho (Instituto Superior Técnico and CAMGSD) DTSTART:20210309T170000Z DTEND:20210309T180000Z DTSTAMP:20260315T011557Z UID:Geolis/26 DESCRIPTION:Title: On the number of fixed points of periodic flows\nby Leonor Godinho (In stituto Superior Técnico and CAMGSD) as part of Geometria em Lisboa (IST) \n\n\nAbstract\nFinding the minimal number of fixed points of a periodic f low on a compact manifold is\, in general\, an open problem. We will consi der almost complex manifolds and see how one can obtain lower bounds by re trieving information from a special Chern number.\n LOCATION:https://researchseminars.org/talk/Geolis/26/ END:VEVENT BEGIN:VEVENT SUMMARY:Paul Biran (ETH Zurich) DTSTART:20210202T170000Z DTEND:20210202T180000Z DTSTAMP:20260315T011557Z UID:Geolis/27 DESCRIPTION:Title: Persistence and Triangulation in Lagrangian Topology\nby Paul Biran (E TH Zurich) as part of Geometria em Lisboa (IST)\n\n\nAbstract\nBoth triang ulated categories as well as persistence homology play an important role i n symplectic topology. The goal of this talk is to explain how to put the two structures\ntogether\, leading to the notion of a triangulated persist ence category. The guiding principle comes from the theory of Lagrangian c obordism.\n\nThe talk is based on ongoing joint work with Octav Cornea and Jun Zhang.\n LOCATION:https://researchseminars.org/talk/Geolis/27/ END:VEVENT BEGIN:VEVENT SUMMARY:Dusa McDuff (Columbia University) DTSTART:20210112T170000Z DTEND:20210112T180000Z DTSTAMP:20260315T011557Z UID:Geolis/28 DESCRIPTION:Title: Counting curves and stabilized symplectic embedding conjecture\nby Dus a McDuff (Columbia University) as part of Geometria em Lisboa (IST)\n\n\nA bstract\nThis is a report on joint work with Kyler Siegel that develops ne w ways to count $J$-holomorphic curves in $4$-dimensions\, both in the pro jective plane with multi-branched tangency constraints\, and in noncompact cobordisms between ellipsoids. These curves stabilize\, i.e. if they exis t in a given four dimensional target manifold $X$ they still exist in the product $X \\times {\\mathbb R}^{2k}$. This allows us to establish new cas es of the stabilized embedding conjecture for symplectic embeddings of an ellipsoid into a ball (or ellipsoid).\n LOCATION:https://researchseminars.org/talk/Geolis/28/ END:VEVENT BEGIN:VEVENT SUMMARY:Thibaut Delcroix (Université de Montpellier) DTSTART:20210105T170000Z DTEND:20210105T180000Z DTSTAMP:20260315T011557Z UID:Geolis/29 DESCRIPTION:Title: On the Yau-Tian-Donaldson conjecture for spherical varieties\nby Thiba ut Delcroix (Université de Montpellier) as part of Geometria em Lisboa (I ST)\n\n\nAbstract\nI will present how uniform $K-$stability translates int o a convex geometric problem for polarized spherical varieties.\nFrom this \, we will derive a combinatorial sufficient condition of existence of con stant scalar curvature Kahler metrics on smooth singular varieties\, and a complete solution to the Yau-Tian-Donaldson conjecture for cohomogeneity one manifolds.\n LOCATION:https://researchseminars.org/talk/Geolis/29/ END:VEVENT BEGIN:VEVENT SUMMARY:Vicente Muñoz (Málaga University) DTSTART:20210209T170000Z DTEND:20210209T180000Z DTSTAMP:20260315T011557Z UID:Geolis/30 DESCRIPTION:Title: A Smale-Barden manifold admitting K-contact but not Sasakian structure \nby Vicente Muñoz (Málaga University) as part of Geometria em Lisboa (I ST)\n\n\nAbstract\nSasakian manifolds are odd-dimensional counterparts of Kahler manifolds in even dimensions\, with K-contact manifolds correspondi ng to symplectic manifolds. In this talk\, we give the first example of a simply connected compact 5-manifold (Smale-Barden manifold) which admits a \nK-contact structure but does not admit any Sasakian structure\, settling a long standing question of Boyer and Galicki. \n\nFor this\, we translat e the question about K-contact 5-manifolds to constructing symplectic 4-or bifolds with cyclic singularities containing disjoint symplectic surfaces of positive genus. The question on Sasakian 5-manifolds translates to the existence of algebraic surfaces with\ncyclic singularities containig disjo int complex curves of positive genus. A key step consists on bounding univ ersally the number of singular points of the algebraic surface.\n LOCATION:https://researchseminars.org/talk/Geolis/30/ END:VEVENT BEGIN:VEVENT SUMMARY:Emilio Franco (Instituto Superior Técnico and CAMGSD) DTSTART:20201110T170000Z DTEND:20201110T180000Z DTSTAMP:20260315T011557Z UID:Geolis/31 DESCRIPTION:Title: Torsion line bundles and branes on the Hitchin system\nby Emilio Franc o (Instituto Superior Técnico and CAMGSD) as part of Geometria em Lisboa (IST)\n\n\nAbstract\nThe locus of the Higgs moduli space fixed under tenso rization by a torsion line bundle a key role in the work of Hausel and Tha ddeus on topological mirror symmetry. We shall describe the behavior under mirror symmetry of this fixed locus.\n LOCATION:https://researchseminars.org/talk/Geolis/31/ END:VEVENT BEGIN:VEVENT SUMMARY:Jonathan Weitsman (Northeastern University) DTSTART:20210216T170000Z DTEND:20210216T180000Z DTSTAMP:20260315T011557Z UID:Geolis/32 DESCRIPTION:by Jonathan Weitsman (Northeastern University) as part of Geom etria em Lisboa (IST)\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/Geolis/32/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexandru Oancea (Institut de Mathématiques de Jussieu\, Sorbonne Université) DTSTART:20210223T170000Z DTEND:20210223T180000Z DTSTAMP:20260315T011557Z UID:Geolis/33 DESCRIPTION:Title: Duality and coproducts in Rabinowitz-Floer homology\nby Alexandru Oanc ea (Institut de Mathématiques de Jussieu\, Sorbonne Université) as part of Geometria em Lisboa (IST)\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/Geolis/33/ END:VEVENT BEGIN:VEVENT SUMMARY:Cristiano Spotti (Aarhus University) DTSTART:20210126T170000Z DTEND:20210126T180000Z DTSTAMP:20260315T011557Z UID:Geolis/34 DESCRIPTION:by Cristiano Spotti (Aarhus University) as part of Geometria e m Lisboa (IST)\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/Geolis/34/ END:VEVENT BEGIN:VEVENT SUMMARY:Justin Sawon (University of North Carolina at Chapel Hill) DTSTART:20210119T170000Z DTEND:20210119T180000Z DTSTAMP:20260315T011557Z UID:Geolis/35 DESCRIPTION:Title: Lagrangian fibrations by Prym varieties\nby Justin Sawon (University o f North Carolina at Chapel Hill) as part of Geometria em Lisboa (IST)\n\n\ nAbstract\nLagrangian fibrations on holomorphic symplectic manifolds and o rbifolds are higher-dimensional generalizations of elliptic K3 surfaces. T hey are fibrations whose general fibres are abelian varieties that are Lag rangian with respect to the symplectic form. Markushevich and Tikhomirov d escribed the first example whose fibres are Prym varieties\, and their con struction was further developed by Arbarello\, Ferretti\, and Sacca and by Matteini to yield more examples. In this talk we describe the general fra mework\, and consider a new example. We describe its singularities and sho w that it is a 'primitive' symplectic variety. We also construct the dual fibration\, using ideas of Menet. This is joint work with Chen Shen.\n LOCATION:https://researchseminars.org/talk/Geolis/35/ END:VEVENT BEGIN:VEVENT SUMMARY:Giulia Saccà (Columbia University) DTSTART:20210316T170000Z DTEND:20210316T180000Z DTSTAMP:20260315T011557Z UID:Geolis/36 DESCRIPTION:Title: Compact Hyper-Kählers and Fano Manifolds\nby Giulia Saccà (Columbia University) as part of Geometria em Lisboa (IST)\n\n\nAbstract\nProjective hyper-Kähler (HK) manifolds are among the building blocks of projective manifolds with trivial first Chern class. Fano manifolds are projective ma nifolds with positive first Chern class.\n\nDespite the fact that these tw o classes of algebraic varieties are very different (HK manifolds have a h olomorphic symplectic form which governs all of its geometry\, Fano manifo lds have no holomorphic forms) their geometries have some strong ties. For example\, starting from some special Fano manifolds one can sometimes con struct HK manifolds as parameter spaces of objects on the Fano. In this ta lk I will explain this circle of ideas and focus on some recent work explo ring the converse: given a projective HK manifold\, how to recover a Fano manifold from it?\n LOCATION:https://researchseminars.org/talk/Geolis/36/ END:VEVENT BEGIN:VEVENT SUMMARY:Andrew Neitzke (Yale University) DTSTART:20210302T170000Z DTEND:20210302T180000Z DTSTAMP:20260315T011557Z UID:Geolis/37 DESCRIPTION:by Andrew Neitzke (Yale University) as part of Geometria em Li sboa (IST)\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/Geolis/37/ END:VEVENT BEGIN:VEVENT SUMMARY:Lorenzo Foscolo (University College London) DTSTART:20210323T170000Z DTEND:20210323T180000Z DTSTAMP:20260315T011557Z UID:Geolis/38 DESCRIPTION:Title: Twistor constructions of non-compact hyperkähler manifolds\nby Lorenz o Foscolo (University College London) as part of Geometria em Lisboa (IST) \n\n\nAbstract\nThe talk is based on joint work with Roger Bielawski about twistor constructions of higher dimensional non-compact hyperkähler mani folds with maximal and submaximal volume growth. In the first part of the talk\, based on arXiv:2012.14895\, I will discuss the case of hyperkähler metrics with maximal volume growth: in the same way that ALE spaces are c losely related to the deformation theory of Kleinian singularities\, we pr oduce large families of hyperkähler metrics asymptotic to cones exploitin g the theory of Poisson deformations of affine symplectic singularities. I n the second part of the talk\, I will report on work in progress about th e construction of hyperkähler metrics generalising to higher dimensions t he geometry of ALF spaces of dihedral type. We produce candidate holomorph ic symplectic manifolds and twistor spaces from Hilbert schemes of hyperto ric manifolds with an action of a Weyl group. The spaces we define are clo sely related to Coulomb branches of 3-dimensional supersymmetric gauge the ories.\n LOCATION:https://researchseminars.org/talk/Geolis/38/ END:VEVENT BEGIN:VEVENT SUMMARY:Marco Mazzuchelli (École normale supérieure de Lyon) DTSTART:20210406T160000Z DTEND:20210406T170000Z DTSTAMP:20260315T011557Z UID:Geolis/39 DESCRIPTION:Title: What does a Besse contact sphere look like?\nby Marco Mazzuchelli (Éc ole normale supérieure de Lyon) as part of Geometria em Lisboa (IST)\n\n\ nAbstract\nA closed connected contact manifold is called Besse when all of its Reeb orbits are closed (the terminology comes from Arthur Besse's mon ograph "Manifolds all of whose geodesics are closed"\, which deals indeed with Besse unit tangent bundles). In recent years\, a few intriguing prope rties of Besse contact manifolds have been established: in particular\, th eir spectral and systolic characterizations. In this talk\, I will focus o n Besse contact spheres. In dimension 3\, it turns out that such spheres a re strictly contactomorphic to rational ellipsoids. In higher dimensions\, an analogous result is unknown and seems out of reach. Nevertheless\, I w ill show that at least those contact spheres that are convex still "resemb le" a contact ellipsoid: any stratum of the stratification defined by thei r Reeb flow is an integral homology sphere\, and the sequence of their Eke land-Hofer capacities coincides with the full sequence of action values\, each one repeated according to a suitable multiplicity. This is joint work with Marco Radeschi.\n LOCATION:https://researchseminars.org/talk/Geolis/39/ END:VEVENT BEGIN:VEVENT SUMMARY:Brian Collier (University of California Riverside) DTSTART:20210413T160000Z DTEND:20210413T170000Z DTSTAMP:20260315T011557Z UID:Geolis/40 DESCRIPTION:Title: Global Slodowy slices for moduli spaces of λ-connections\nby Brian Co llier (University of California Riverside) as part of Geometria em Lisboa (IST)\n\n\nAbstract\nThe moduli spaces of Higgs bundles and holomorphic co nnections both have important affine holomorphic Lagrangian subvarieties\, these are the Hitchin section and the space of opers\, respectively. Both of these spaces arise from the same Lie theoretic mechanism\, namely a re gular nilpotent element of a Lie algebra. In this talk we will generalize these parameterizations to other nilpotents. The resulting objects are not related by the nonabelian Hodge correspondence\, but by an operation call ed the conformal limit. Time permitting\, we will also discuss their relat ion to Higher Teichmuller spaces.\n LOCATION:https://researchseminars.org/talk/Geolis/40/ END:VEVENT BEGIN:VEVENT SUMMARY:Tomasso Pacini (SNS Pisa) DTSTART:20210420T160000Z DTEND:20210420T170000Z DTSTAMP:20260315T011557Z UID:Geolis/41 DESCRIPTION:Title: Minimal Lagrangian submanifolds\, totally real geometry and the anti-canon ical line bundle\nby Tomasso Pacini (SNS Pisa) as part of Geometria em Lisboa (IST)\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/Geolis/41/ END:VEVENT BEGIN:VEVENT SUMMARY:Laura Schaposnik (University of Illinois at Chicago) DTSTART:20210427T160000Z DTEND:20210427T170000Z DTSTAMP:20260315T011557Z UID:Geolis/42 DESCRIPTION:Title: On generalized hyperpolygons\nby Laura Schaposnik (University of Illin ois at Chicago) as part of Geometria em Lisboa (IST)\n\n\nAbstract\nIn thi s talk we will introduce generalized hyperpolygons\, which arise as Nakaji ma-type representations of a comet-shaped quiver\, following recent work j oint with Steven Rayan. After showing how to identify these representation s with pairs of polygons\, we shall associate to the data an explicit mero morphic Higgs bundle on a\ngenus-g Riemann surface\, where g is the number of loops in the comet. We shall see that\, under certain assumptions on f lag types\, the moduli space of generalized hyperpolygons admits the struc ture of a completely integrable Hamiltonian system.\n LOCATION:https://researchseminars.org/talk/Geolis/42/ END:VEVENT BEGIN:VEVENT SUMMARY:Yu-Shen Lin (Boston University) DTSTART:20210504T160000Z DTEND:20210504T170000Z DTSTAMP:20260315T011557Z UID:Geolis/43 DESCRIPTION:Title: Correspondence theorem between holomorphic discs and tropical discs on (Lo g)-Calabi-Yau Surfaces\nby Yu-Shen Lin (Boston University) as part of Geometria em Lisboa (IST)\n\n\nAbstract\nTropical geometry is a useful too l to study the Gromov-Witten type invariants\, which count the number of h olomorphic curves with incidence conditions. On the other hand\, holomorph ic discs with boundaries on the Lagrangian fibration of a Calabi-Yau manif old plays an important role in the quantum correction of the mirror comple x structure. In this talk\, I will introduce a version of open Gromov-Witt en invariants counting such discs and the corresponding tropical geometry on (log) Calabi-Yau surfaces. Using Lagrangian Floer theory\, we will esta blish the equivalence between the open Gromov-Witten invariants with weigh ted count of tropical discs. In particular\, the correspondence theorem im plies the folklore conjecture that certain open Gromov-Witten invariants c oincide with the log Gromov-Witten invariants with maximal tangency for th e projective plane.\n LOCATION:https://researchseminars.org/talk/Geolis/43/ END:VEVENT BEGIN:VEVENT SUMMARY:Marcos Jardim (Campinas State University) DTSTART:20210511T160000Z DTEND:20210511T170000Z DTSTAMP:20260315T011557Z UID:Geolis/44 DESCRIPTION:Title: Walls and asymptotics for Bridgeland stability conditions on 3-folds\n by Marcos Jardim (Campinas State University) as part of Geometria em Lisbo a (IST)\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/Geolis/44/ END:VEVENT BEGIN:VEVENT SUMMARY:Carolina Araujo (IMPA) DTSTART:20210601T160000Z DTEND:20210601T170000Z DTSTAMP:20260315T011557Z UID:Geolis/45 DESCRIPTION:Title: Higher Fano Manifolds\nby Carolina Araujo (IMPA) as part of Geometria em Lisboa (IST)\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/Geolis/45/ END:VEVENT BEGIN:VEVENT SUMMARY:Camilla Felisetti (Università di Trento) DTSTART:20210518T160000Z DTEND:20210518T170000Z DTSTAMP:20260315T011557Z UID:Geolis/46 DESCRIPTION:Title: P=W conjectures for character varieties with a symplectic resolution\n by Camilla Felisetti (Università di Trento) as part of Geometria em Lisbo a (IST)\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/Geolis/46/ END:VEVENT BEGIN:VEVENT SUMMARY:Antoine Song (Princeton) DTSTART:20210615T160000Z DTEND:20210615T170000Z DTSTAMP:20260315T011557Z UID:Geolis/47 DESCRIPTION:Title: The essential minimal volume of manifolds\nby Antoine Song (Princeton) as part of Geometria em Lisboa (IST)\n\n\nAbstract\nOne way to measure th e complexity of a smooth manifold M is to consider its minimal volume\, de noted by MinVol\, introduced by Gromov\, which is simply defined as the in fimum of the volume among metrics with sectional curvature between -1 and 1. I will introduce a variant of MinVol\, called the essential minimal vol ume\, defined as the infimum of the volume over a closure of the space of metrics with sectional curvature between -1 and 1. I will discuss the main properties of this invariant\, and present estimates for negatively curve d manifolds\, Einstein 4-manifolds and most complex surfaces.\n LOCATION:https://researchseminars.org/talk/Geolis/47/ END:VEVENT BEGIN:VEVENT SUMMARY:Yael Karshon (University of Toronto) DTSTART:20210622T160000Z DTEND:20210622T170000Z DTSTAMP:20260315T011557Z UID:Geolis/48 DESCRIPTION:Title: Bott canonical basis?\nby Yael Karshon (University of Toronto) as part of Geometria em Lisboa (IST)\n\n\nAbstract\nTogether with Jihyeon Jessie Yang\, we are resurrecting an old idea of Raoul Bott for using large torus actions to construct canonical bases for unitary representations of compa ct Lie groups. Our methods are complex analytic\; we apply them to familie s of Bott-Samelson manifolds parametrized by C^n. Our construction require s the vanishing of higher cohomology of sheaves of holomorphic sections of certain line bundles over the total spaces of such families\; this vanish ing is conjectural\, hence the question mark in the title.\n LOCATION:https://researchseminars.org/talk/Geolis/48/ END:VEVENT BEGIN:VEVENT SUMMARY:Alberto Abbondandolo (Ruhr-Universität Bochum) DTSTART:20210525T160000Z DTEND:20210525T170000Z DTSTAMP:20260315T011557Z UID:Geolis/50 DESCRIPTION:Title: Systolic questions in metric and symplectic geometry\nby Alberto Abbon dandolo (Ruhr-Universität Bochum) as part of Geometria em Lisboa (IST)\n\ nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/Geolis/50/ END:VEVENT BEGIN:VEVENT SUMMARY:Mirko Mauri (Max Planck (Bonn)) DTSTART:20210608T160000Z DTEND:20210608T170000Z DTSTAMP:20260315T011557Z UID:Geolis/51 DESCRIPTION:Title: On the geometric P=W conjecture\nby Mirko Mauri (Max Planck (Bonn)) as part of Geometria em Lisboa (IST)\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/Geolis/51/ END:VEVENT BEGIN:VEVENT SUMMARY:Siu-Cheong Lau (Boston University) DTSTART:20210706T160000Z DTEND:20210706T170000Z DTSTAMP:20260315T011557Z UID:Geolis/52 DESCRIPTION:Title: Kaehler geometry of quiver moduli in application to machine learning\n by Siu-Cheong Lau (Boston University) as part of Geometria em Lisboa (IST) \n\n\nAbstract\nNeural network in machine learning has interesting similar ity with quiver representation theory. In this talk\, I will build an alg ebro-geometric formulation of a `computing machine'\, which is well-define d over the moduli space of representations. The main algebraic ingredient is to extend noncommutative geometry of Connes\, Cuntz-Quillen\, Ginzburg to near-rings\, which capture the non-linear activation functions in neur al network. I will also explain a uniformization between spherical\, Eucl idean and hyperbolic moduli of framed quiver representations.\n LOCATION:https://researchseminars.org/talk/Geolis/52/ END:VEVENT BEGIN:VEVENT SUMMARY:Olivia Dumitrescu (University of North Carolina at Chapel Hill) DTSTART:20210720T160000Z DTEND:20210720T170000Z DTSTAMP:20260315T011557Z UID:Geolis/53 DESCRIPTION:Title: On stratifications and moduli\nby Olivia Dumitrescu (University of Nor th Carolina at Chapel Hill) as part of Geometria em Lisboa (IST)\n\n\nAbst ract\nThere exist two approaches to the conformal limit mechanism: first w as defined by Gaiotto using Analysis techniques and the method of computin g was first established for the Hitchin Section and Opers in 2016. The sec ond approach to conformal limits as algebraic shifts via extension classes of vector bundles was established by Dumitrescu and Mulase in 2017 for th e lagrangians Hitchin section and opers. In this talk I will report on wor k in progress with Jennifer Brown and Motohico Mulase of the algebraic app roach of conformal limits to a family of Lagrangians covering the Dolbeaul t and the De Rham moduli space of Higgs bundles and irreducible connection s over a curve in rank 2.\n LOCATION:https://researchseminars.org/talk/Geolis/53/ END:VEVENT BEGIN:VEVENT SUMMARY:Umberto Hryniewicz (Aachen University) DTSTART:20210727T160000Z DTEND:20210727T170000Z DTSTAMP:20260315T011557Z UID:Geolis/54 DESCRIPTION:Title: Contact three-manifolds with exactly two simple Reeb orbits\nby Umbert o Hryniewicz (Aachen University) as part of Geometria em Lisboa (IST)\n\n\ nAbstract\nThe goal of this talk is to present a complete characterization of Reeb flows on closed 3-manifolds with precisely two periodic orbits. T he main step consists in showing that a contact form with exactly two peri odic Reeb orbits is non-degenerate. The proof combines the ECH volume form ula with a study of the behavior of the ECH index under non-degenerate per turbations of the contact form. As a consequence\, the ambient contact 3-m anifold is a standard lens space\, the contact form is dynamically convex\ , the Reeb flow admits a rational disk-like global surface of section and the dynamics are described by a pseudorotation of the 2-disk. Moreover\, t he periods and rotation numbers of the closed orbits satisfy the same rela tions as (quotients of) irrational ellipsoids\, and in the case of S^3 the transverse knot-type of the periodic orbits is determined. Joint work wit h Cristofaro-Gardiner\, Hutchings and Liu.\n LOCATION:https://researchseminars.org/talk/Geolis/54/ END:VEVENT BEGIN:VEVENT SUMMARY:Daniele Alessandrini (Columbia University) DTSTART:20210907T153000Z DTEND:20210907T163000Z DTSTAMP:20260315T011557Z UID:Geolis/55 DESCRIPTION:Title: The nilpotent cone in rank one and minimal surfaces\nby Daniele Alessa ndrini (Columbia University) as part of Geometria em Lisboa (IST)\n\n\nAbs tract\nI will describe two interesting and closely related moduli spaces: the nilpotent cone in the moduli spaces of Higgs bundles for SL_2(C) and P SL_2(C)\, and the moduli space of equivariant minimal surfaces in the hype rbolic 3-space.\nA deep understanding of these objects is important becaus e of their relations with several fundamental constructions in geometry: s ingular fibers of the Hitchin fibration\, branes\, mirror symmetry\, branc hed hyperbolic structures\, minimal surfaces in hyperbolic 3-manifolds and so on.\n\nA stratification of the nilpotent cone is well known and was re discovered by many people. The closures of the strata are the irreducible components of the nilpotent cone. The talk will focus on describing the in tersections between the different irreducible components.\n\nThis is joint work with Qiongling Li and Andrew Sanders\n LOCATION:https://researchseminars.org/talk/Geolis/55/ END:VEVENT BEGIN:VEVENT SUMMARY:Christine Breiner (Brown University) DTSTART:20210914T150000Z DTEND:20210914T160000Z DTSTAMP:20260315T011557Z UID:Geolis/56 DESCRIPTION:Title: Harmonic branched coverings and uniformization of CAT(k) spheres\nby C hristine Breiner (Brown University) as part of Geometria em Lisboa (IST)\n \n\nAbstract\nConsider a metric space $(S\,d)$ with an upper curvature bou nd in the sense of Alexandrov (i.e.~via triangle comparison). We show that if $(S\,d)$ is homeomorphically equivalent to the $2$-sphere\, then it is conformally equivalent to the $2$-sphere. The method of proof is through harmonic maps\, and we show that the conformal equivalence is achieved by an almost conformal harmonic map. The proof relies on the analysis of the local behavior of harmonic maps between surfaces\, and the key step is to show that an almost conformal harmonic map from a compact surface onto a s urface with an upper curvature bound is a branched covering. This work is joint with Chikako Mese.\n LOCATION:https://researchseminars.org/talk/Geolis/56/ END:VEVENT BEGIN:VEVENT SUMMARY:Barbara Fantechi (SISSA) DTSTART:20210928T153000Z DTEND:20210928T163000Z DTSTAMP:20260315T011557Z UID:Geolis/57 DESCRIPTION:Title: Smoothability of non normal stable Gorenstein Godeaux surfaces\nby Bar bara Fantechi (SISSA) as part of Geometria em Lisboa (IST)\n\n\nAbstract\n This is joint work with Marco Franciosi and Rita Pardini.\n\nGodeaux surfa ces\, with $K^2=1$ and $p_g=q=0$\, are the (complex projective) surfaces o f general type with the smallest possible invariants. A complete classific ation\, i.e. an understanding of their moduli space\, has been an open pro blem for many decades.\n\nThe KSBA (after Kollár\, Sheperd-Barron and Ale xeev) compactification of the moduli includes so called stable surfaces. F ranciosi\, Pardini and Rollenske classified all such surfaces in the bound ary which are Gorenstein (i.e.\, not too singular).\n\nWe prove that most of these surfaces corresponds to a point in the moduli which is nonsingula r of the expected dimension 8. We expect that the methods used (which incl ude classical and recent infinitesimal deformation theory\, as well as alg ebraic stacks and the cotangent complex) can be applied to all cases\, and to more general moduli as well.\n\nThe talk is aimed at a non specialist mathematical audience\, and will focus on the less technical aspects of th e paper.\n LOCATION:https://researchseminars.org/talk/Geolis/57/ END:VEVENT BEGIN:VEVENT SUMMARY:Felix Schlenk (Université de Neuchâtel) DTSTART:20211012T153000Z DTEND:20211012T163000Z DTSTAMP:20260315T011557Z UID:Geolis/58 DESCRIPTION:Title: On the group of symplectomorphisms of starshaped domains\nby Felix Sch lenk (Université de Neuchâtel) as part of Geometria em Lisboa (IST)\n\n\ nAbstract\nTake a simply connected compact domain $K$ in $\\mathbb R^{2n}$ with smooth boundary. We study the topology of the group $\\mathrm{Symp} (K)$ of those symplectomorphisms of $K$ that are defined on a neighbourhoo d of $K$. A main tool is a Serre fibration $\\mathrm{Symp} (K) \\to \\math rm{SCont} (\\partial K)$ to the group of strict contactomorphisms of the b oundary. The fiber is contractible if $K$ is 4-dimensional and starshaped\ , by Gromov's theorem. The topology (or at least the connectivity) of the group $\\mathrm{SCont} (\\partial K)$ can be understood in many examples. In case this group is connected\, so is $\\mathrm{Symp} (K)$. This has app lications to the problem of understanding the topology of the space of sym plectic embeddings of $K$ into any symplectic manifold. If $\\mathrm{Symp} (K)$ is connected\, then for embeddings that are not related by an ambien t symplectomorphism there is not even an ambient symplectomorphism that ma ps one image to the other. \n\nThe talk is based on work with Joé Brendel and Grisha Mikhalkin.\n LOCATION:https://researchseminars.org/talk/Geolis/58/ END:VEVENT BEGIN:VEVENT SUMMARY:Pranav Chakravarthy (Hebrew University of Jerusalem) DTSTART:20211102T163000Z DTEND:20211102T173000Z DTSTAMP:20260315T011557Z UID:Geolis/59 DESCRIPTION:Title: Homotopy type of equivariant symplectomorphisms of rational ruled surfaces \nby Pranav Chakravarthy (Hebrew University of Jerusalem) as part of G eometria em Lisboa (IST)\n\n\nAbstract\nIn this talk\, we present results on the homotopy type of the group of equivariant symplectomorphisms of $S^ 2 \\times S^2$ and $CP^2$ blown up once\, under the presence of Hamiltonia n group actions of either $S^1$ or finite cyclic groups. For Hamiltonian c ircle actions\, we prove that the centralizers are homotopy equivalent to either a torus or to the homotopy pushout of two tori depending on whether the circle action extends to a single toric action or to exactly two non- equivalent toric actions. We can show that the same holds for the centrali zers of most finite cyclic groups in the Hamiltonian group. Our results re ly on J-holomorphic techniques\, on Delzant's classification of toric acti ons\, on Karshon's classification of Hamiltonian circle actions on 4-manif olds\, and on the Chen-Wilczynski smooth classification of $\\mathbb Z_n$- actions on Hirzebruch surfaces.\n LOCATION:https://researchseminars.org/talk/Geolis/59/ END:VEVENT BEGIN:VEVENT SUMMARY:Ciprian Manolescu (Standford University) DTSTART:20211207T163000Z DTEND:20211207T173000Z DTSTAMP:20260315T011557Z UID:Geolis/61 DESCRIPTION:Title: Khovanov homology and the search for exotic 4-spheres\nby Ciprian Mano lescu (Standford University) as part of Geometria em Lisboa (IST)\n\n\nAbs tract\nA well-known strategy to disprove the smooth 4D Poincare conjecture is to find a knot that bounds a disk in a homotopy 4-ball but not in the standard 4-ball. Freedman\, Gompf\, Morrison and Walker suggested that Ras mussen’s invariant from Khovanov homology could be useful for this purpo se. I will describe three recent results about this strategy: that it fail s for Gluck twists (joint work with Marengon\, Sarkar and Willis)\; that a n analogue works for other 4-manifolds (joint work with Marengon and Picci rillo)\; and that 0-surgery homeomorphisms provide a large class of potent ial examples (joint work with Piccirillo).\n LOCATION:https://researchseminars.org/talk/Geolis/61/ END:VEVENT BEGIN:VEVENT SUMMARY:Luca Asselle (Ruhr University Bochum) DTSTART:20211019T153000Z DTEND:20211019T163000Z DTSTAMP:20260315T011557Z UID:Geolis/62 DESCRIPTION:Title: A Morse complex for the Hamiltonian action in cotangent bundles\nby Lu ca Asselle (Ruhr University Bochum) as part of Geometria em Lisboa (IST)\n \n\nAbstract\nCritical points having infinite Morse index and co-index are invisible to homotopy theory\, since attaching an infinite dimensional ce ll does not produce any change in the topology of sublevel sets. Therefore \, no classical Morse theory can possibly exist for strongly indefinite fu nctionals (i.e. functionals whose all critical points have infinite Morse index and co-index). In this talk\, we will briefly explain how to instead construct a Morse complex for certain classes of strongly indefinite func tionals on a Hilbert manifold by looking at the intersection between stabl e and unstable manifolds of critical points whose difference of (suitably defined) relative indices is one. As a concrete example\, we will consider the case of the Hamiltonian action functional defined by a smooth time-pe riodic Hamiltonian $H: S^1 \\times T^*Q \\to \\mathbb R$\, where $T^*Q$ is the cotangent bundle of a closed manifold $Q$. As one expects\, in this c ase the resulting Morse homology is isomorphic to the Floer homology of $T ^*Q$\, however the Morse complex approach has several advantages over Floe r homology which will be discussed if time permits. This is joint work wit h Alberto Abbondandolo and Maciej Starostka.\n LOCATION:https://researchseminars.org/talk/Geolis/62/ END:VEVENT BEGIN:VEVENT SUMMARY:Ely Kerman (University of Illinois Urbana-Champaign) DTSTART:20211123T163000Z DTEND:20211123T173000Z DTSTAMP:20260315T011557Z UID:Geolis/63 DESCRIPTION:Title: On symplectic capacities and their blind spots\nby Ely Kerman (Univers ity of Illinois Urbana-Champaign) as part of Geometria em Lisboa (IST)\n\n \nAbstract\nIn this talk I will discuss a joint work with Yuanpu Liang in which we establish some results concerning the symplectic capacities defin ed by Gutt and Hutchings using $S^1$-equivariant symplectic homology. Our primary result settles a version of the recognition question in the negati ve. We prove that the Gutt-Hutchings capacities\, together with the volume \, do not constitute a complete set of symplectic invariants for star-shap ed (in fact convex) domains with smooth boundary. We also prove that\, eve n for star-shaped domains with smooth boundaries\, these capacities are mu tually independent and are independent from the volume. The constructions that demonstrate these independence properties​ are not exotic. They are convex and concave toric domains. The new tool used here is a significant simplification of the formulae of Gutt and Hutchings for the capacities o f convex/concave toric domains\, that holds under an additional symmetry a ssumption. This allows us to identify new mutual blind spots of the capaci ties which are then used to construct the desired examples.\n LOCATION:https://researchseminars.org/talk/Geolis/63/ END:VEVENT BEGIN:VEVENT SUMMARY:Henrique Bursztyn (IMPA) DTSTART:20211116T163000Z DTEND:20211116T173000Z DTSTAMP:20260315T011557Z UID:Geolis/64 DESCRIPTION:Title: Revisiting and extending Poisson-Nijenhuis structures\nby Henrique Bur sztyn (IMPA) as part of Geometria em Lisboa (IST)\n\n\nAbstract\nPoisson-N ijenhuis structures arise in various settings\, such as the theory of inte grable systems\, Poisson-Lie theory and quantization. By revisiting this notion from a new viewpoint\, I will show how it can be naturally extended to the realm of Dirac structures\, with applications to integration resul ts in (holomorphic) Poisson geometry.\n LOCATION:https://researchseminars.org/talk/Geolis/64/ END:VEVENT BEGIN:VEVENT SUMMARY:André Neves (University of Chicago) DTSTART:20211026T153000Z DTEND:20211026T163000Z DTSTAMP:20260315T011557Z UID:Geolis/65 DESCRIPTION:Title: Minimal surfaces in hyperbolic manifolds\nby André Neves (University of Chicago) as part of Geometria em Lisboa (IST)\n\n\nAbstract\nThe study of geodesics in negatively curved manifolds is a rich subject which has be en at the core of geometry and dynamical systems. Comparatively\, much les s is known about minimal surfaces on those spaces. I will survey some of t he recent progress in that area.\n LOCATION:https://researchseminars.org/talk/Geolis/65/ END:VEVENT BEGIN:VEVENT SUMMARY:Carlos Florentino (Faculty of Sciences - University of Lisbon) DTSTART:20211109T163000Z DTEND:20211109T173000Z DTSTAMP:20260315T011557Z UID:Geolis/66 DESCRIPTION:Title: The geometry of commuting varieties of reductive groups\nby Carlos Flo rentino (Faculty of Sciences - University of Lisbon) as part of Geometria em Lisboa (IST)\n\n\nAbstract\nLet $R_r(G)$ be the (connected component of the identity of the) variety of commuting $r$-tuples of elements of a com plex reductive group $G$. We determine the mixed Hodge structure on the co homology of the representation variety $R_r(G)$ and of the character varie ty $R_r(G)/G$\, for general $r$ and $G$. We also obtain explicit formulae (both closed and recursive) for the mixed Hodge polynomials\, Poincaré po lynomials and Euler characteristics of these representation and character varieties. In the character variety case\, this gives the counting polynom ial over finite fields\, and some results also apply to character varietie s of nilpotent groups.\n\nThis is joint work with S. Lawton and J. Silva ( arXiv:2110.07060).\n LOCATION:https://researchseminars.org/talk/Geolis/66/ END:VEVENT BEGIN:VEVENT SUMMARY:Alfonso Zamora (Polytechnic University of Madrid) DTSTART:20211130T163000Z DTEND:20211130T173000Z DTSTAMP:20260315T011557Z UID:Geolis/67 DESCRIPTION:Title: E-polynomials and geometry of character varieties\nby Alfonso Zamora ( Polytechnic University of Madrid) as part of Geometria em Lisboa (IST)\n\n Abstract: TBA\n LOCATION:https://researchseminars.org/talk/Geolis/67/ END:VEVENT BEGIN:VEVENT SUMMARY:Hossein Movasati (IMPA) DTSTART:20220118T163000Z DTEND:20220118T173000Z DTSTAMP:20260315T011557Z UID:Geolis/68 DESCRIPTION:Title: A quest for new theories of automorphic forms: Gauss-Manin connection in d isguise\nby Hossein Movasati (IMPA) as part of Geometria em Lisboa (IS T)\n\n\nAbstract\nIn this talk I will consider a moduli space of projectiv e varieties enhanced with a certain frame of its cohomology bundle. In man y examples such as elliptic curves\, abelian varieties and Calabi-Yau vari eties\, and conjecturally in general\, this moduli space is a quasi-affine variety. There are certain vector fields on this moduli which are algebra ic incarnation of differential equations of automorphic forms. Using these vector fields one can construct foliations with algebraic leaves related to Hodge loci. The talk is based on my book "Modular and Automorphic Forms & Beyond\, Monographs in Number Theory\, World Scientific (2021)" in whic h the Tupi name ibiporanga (pretty land) for such a moduli space is sugges ted.\n LOCATION:https://researchseminars.org/talk/Geolis/68/ END:VEVENT BEGIN:VEVENT SUMMARY:Lars Sketnan (University of Gothenburg) DTSTART:20220111T163000Z DTEND:20220111T173000Z DTSTAMP:20260315T011557Z UID:Geolis/69 DESCRIPTION:Title: Blowing up extremal Kähler manifolds\nby Lars Sketnan (University of Gothenburg) as part of Geometria em Lisboa (IST)\n\n\nAbstract\nExtremal K ähler metrics were introduced by Calabi in the 80’s as a type of canoni cal Kähler metric on a Kähler manifold\, and are a generalisation of con stant scalar curvature Kähler metrics in the case when the manifold admit s automorphisms. A natural question is when the blowup of a manifold in a point admits an extremal Kähler metric. We completely settle the question in terms of a finite dimensional moment map/GIT condition\, generalising work of Arezzo-Pacard\, Arezzo-Pacard-Singer and Székelyhidi. Our methods also allow us to deal with a certain semistable case that has not been co nsidered before\, where the original manifold does not admit an extremal m etric\, but is infinitesimally close to doing so. As a consequence of this \, we solve the first non-trivial special case of a conjecture of Donaldso n. This is joint work with Ruadhaí Dervan.\n LOCATION:https://researchseminars.org/talk/Geolis/69/ END:VEVENT BEGIN:VEVENT SUMMARY:Eva Miranda (Universitat Politècnica de Catalunya) DTSTART:20211221T163000Z DTEND:20211221T173000Z DTSTAMP:20260315T011557Z UID:Geolis/70 DESCRIPTION:Title: Looking at the Euler flows through a contact mirror\nby Eva Miranda (U niversitat Politècnica de Catalunya) as part of Geometria em Lisboa (IST) \n\n\nAbstract\nThe dynamics of an inviscid and incompressible fluid flow on a Riemannian manifold is governed by the Euler equations. Recently\, Ta o [6\, 7\, 8] launched a programme to address the global existence problem for the Euler and Navier-Stokes equations based on the concept of univers ality. Inspired by this proposal\, we show that the stationary Euler equat ions exhibit several universality features\, in the sense that\, any non-a utonomous flow on a compact manifold can be extended to a smooth stationar y solution of the Euler equations on some Riemannian manifold of possibly higher dimension [1].\n\nA key point in the proof is looking at the h-prin ciple in contact geometry through a contact mirror\, unveiled by Etnyre an d Ghrist in [4] more than two decades ago. We end this talk addressing a q uestion raised by Moore in [5] : “Is hydrodynamics capable of performing computations?”. The universality result above yields the Turing complet eness of the steady Euler flows on a 17-dimensional sphere. Can this resul t be improved? In [2] we construct a Turing complete steady Euler flow in dimension 3. Time permitting\, we discuss this and other generalizations f or t-dependent Euler flows contained in [3].\n\nIn all the constructions a bove\, the metric is seen as an additional "variable" and thus the method of proof does not work if the metric is prescribed.\n\nIs it still possibl e to construct a Turing complete Euler flow on a 3-dimensional space with the standard metric? Yes\, see our recent preprint https://arxiv.org/abs/2 111.03559 (joint with Cardona and Peralta).\n\nThis talk is based on sever al joint works with Cardona\, Peralta-Salas and Presas.\n\n[1] R. Cardona\ , E. Miranda\, D. Peralta-Salas\, F. Presas. Universality of Euler flows a nd flexibility of Reeb embeddings\, arXiv:1911.01963.\n\n[2] R. Cardona\, E. Miranda\, D. Peralta-Salas\, F. Presas. Constructing Turing complete Eu ler flows in dimension 3. PNAS May 11\, 2021 118 (19) e2026818118\; https: //doi.org/10.1073/pnas.2026818118.\n\n[3] R. Cardona\, E. Miranda and D. P eralta-Salas\, Turing universality of the incompressible Euler equations a nd a conjecture of Moore\, International Mathematics Research Notices\, rn ab233\, https://doi.org/10.1093/imrn/rnab233\n\n[4] J. Etnyre\, R. Ghrist. Contact topology and hydrodynamics I. Beltrami fields and the Seifert con jecture. Nonlinearity 13 (2000) 441–458.\n\n[5] C. Moore. Generalized sh ifts: unpredictability and undecidability in dynamical systems. Nonlineari ty 4 (1991) 199–230.\n\n[6] T. Tao. On the universality of potential wel l dynamics. Dyn. PDE 14 (2017) 219–238.\n\n[7] T. Tao. On the universali ty of the incompressible Euler equation on compact manifolds. Discrete Con t. Dyn. Sys. A 38 (2018) 1553–1565.\n\n[8] T. Tao. Searching for singula rities in the Navier-Stokes equations. Nature Rev. Phys. 1 (2019) 418–41 9.\n LOCATION:https://researchseminars.org/talk/Geolis/70/ END:VEVENT BEGIN:VEVENT SUMMARY:Jonny Evans (University of Lancaster) DTSTART:20220208T163000Z DTEND:20220208T173000Z DTSTAMP:20260315T011557Z UID:Geolis/71 DESCRIPTION:Title: Symplectic cohomology of compound Du Val singularities\nby Jonny Evans (University of Lancaster) as part of Geometria em Lisboa (IST)\n\n\nAbstr act\n(Joint with Y. Lekili) If someone gives you a variety with a singular point\, you can try and get some understanding of what the singularity lo oks like by taking its “link”\, that is you take the boundary of a nei ghbourhood of the singular point. For example\, the link of the complex pl ane curve with a cusp y^2 = x^3 is a trefoil knot in the 3-sphere. I want to talk about the links of a class of 3-fold singularities which come up i n Mori theory: the compound Du Val (cDV) singularities. These links are 5- dimensional manifolds. It turns out that many cDV singularities have the s ame 5-manifold as their link\, and to tell them apart you need to keep tra ck of some extra structure (a contact structure). We use symplectic cohomo logy to distinguish the contact structures on many of these links.\n LOCATION:https://researchseminars.org/talk/Geolis/71/ END:VEVENT BEGIN:VEVENT SUMMARY:Johannes Horn (Johann Wolfgang Goethe-Universität in Frankfurt) DTSTART:20220201T163000Z DTEND:20220201T173000Z DTSTAMP:20260315T011557Z UID:Geolis/72 DESCRIPTION:Title: Resolving the rank 2 Hitchin system by compactified Jacobians of semi-stab le curves\nby Johannes Horn (Johann Wolfgang Goethe-Universität in Fr ankfurt) as part of Geometria em Lisboa (IST)\n\n\nAbstract\n(joint work w ith M. Möller) The complexity of singular fibers of the Hitchin system st ems from the variety of singularities of the spectral curve. In this talk I will explain how to modify the rank 2 Hitchin base\, such that the famil y of spectral curves can be resolved to a family of semi-stable nodal curv es. This allows to extend the Hitchin system to the singular locus of the modified Hitchin base by well-understood compactified Jacobians of semi-st able curves\n LOCATION:https://researchseminars.org/talk/Geolis/72/ END:VEVENT BEGIN:VEVENT SUMMARY:Giancarlo Urzua (Pontificia Universidad Católica de Chile) DTSTART:20220125T163000Z DTEND:20220125T173000Z DTSTAMP:20260315T011557Z UID:Geolis/74 DESCRIPTION:Title: What is the right combinatorics for spheres in K3 surfaces?\nby Gianca rlo Urzua (Pontificia Universidad Católica de Chile) as part of Geometria em Lisboa (IST)\n\n\nAbstract\nTogether with Javier Reyes\, in https://ar xiv.org/abs/2110.10629 we have been able to construct compact 4-manifolds $3\\mathbb{CP}^2\\#(19-K^2)\\overline{\\mathbb{CP}}^2$ with complex struct ures for $K^2=1\,2\,3\,4\,5\,6\,7\,8\,9$. The cases $K^2=7\,9$ are complet ely new in the literature\, and this finishes with the whole range allowed by the technique of Q-Gorenstein smoothing (rational blow-down). But one can go further: Is it possible to find minimal exotic $3\\mathbb{CP}^2\\#( 19-K^2)\\overline{\\mathbb{CP}}^2$ for $K^2\\geq10$? Here it would be much harder to prove the existence of complex structures\, but\, as a motivati on\, there is not even one example for $K^2 > 15$\, and very few for $10 \ \leq K^2 \\leq 15$ (see e.g. works by Akhmedov\, Park\, Baykur). In this t alk I will explain the constructions in connection with the geography of s pheres arrangements in $K3$ surfaces\, where the question of the title ari ses. We do not have an answer. So far we have been implementing what we kn ow in computer searches\, finding these very rare exotic surfaces for $K^2 =10\,11\,12$. This is a new and huge world which promises more findings\, we have explored very little.\n LOCATION:https://researchseminars.org/talk/Geolis/74/ END:VEVENT BEGIN:VEVENT SUMMARY:Louis Ioos (Max Planck Institute for Mathematics (Bonn)) DTSTART:20220222T163000Z DTEND:20220222T173000Z DTSTAMP:20260315T011557Z UID:Geolis/75 DESCRIPTION:Title: Berezin-Toeplitz quantization in the Yau-Tian-Donaldson program\nby Lo uis Ioos (Max Planck Institute for Mathematics (Bonn)) as part of Geometri a em Lisboa (IST)\n\n\nAbstract\nA celebrated conjecture of Yau states tha t the existence of a Kähler metric of constant scalar curvature on a proj ective manifold should be equivalent to a purely algebraic stability condi tion. Much progress have been done on this conjecture\, which culminated i n what is now called the Yau-Tian-Donaldson program. In this talk\, I will explain the key role played by quantization methods in this program\, and how they can be improved by a semiclassical study of the quantum noise of Berezin-Toeplitz quantization.\nThis is partly based on joint works in co llaboration with Victoria Kaminker\, Leonid Polterovich and Dor Shmoish.\n LOCATION:https://researchseminars.org/talk/Geolis/75/ END:VEVENT BEGIN:VEVENT SUMMARY:Richard Hind (University of Notre Dame) DTSTART:20220215T163000Z DTEND:20220215T173000Z DTSTAMP:20260315T011557Z UID:Geolis/76 DESCRIPTION:Title: The Gromov width of Lagrangian complements\nby Richard Hind (Universit y of Notre Dame) as part of Geometria em Lisboa (IST)\n\n\nAbstract\nQuest ions can be motivated from dynamical systems about the size of complements of a disjoint collection of Lagrangian tori in a symplectic manifold. We will discuss the simplest case\, namely the complement of the integral pro duct Lagrangians\, $L(k\,l)$ with $k\,l \\in \\mathbb{N}$\, inside $\\math bb{C}^2$. Here $L(k\,l) = \\{ |z_1| = k\, |z_2|=l \\}$. We will make some computations of the Gromov width and then describe joint work with Ely Ker man on the existence of Lagrangian tori in the complement.\n LOCATION:https://researchseminars.org/talk/Geolis/76/ END:VEVENT BEGIN:VEVENT SUMMARY:Joel Fine (Université Libre de Bruxelles) DTSTART:20220315T163000Z DTEND:20220315T173000Z DTSTAMP:20260315T011557Z UID:Geolis/77 DESCRIPTION:Title: Knots\, minimal surfaces and J-holomorphic curves\nby Joel Fine (Unive rsité Libre de Bruxelles) as part of Geometria em Lisboa (IST)\n\n\nAbstr act\nLet K be a knot in the 3-sphere. I will explain how one can count min imal discs in hyperbolic 4-space which have ideal boundary equal to K\, an d in this way obtain a knot invariant. In other words the number of minima l discs depends only on the isotopy class of the knot. I think it should a ctually be possible to define a family of link invariants\, counting minim al surfaces filling links\, but at this stage this is still just a conject ure. “Counting minimal surfaces” needs to be interpreted carefully her e\, similar to how Gromov-Witten invariants “count” J-holomorphic curv es. Indeed I will explain how these counts of minimal discs can be seen as Gromov-Witten invariants for the twistor space of hyperbolic 4-space. Whi lst Gromov-Witten theory suggests the overall strategy for defining the mi nimal surface link-invariant\, there are significant differences in how to actually implement it. This is because the geometry of both hyperbolic sp ace and its twistor space become singular at infinity. As a consequence\, the PDEs involved (both the minimal surface equation and J-holomorphic cur ve equation) are degenerate rather than elliptic at the boundary. I will t ry and explain how to overcome these complications.\n LOCATION:https://researchseminars.org/talk/Geolis/77/ END:VEVENT BEGIN:VEVENT SUMMARY:Ana Peón-Nieto (University of Birmingham) DTSTART:20220308T160000Z DTEND:20220308T170000Z DTSTAMP:20260315T011557Z UID:Geolis/78 DESCRIPTION:Title: Higher wobbly bundles\nby Ana Peón-Nieto (University of Birmingham) a s part of Geometria em Lisboa (IST)\n\n\nAbstract\nWobbly bundles are the complement to very stable bundles\, a dense open set of the moduli space o f vector bundles. This notion was generalised to arbitrary fixed points of the C* action on the moduli space of Higgs bundles by Hausel and Hitchin. In this talk\, after introducing the meaningful notions and motivating th em\, I will analyse the geometry of higher wobbly components in rank three . In particular\, I will focus on an extension of Drinfeld's conjecture ab out pure codimensionality of the wobbly locus\, as well as the relation wi th real forms. This is joint work with Pauly.\n LOCATION:https://researchseminars.org/talk/Geolis/78/ END:VEVENT BEGIN:VEVENT SUMMARY:Christian Pauly (Université de Nice Sophia-Antipolis) DTSTART:20220405T150000Z DTEND:20220405T160000Z DTSTAMP:20260315T011557Z UID:Geolis/79 DESCRIPTION:Title: On very stable bundles\nby Christian Pauly (Université de Nice Sophia -Antipolis) as part of Geometria em Lisboa (IST)\n\n\nAbstract\nA very sta ble vector bundle over a curve is a vector bundle having no non-zero nilpo tent Higgs fields. They were introduced by Drinfeld and studied by Laumon in connection with the nilpotent cone of the Hitchin system. According to Drinfeld non-very stable bundles\, also called wobbly bundles\, form a div isor in the moduli space of vector bundles. In this talk I will try to exp lain the motivations for studying the properties of wobbly divisors\, with a special focus on the rank-2 (joint work with S. Pal) and rank-3 case (j oint work with A. Peon-Nieto).\n LOCATION:https://researchseminars.org/talk/Geolis/79/ END:VEVENT BEGIN:VEVENT SUMMARY:Michael R. Douglas (Simons Center for Geometry and Physics) DTSTART:20220412T150000Z DTEND:20220412T160000Z DTSTAMP:20260315T011557Z UID:Geolis/80 DESCRIPTION:Title: Holomorphic feedforward networks\nby Michael R. Douglas (Simons Center for Geometry and Physics) as part of Geometria em Lisboa (IST)\n\n\nAbstr act\nA very popular model in machine learning is the feedforward neural ne twork (FFN). After a brief introduction to machine learning\, we describe FFNs which represent sections of holomorphic line bundles on complex manif olds\, and software which uses them to get numerical approximations to Ric ci flat Kähler metrics.\n LOCATION:https://researchseminars.org/talk/Geolis/80/ END:VEVENT BEGIN:VEVENT SUMMARY:Yang Zhou (Shanghai Center for Mathematical Sciences\, Fudan Unive rsity) DTSTART:20220322T100000Z DTEND:20220322T110000Z DTSTAMP:20260315T011557Z UID:Geolis/81 DESCRIPTION:Title: Quasimap wall-crossing in enumerative geometry\nby Yang Zhou (Shanghai Center for Mathematical Sciences\, Fudan University) as part of Geometria em Lisboa (IST)\n\n\nAbstract\nThe theory of Gromov-Witten invariants is a curve counting theory defined by integration on the moduli of stable map s. Varying the stability condition gives alternative compactifications of the moduli space and defines similar invariants. One example is epsilon-st able quasimaps\, defined for a large class of GIT quotients. When epsilon tends to infinity\, one recovers Gromov-Witten invariants. When epsilon te nds to zero\, the invariants are closely related to the B-model in physics . The space of epsilon's has a wall-and-chamber structure. In this talk\, I will explain how wall-crossing helps to compute the Gromov-Witten invari ants and sketch a proof of the wall-crossing formula.\n LOCATION:https://researchseminars.org/talk/Geolis/81/ END:VEVENT BEGIN:VEVENT SUMMARY:Jun Li (University of Michigan-Ann Arbor) DTSTART:20220329T150000Z DTEND:20220329T160000Z DTSTAMP:20260315T011557Z UID:Geolis/82 DESCRIPTION:Title: Stability and isotopy of symplectomorphism groups of ruled surfaces\nb y Jun Li (University of Michigan-Ann Arbor) as part of Geometria em Lisboa (IST)\n\n\nAbstract\nThe symplectomorphism groups $Symp(M\, \\omega)$ of ruled surfaces have been started by Gromov\, McDuff\, and Abreu\, etc\, us ing J-holomorphic techniques. For rational ruled surfaces\, the topologica l structure of $Symp(M\, \\omega)$ is better understood\, while for irrati onal cases our only knowledge is for minimal ruled surfaces. In this talk\ , we apply the J-inflation techniques of Anjos-Li-Li-Pinsonnault to irrati onal non-minimal ruled surfaces and prove a stability result for $Symp(M\, \\omega)$. As an application\, we find symplectic mapping classes that ar e smoothly but not symplectically isotopic to identity. The talk is based on joint works with Olguta Buse.\n LOCATION:https://researchseminars.org/talk/Geolis/82/ END:VEVENT BEGIN:VEVENT SUMMARY:Miguel Abreu (Instituto Superior Técnico - University of Lisbon) DTSTART:20220510T150000Z DTEND:20220510T160000Z DTSTAMP:20260315T011557Z UID:Geolis/83 DESCRIPTION:Title: Contact invariants of Q-Gorenstein toric contact manifolds and the Ehrhart (quasi-) polynomials of their toric diagrams\nby Miguel Abreu (Instit uto Superior Técnico - University of Lisbon) as part of Geometria em Lisb oa (IST)\n\n\nAbstract\nQ-Gorenstein toric contact manifolds provide an in teresting class of examples of contact manifolds with torsion first Chern class. They are completely determined by certain rational convex polytopes \, called toric diagrams. The main goal of this talk is to describe how th e cylindrical contact homology invariants of a Q-Gorenstein toric contact manifold are related to the Ehrhart (quasi-)polynomial of its toric diagra m. This is part of joint work with Leonardo Macarini and Miguel Moreira (a rXiv:2202.00442).\n LOCATION:https://researchseminars.org/talk/Geolis/83/ END:VEVENT BEGIN:VEVENT SUMMARY:Vincent Humilière (Institut de Mathématiques de Jussieu - Paris Rive Gauche) DTSTART:20220517T150000Z DTEND:20220517T160000Z DTSTAMP:20260315T011557Z UID:Geolis/84 DESCRIPTION:Title: Groups of area preserving homeomorphisms and their simplicity\nby Vinc ent Humilière (Institut de Mathématiques de Jussieu - Paris Rive Gauche) as part of Geometria em Lisboa (IST)\n\n\nAbstract\nAlbert Fathi proved i n the late 70's that the group of volume preserving homeomorphisms of the n-sphere is simple for n at least 3\, but the case of the 2-sphere remaine d open until recently. In this talk\, I will present results obtained in s everal works with Dan Cristofaro-Gardiner\, Cheuk-Yu Mak\, Sobhan Seyfaddi ni and Ivan Smith on the structure of the group of area preserving homeomo rphisms of surfaces\, which include in particular a solution of this probl em. Even if the considered objects are not smooth (they are just homeomorp hisms)\, the tools we use come from symplectic topology.\n LOCATION:https://researchseminars.org/talk/Geolis/84/ END:VEVENT BEGIN:VEVENT SUMMARY:Miguel Pereira (University of Augsburg) DTSTART:20220419T150000Z DTEND:20220419T160000Z DTSTAMP:20260315T011557Z UID:Geolis/85 DESCRIPTION:Title: The Lagrangian capacity of toric domains\nby Miguel Pereira (Universit y of Augsburg) as part of Geometria em Lisboa (IST)\n\n\nAbstract\nA sympl ectic capacity is a functor that to each symplectic manifold (possibly in a restricted subclass) assigns a nonnegative number. The Lagrangian capaci ty is an example of such an object. In this talk\, I will state a conjectu re concerning the Lagrangian capacity of a toric domain. Then\, I will pre sent two results concerning this conjecture. First\, I will explain a proo f of the conjecture in the case where the toric domain is convex and 4-dim ensional. This proof makes use of the Gutt-Hutchings capacities as well as the McDuff-Siegel capacities. Second\, I will explain a proof of the conj ecture in full generality\, but assuming the existence of a suitable virtu al perturbation scheme which defines the curve counts of linearized contac t homology. This second proof makes use of Siegel's higher symplectic capa cities.\n LOCATION:https://researchseminars.org/talk/Geolis/85/ END:VEVENT BEGIN:VEVENT SUMMARY:Lucas Ambrozio (IMPA) DTSTART:20220426T150000Z DTEND:20220426T160000Z DTSTAMP:20260315T011557Z UID:Geolis/86 DESCRIPTION:Title: Analogues of Zoll surfaces in minimal surface theory\nby Lucas Ambrozi o (IMPA) as part of Geometria em Lisboa (IST)\n\n\nAbstract\nA Riemannian metric on a closed manifold is called Zoll when all of its geodesics are c losed and have the same period. An infinite dimensional family of Zoll met rics on the two-dimensional sphere were constructed by Otto Zoll in the be ginning of 1900's\, but many questions about them remain unanswered. In th is talk\, I will explain my motivation to look for higher dimensional anal ogues of Zoll metrics\, where closed geodesics are replaced by embedded mi nimal spheres of codimension one. Then\, I will discuss some recent result s about the construction and geometric understanding of these new geometri es. This is a joint project with F. Marques (Princeton) and A. Neves (UChi cago).\n LOCATION:https://researchseminars.org/talk/Geolis/86/ END:VEVENT BEGIN:VEVENT SUMMARY:Gleb Smirnov (University of Geneve) DTSTART:20220524T150000Z DTEND:20220524T160000Z DTSTAMP:20260315T011557Z UID:Geolis/87 DESCRIPTION:Title: Symplectic mapping class groups of K3 surfaces and gauge theory\nby Gl eb Smirnov (University of Geneve) as part of Geometria em Lisboa (IST)\n\n \nAbstract\nWe will discuss a simple proof that the symplectic mapping cla ss groups of many K3s are infinitely generated\, extending a recent result of Sheridan and Smith. The argument will be based on some basic family Se iberg-Witten theory and algebraic geometry.\n LOCATION:https://researchseminars.org/talk/Geolis/87/ END:VEVENT BEGIN:VEVENT SUMMARY:Vinicius Ramos (Instituto de Matemática Pura e Aplicada) DTSTART:20220607T150000Z DTEND:20220607T160000Z DTSTAMP:20260315T011557Z UID:Geolis/88 DESCRIPTION:Title: The Toda lattice and the Viterbo conjecture\nby Vinicius Ramos (Instit uto de Matemática Pura e Aplicada) as part of Geometria em Lisboa (IST)\n \n\nAbstract\nThe Toda lattice is one of the earliest examples of non-line ar completely integrable systems. Under a large deformation\, the Hamilton ian flow can be seen to converge to a billiard flow in a simplex. In the 1 970s\, action-angle coordinates were computed for the standard system usin g a non-canonical transformation and some spectral theory. In this talk\, I will explain how to adapt these coordinates to the situation to a large deformation and how this leads to new examples of symplectomorphisms of La grangian products with toric domains. In particular\, we find a sequence o f Lagrangian products whose symplectic systolic ratio is one and we prove that they are symplectomorphic to balls. This is joint work with Y. Ostrov er and D. Sepe.\n LOCATION:https://researchseminars.org/talk/Geolis/88/ END:VEVENT BEGIN:VEVENT SUMMARY:Michael Albanese (Université du Québec à Montréal) DTSTART:20220614T150000Z DTEND:20220614T160000Z DTSTAMP:20260315T011557Z UID:Geolis/89 DESCRIPTION:Title: The Yamabe Invariant of Complex Surfaces\nby Michael Albanese (Univers ité du Québec à Montréal) as part of Geometria em Lisboa (IST)\n\n\nAb stract\nThe Yamabe invariant is a real-valued diffeomorphism invariant com ing from Riemannian geometry. Using Seiberg-Witten theory\, LeBrun showed that the sign of the Yamabe invariant of a Kähler surface is determined b y its Kodaira dimension. We consider the extent to which this remains true when the Kähler hypothesis is removed. This is joint work with Claude Le Brun.\n LOCATION:https://researchseminars.org/talk/Geolis/89/ END:VEVENT BEGIN:VEVENT SUMMARY:Aleksandar Milivojevic (Max Planck Institute for Mathematics - Bon n) DTSTART:20220621T150000Z DTEND:20220621T160000Z DTSTAMP:20260315T011557Z UID:Geolis/90 DESCRIPTION:Title: Holomorphic notions of formality and Massey products\nby Aleksandar Mi livojevic (Max Planck Institute for Mathematics - Bonn) as part of Geometr ia em Lisboa (IST)\n\n\nAbstract\nI will discuss joint work with Jonas Ste lzig in which we consider the beginnings of a bigraded analogue of rationa l homotopy theory adapted to complex manifolds\, in a somewhat different f ashion than that of Neisendorfer-Taylor which appeared in the 1970’s soo n after Sullivan’s Infinitesimal Computations in Topology. Taking cues f rom an additive decomposition theorem for double complexes\, we define two natural notions of formality for our basic objects — commutative bigrad ed bidifferential algebras — which place both bigraded components of the de Rham differential on equal footing. These notions are related by the d dbar-lemma (the additive property used to show formality\, in the usual se nse\, of compact complex manifolds admitting a Kähler metric). We conside r obstructions to these notions of formality\, taking in Bott-Chern cohomo logy classes and outputting classes in a chain complex of Demailly-Schweit zer\, whose construction mimics those of classical Massey products and ext ends the triple products landing in Aeppli cohomology considered by Angell a-Tomassini\; we also touch upon their behavior under blow-ups and more ge nerally positive-degree holomorphic maps.\n LOCATION:https://researchseminars.org/talk/Geolis/90/ END:VEVENT BEGIN:VEVENT SUMMARY:Bruno de Oliveira (University of Miami) DTSTART:20220705T150000Z DTEND:20220705T160000Z DTSTAMP:20260315T011557Z UID:Geolis/91 DESCRIPTION:Title: $A_n$ singularities and bigness of the cotangent bundle\nby Bruno de O liveira (University of Miami) as part of Geometria em Lisboa (IST)\n\n\nAb stract\nIt is well known that for surfaces the positivity property of the cotangent bundle $\\Omega^1_X$ called bigness implies hyperbolic propertie s. We give a criterion for bigness of $\\Omega^1_X$ involving the singular ities of the canonical model of $X$ and compare it with other criterions. The criterion involves invariants of the canonical singularities whose val ues were unknown. We describe a method to find the invariants and obtain f ormulas for the $A_n$ singularities. An application of this work is to det ermine for which degrees do hypersurfaces in $\\mathbb {P}^3$ have deforma tions with big cotangent bundles and have symmetric differentials of low d egrees.\n LOCATION:https://researchseminars.org/talk/Geolis/91/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexander Givental (University of Berkeley) DTSTART:20220916T150000Z DTEND:20220916T160000Z DTSTAMP:20260315T011557Z UID:Geolis/92 DESCRIPTION:Title: K-theoretic Gromov-Witten invariants and their adelic characterization \nby Alexander Givental (University of Berkeley) as part of Geometria em L isboa (IST)\n\n\nAbstract\nGromov-Witten invariants of a given Kahler targ et space are defined as suitable intersection numbers in moduli spaces of stable maps of complex curves into the target space. Their K-theoretic ana logues are defined as holomorphic Euler characteristics of suitable vector bundles over these moduli spaces.\nWe will describe how the Kawasaki-Riem ann-Roch theorem expressing holomorphic Euler characteristics in cohomolog ical terms leads to the adelic formulas for generating functions encoding K-theoretic Gromov-Witten invariants.\n LOCATION:https://researchseminars.org/talk/Geolis/92/ END:VEVENT BEGIN:VEVENT SUMMARY:Inder Kaur (Goethe University Frankfurt am Main) DTSTART:20220531T150000Z DTEND:20220531T160000Z DTSTAMP:20260315T011557Z UID:Geolis/93 DESCRIPTION:Title: Birational geometry of blow-ups of projective spaces\nby Inder Kaur (G oethe University Frankfurt am Main) as part of Geometria em Lisboa (IST)\n \nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/Geolis/93/ END:VEVENT BEGIN:VEVENT SUMMARY:Simon Jubert (Université du Québec à Montréal) DTSTART:20221108T160000Z DTEND:20221108T170000Z DTSTAMP:20260315T011557Z UID:Geolis/94 DESCRIPTION:Title: A Yau-Tian-Donaldson correspondence on a class of toric fibration\nby Simon Jubert (Université du Québec à Montréal) as part of Geometria em Lisboa (IST)\n\n\nAbstract\nThe Yau-Tian-Donaldson (YTD) conjecture predi cts that the existence of an extremal metric (in the sense of Calabi) in a given Kahler class of Kahler manifold is equivalent to a certain algebro- geometric notion of stability of this class. In this talk\, we will discus s the resolution of this conjecture for a certain class of toric fibration s\, called semisimple principal toric fibrations. After an introduction to the Calabi Problem for general Kahler manifolds\, we will focus on the to ric setting. Then we will see how to reduce the Calabi problem on the tota l space of a semisimple principal toric fibration to a weighted constant s calar curvature K\\"ahler problem on the toric fibers. If the time allows\ , I will give elements of proof.\n LOCATION:https://researchseminars.org/talk/Geolis/94/ END:VEVENT BEGIN:VEVENT SUMMARY:Matias del Hoyo (Universidade Federal Fluminense) DTSTART:20221115T160000Z DTEND:20221115T170000Z DTSTAMP:20260315T011557Z UID:Geolis/95 DESCRIPTION:Title: Completeness of metrics and linearization of Lie groupoids\nby Matias del Hoyo (Universidade Federal Fluminense) as part of Geometria em Lisboa (IST)\n\n\nAbstract\nEvery smooth fiber bundle admits a complete Ehresmann connection. I will talk about the story of this theorem and its relation with Riemannian submersions. Then\, after discussing some foundations of R iemannian geometry of Lie groupoids and stacks\, I will present a generali zation of the theorem into this framework\, which somehow answers an open problem on linearization. Talk based on collaborations with my former stud ent M. de Melo.\n LOCATION:https://researchseminars.org/talk/Geolis/95/ END:VEVENT BEGIN:VEVENT SUMMARY:João Pimentel Nunes (Instituto Superior Técnico) DTSTART:20221122T160000Z DTEND:20221122T170000Z DTSTAMP:20260315T011557Z UID:Geolis/96 DESCRIPTION:Title: The geometric interpretation of the Peter-Weyl theorem\nby João Pimen tel Nunes (Instituto Superior Técnico) as part of Geometria em Lisboa (IS T)\n\n\nAbstract\nLet $K$ be a compact Lie group. I will review the constr uction of Mabuchi geodesic families of $K\\times K-$invariant Kahler struc tures on $T^*K$\, via Hamiltonian flows in imaginary time generated by a s trictly convex invariant function on $Lie \\\, K$\, and the corresponding geometric quantization. At infinite geodesic time\, one obtains a rich mix ed polarization of $T^*K$\, the Kirwin-Wu polarization\, which is then con tinuously connected to the vertical polarization of $T^*K$. The geometric quantization of $T^*K$ along this family of polarizations is described by a generalized coherent state transform that\, as geodesic time goes to inf inity\, describes the convergence of holomorphic sections to distributiona l sections supported on Bohr-Sommerfeld cycles. These are in correspondenc e with coadjoint orbits $O_{\\lambda+\\rho}$. One then obtains a concrete (quantum) geometric interpretation of the Peter-Weyl theorem\, where terms in the non-abelian Fourier series are directly related to geometric cycle s in $T^*K$. The role of a singular torus action in this construction will also be emphasized. This is joint work with T.Baier\, J. Hilgert\, O. Kay a and J. Mourão.\n LOCATION:https://researchseminars.org/talk/Geolis/96/ END:VEVENT BEGIN:VEVENT SUMMARY:Gustavo Granja (Instituto Superior Técnico - Universidade de Lisb oa) DTSTART:20221004T150000Z DTEND:20221004T160000Z DTSTAMP:20260315T011557Z UID:Geolis/97 DESCRIPTION:Title: Topology of almost complex structures\nby Gustavo Granja (Instituto Su perior Técnico - Universidade de Lisboa) as part of Geometria em Lisboa ( IST)\n\n\nAbstract\nI will report on joint work in progress with Aleksanda r Milivojevic (MPIM Bonn) on the elementary topology of the space of almos t complex structures on a manifold. First I will describe a certain natura l parametrization and associated stratification of the space of linear com plex structures on a vector space and give a lower bound for the number of complex k-planes jointly preserved by two linear complex structures. Then I will focus on dimension 6 and prove a formula for the homological inter section of two orthogonal almost complex structures on a Riemannian 6-mani fold when these are regarded as sections of the twistor space.\n LOCATION:https://researchseminars.org/talk/Geolis/97/ END:VEVENT BEGIN:VEVENT SUMMARY:Antonella Grassi (Università di Bologna) DTSTART:20221011T150000Z DTEND:20221011T160000Z DTSTAMP:20260315T011557Z UID:Geolis/98 DESCRIPTION:Title: A family of threefolds with several unusual features\nby Antonella Gra ssi (Università di Bologna) as part of Geometria em Lisboa (IST)\n\n\nAbs tract\nI will discuss some of the unusual properties\, in geometry and phy sics\, of a family of Calabi-Yau threefolds fibered by elliptic curves. I will compare it to a construction by Elkies and a classical results of Bur khardt. This leads to some open questions.\n LOCATION:https://researchseminars.org/talk/Geolis/98/ END:VEVENT BEGIN:VEVENT SUMMARY:Lino Amorim (Kansas State University) DTSTART:20220927T150000Z DTEND:20220927T160000Z DTSTAMP:20260315T011557Z UID:Geolis/99 DESCRIPTION:Title: From categories to Gromov-Witten invariants\nby Lino Amorim (Kansas St ate University) as part of Geometria em Lisboa (IST)\n\n\nAbstract\nKontse vich suggested that enumerative predictions of Mirror Symmetry should foll ow directly from Homological Mirror Symmetry. This requires a natural cons truction of analogues of Gromov-Witten invariants associated to any A-infi nity Calabi-Yau category\, with some extra choices. I will explain what th ese choices are and survey two approaches to this construction\, one in ge nus zero and another (conjectural) in all genera.\n LOCATION:https://researchseminars.org/talk/Geolis/99/ END:VEVENT BEGIN:VEVENT SUMMARY:Miguel Moreira (ETH Zurich) DTSTART:20221018T150000Z DTEND:20221018T160000Z DTSTAMP:20260315T011557Z UID:Geolis/100 DESCRIPTION:Title: Virasoro constraints in sheaf theory\nby Miguel Moreira (ETH Zurich) as part of Geometria em Lisboa (IST)\n\n\nAbstract\nVirasoro constraints f or Gromov-Witten invariants have a rich history tied to the very beginning of the subject\, but recently there have been many developments on the sh eaf side. In this talk I will survey those developments and talk about joi nt work with A. Bojko and W. Lim where we propose a general conjecture of Virasoro constraints for moduli spaces of sheaves and formulate it using t he vertex algebra that D. Joyce recently introduced to study wall-crossing . Using Joyce's framework we can show compatibility between wall-crossing and the constraints\, which we then use to prove that they hold for moduli of stable sheaves on curves and surfaces with $h^{0\,1}=h^{0\,2}=0$. In t he talk I will give a rough overview of the vertex algebra story and focus on the ideas behind the proof in the case of curves.\n LOCATION:https://researchseminars.org/talk/Geolis/100/ END:VEVENT BEGIN:VEVENT SUMMARY:Luis Diogo (Uppsala University) DTSTART:20221220T160000Z DTEND:20221220T170000Z DTSTAMP:20260315T011557Z UID:Geolis/101 DESCRIPTION:Title: Lagrangian tori in the cotangent bundle of the 2-sphere\nby Luis Diog o (Uppsala University) as part of Geometria em Lisboa (IST)\n\n\nAbstract\ nGiven a symplectic manifold\, one can ask what Lagrangian submanifolds it contains. I will discuss this question for one of the simplest examples o f a non-trivial symplectic manifold\, namely the cotangent bundle of the 2 -sphere. Specifically\, I will present a result about monotone Lagrangian tori as objects in the Fukaya category. If time permits\, I will also disc uss the problem of classifying Lagrangian tori up to Hamiltonian isotopy.\ n LOCATION:https://researchseminars.org/talk/Geolis/101/ END:VEVENT BEGIN:VEVENT SUMMARY:Sofia Tirabassi (Stockholm University) DTSTART:20221206T160000Z DTEND:20221206T170000Z DTSTAMP:20260315T011557Z UID:Geolis/102 DESCRIPTION:Title: Characterization of quasi-abelian surfaces\nby Sofia Tirabassi (Stock holm University) as part of Geometria em Lisboa (IST)\n\n\nAbstract\nWe gi ve an effective characterization of quasi-abelian surfaces extending to th e quasi-projective setting results of Enriques and Chen--Hacon. This is a joint work with M. Mendes Lopes and R. Pardini.\n LOCATION:https://researchseminars.org/talk/Geolis/102/ END:VEVENT BEGIN:VEVENT SUMMARY:Nicki Magill (Cornell University) DTSTART:20221213T160000Z DTEND:20221213T170000Z DTSTAMP:20260315T011557Z UID:Geolis/103 DESCRIPTION:Title: Symplectic embeddings of Hirzebruch surfaces\nby Nicki Magill (Cornel l University) as part of Geometria em Lisboa (IST)\n\n\nAbstract\nThe four dimensional ellipsoid embedding function of a toric symplectic manifold M measures when a symplectic ellipsoid embeds into M. It generalizes the Gr omov width and ball packing numbers. In 2012\, McDuff and Schlenk computed this function for a ball. The function has a delicate structure known as an infinite staircase. This implies infinitely many obstructions are neede d to know when an embedding can exist. Based on work with McDuff\, Pires\, and Weiler\, we will discuss the classification of which Hirzebruch surfa ces have infinite staircases. We will focus on the part of the argument wh ere symplectic embeddings are constructed via almost toric fibrations.\n LOCATION:https://researchseminars.org/talk/Geolis/103/ END:VEVENT BEGIN:VEVENT SUMMARY:Sobhan Seyfaddini (Institut de Mathématiques de Jussieu - Paris R ive Gauche) DTSTART:20221129T160000Z DTEND:20221129T170000Z DTSTAMP:20260315T011557Z UID:Geolis/104 DESCRIPTION:Title: On the algebraic structure of groups of area-preserving homeomorphisms\nby Sobhan Seyfaddini (Institut de Mathématiques de Jussieu - Paris Riv e Gauche) as part of Geometria em Lisboa (IST)\n\n\nAbstract\nIn an influe ntial article from the 1970s\, Albert Fathi\, having proven that the group of compactly supported volume-preserving homeomorphisms of the $n$-ball i s simple for $n\\geq 3$\, asked if the same statement holds in dimension $ 2$. In a joint work with Cristofaro-Gardiner and Humilière\, we proved th at the group of compactly supported area-preserving homeomorphisms of the $2$-disc is not simple. This answers Fathi's question and settles what is known as "the simplicity conjecture" in the affirmative.\n\nIn fact\, Fath i posed a more general question about all compact surfaces: is the group o f "Hamiltonian homeomorphisms" (which I will define) simple? In my talk\, I will review recent joint work with Cristofaro-Gardiner\, Humilière\, Ma k and Smith answering this more general question of Fathi. The talk will b e for the most part elementary and will only briefly touch on Floer homolo gy which is a crucial ingredient of the solution.\n LOCATION:https://researchseminars.org/talk/Geolis/104/ END:VEVENT BEGIN:VEVENT SUMMARY:Leonardo Macarini (Instituto Superior Técnico\, Universidade de L isboa) DTSTART:20230103T160000Z DTEND:20230103T170000Z DTSTAMP:20260315T011557Z UID:Geolis/106 DESCRIPTION:Title: Symmetric periodic Reeb orbits on the sphere\nby Leonardo Macarini (I nstituto Superior Técnico\, Universidade de Lisboa) as part of Geometria em Lisboa (IST)\n\n\nAbstract\nA long standing conjecture in Hamiltonian D ynamics states that every contact form on the standard contact sphere $S^{ 2n+1}$ has at least $n+1$ simple periodic Reeb orbits. In this talk\, I wi ll consider a refinement of this problem when the contact form has a suita ble symmetry and we ask if there are at least $n+1$ simple symmetric perio dic orbits. We show that there is at least one symmetric periodic orbit fo r any contact form and at least two symmetric closed orbits whenever the c ontact form is dynamically convex. This is joint work with Miguel Abreu an d Hui Liu.\n LOCATION:https://researchseminars.org/talk/Geolis/106/ END:VEVENT BEGIN:VEVENT SUMMARY:Stéphanie Cupit-Foutou (Ruhr-Universität Bochum) DTSTART:20230207T160000Z DTEND:20230207T170000Z DTSTAMP:20260315T011557Z UID:Geolis/107 DESCRIPTION:Title: The Gromov width of compact toric manifolds\nby Stéphanie Cupit-Fout ou (Ruhr-Universität Bochum) as part of Geometria em Lisboa (IST)\n\n\nAb stract\nAfter some basic recalls on the notion of Gromov width of a symple ctic manifold\, I will focus on the case of toric manifolds. I shall expla in how this symplectic capacity can be estimated and even computed. This i s a joint work with C. Bonala.\n LOCATION:https://researchseminars.org/talk/Geolis/107/ END:VEVENT BEGIN:VEVENT SUMMARY:Emilio Franco (Universidad Autónoma de Madrid) DTSTART:20230110T160000Z DTEND:20230110T170000Z DTSTAMP:20260315T011557Z UID:Geolis/108 DESCRIPTION:Title: Lagrangians of Hecke cycles in the moduli space of Higgs bundles\nby Emilio Franco (Universidad Autónoma de Madrid) as part of Geometria em Li sboa (IST)\n\n\nAbstract\nThe moduli space of Higgs bundles over a curve i s a well known (singular) variety with an extremely rich geometry\, in par ticular it is hyperKähler and becomes an integrable system after being eq uipped with the so called Hitchin morphism which\, to any Higgs bundle\, a ssociates a finite cover of the base curve named spectral curve. Associate d to the hyperKähler structure\, Kapustin and Witten introduced in 2007\, BBB and BAA-branes\, predicting that they occur in pairs dual under mirro r symmetry. An example of BBB-brane is a hyperKähler bundle supported on hyperKähler subvariety\, and an example of BAA-brane is a flat bundle sup ported on a complex Lagrangian subvariety. Hitchin described in 2019 a fam ily of subintegral systems lying on the critical loci of the Hitchin integ rable system parametrized by spectral curves with a fixed number of singul arities. The critical subsystem obtained by considering spectral curves wi th maximal number of singularities is a hyperKähler subvariety and the au thor\, along with Oliveira\, Peón-Nieto and Gothen\, studied the BBB-bran es constructed over it\, and their image under Fourier-Mukai transform\, w hich are supported on complex Lagrangian subvarieties. Surprinsingly\, Hit chin showed that the critical subsystem obtained by considering spectral c urves with 1 singularity is not a hyperKähler subvariety and he conjectur ed that only the critical subsystem with a maximal number of singularities is hyperKähler.\n\nIn this work\, joint with Hanson\, Horn and Oliveira\ , we study the critical subsystems with any number of singularities\, show ing that their image under Fourier-Mukai is supported on a certain family of complex Lagrangian subvarieties which we describe.\n LOCATION:https://researchseminars.org/talk/Geolis/108/ END:VEVENT BEGIN:VEVENT SUMMARY:Yaiza Canzani (University of North Carolina at Chapel Hill) DTSTART:20230117T160000Z DTEND:20230117T170000Z DTSTAMP:20260315T011557Z UID:Geolis/109 DESCRIPTION:Title: Counting closed geodesics and improving Weyl’s law for predominant sets of metrics\nby Yaiza Canzani (University of North Carolina at Chapel Hill) as part of Geometria em Lisboa (IST)\n\n\nAbstract\nWe discuss the t ypical behavior of two important quantities on compact manifolds with a Ri emannian metric g: the number\, c(T\, g)\, of primitive closed geodesics o f length smaller than T\, and the error\, E(L\, g)\, in the Weyl law for c ounting the number of Laplace eigenvalues that are smaller than L. For Bai re generic metrics\, the qualitative behavior of both of these quantities has been understood since the 1970’s and 1980’s. In terms of quantitat ive behavior\, the only available result is due to Contreras and it says t hat an exponential lower bound on c(T\, g) holds for g in a Baire-generic set. Until now\, no upper bounds on c(T\, g) or quantitative improvements on E(L\, g) were known to hold for most metrics\, not even for a dense set of metrics. In this talk\, we will introduce the concept of predominance in the space of Riemannian metrics. This is a notion that is analogous to having full Lebesgue measure in finite dimensions\, and which\, in particu lar\, implies density. We will then give stretched exponential upper bound s for c(T\, g) and logarithmic improvements for E(L\, g) that hold for a p redominant set of metrics. This is based on joint work with J. Galkowski.\ n LOCATION:https://researchseminars.org/talk/Geolis/109/ END:VEVENT BEGIN:VEVENT SUMMARY:Gonçalo Oliveira (Instituto Superior Técnico\, Universidade de L isboa) DTSTART:20230214T160000Z DTEND:20230214T170000Z DTSTAMP:20260315T011557Z UID:Geolis/110 DESCRIPTION:Title: From electrostatics to geodesics in K3 surfaces\nby Gonçalo Oliveira (Instituto Superior Técnico\, Universidade de Lisboa) as part of Geometr ia em Lisboa (IST)\n\n\nAbstract\nMotivated by some conjectures originatin g in the Physics literature\, I have recently been looking for closed geod esics in the K3 surfaces constructed by Lorenzo Foscolo. It turns out to b e possible to locate several such with high precision and compute their in dex (their length is also approximately known). Interestingly\, in my view \, the construction of these geodesics is related to an open problem in el ectrostatics posed by Maxwell in 1873.\n LOCATION:https://researchseminars.org/talk/Geolis/110/ END:VEVENT BEGIN:VEVENT SUMMARY:Tiago Guerreiro (University of Essex) DTSTART:20230228T160000Z DTEND:20230228T170000Z DTSTAMP:20260315T011557Z UID:Geolis/111 DESCRIPTION:Title: On the birational geometry of Fano threefold complete intersections\n by Tiago Guerreiro (University of Essex) as part of Geometria em Lisboa (I ST)\n\n\nAbstract\nThe Minimal Model Program (MMP) is a far reaching conje cture in birational geometry which aims at constructing a good representat ive (minimal model) of any given complex projective variety W. When such a model exists it might not be unique and so it becomes natural to study th e relations between them. In the case when W is covered by rational curves \, its minimal model is a Mori fibre space\, that is\, a fibration whose g eneric fibre is positively curved\, and its uniqueness is encoded in the n otion of birational rigidity. In this talk we will give an introduction to the ideas of the MMP with the background of Fano threefold complete inter sections.\n LOCATION:https://researchseminars.org/talk/Geolis/111/ END:VEVENT BEGIN:VEVENT SUMMARY:Yunhyung Cho (Sungkyunkwan University) DTSTART:20230119T160000Z DTEND:20230119T170000Z DTSTAMP:20260315T011557Z UID:Geolis/112 DESCRIPTION:Title: Monotone Lagrangian tori and Mirror symmetry of Fano varieties\nby Yu nhyung Cho (Sungkyunkwan University) as part of Geometria em Lisboa (IST)\ n\n\nAbstract\nThis is a survey talk of current progress of mirror symmetr y of Fano varieties. For a given smooth Fano variety X\, it has been conje ctured that there exists a Laurent polynomial called a (weak) Landau-Ginzb urg mirror (or weak LG mirror shortly) which encodes a quantum cohomology ring structure of X. Tonkonog proved that one can find a weak LG mirror us ing a monotone Lagrangian torus in X. In this talk I will explain how to f ind a monotone Lagrangian torus using a Fano toric degeneration of X. If t ime permits\, I will also describe a monotone Lagrangian torus in a given flag variety.\n LOCATION:https://researchseminars.org/talk/Geolis/112/ END:VEVENT BEGIN:VEVENT SUMMARY:Vestislav Apostolov (Université du Québec à Montréal) DTSTART:20230411T150000Z DTEND:20230411T160000Z DTSTAMP:20260315T011557Z UID:Geolis/113 DESCRIPTION:Title: A Calabi type problem in generalized Kahler geometry\nby Vestislav Ap ostolov (Université du Québec à Montréal) as part of Geometria em Lisb oa (IST)\n\n\nAbstract\nThe notion of a generalized Kahler (GK) structure was introduced in the early 2000's by Hitchin and Gualtieri in order to pr ovide a mathematically rigorous framework of certain nonlinear sigma model theories in physics. Since then\, the subject has developed rapidly. It i s now realized\, thanks to more recent works of Hitchin\, Goto\, Gualtieri \, Bischoff and Zabzine\, that GK structures are naturally attached to Kah ler manifolds endowed with a holomorphic Poisson structure. Inspired by Ca labi's program in Kahler geometry\, which aims at finding a "canonical" Ka hler metric in a fixed deRham class\, I will present in this talk an appro ach towards a “generalized Kahler" version of Calabi's problem motivated by an infinite dimensional moment map formalism\, and using the Bismut-Ri cci flow introduced by Streets and Tian as analytical tool. As an applicat ion\, we give an essentially complete resolution of the problem in the cas e of a toric complex Poisson variety. Based on a joint works with J. Stree ts and Y. Ustinovskiy.\n LOCATION:https://researchseminars.org/talk/Geolis/113/ END:VEVENT BEGIN:VEVENT SUMMARY:Ruobing Zhang (Princeton University) DTSTART:20230307T160000Z DTEND:20230307T170000Z DTSTAMP:20260315T011557Z UID:Geolis/114 DESCRIPTION:Title: Degenerations and metric geometry of collapsing Calabi-Yau manifolds\ nby Ruobing Zhang (Princeton University) as part of Geometria em Lisboa (I ST)\n\n\nAbstract\nWe will give a complete picture of the metric geometry of Calabi-Yau manifolds along degenerations of complex structures\, which holds for all dimensions. In particular\, we will classify the Gromov-Hau sdorff limits on all scales\, describe the singularity formation\, and for mulate a more general conjecture. This is based on my joint work with Song Sun (arXiv: 1906.03368).\n LOCATION:https://researchseminars.org/talk/Geolis/114/ END:VEVENT BEGIN:VEVENT SUMMARY:Weiwei Wu (Zhejiang University) DTSTART:20230321T130000Z DTEND:20230321T140000Z DTSTAMP:20260315T011557Z UID:Geolis/115 DESCRIPTION:Title: Symplectic Torelli groups for positive rational surfaces\nby Weiwei W u (Zhejiang University) as part of Geometria em Lisboa (IST)\n\n\nAbstract \nDonaldson (folklore) asked whether Lagrangian Dehn twists always generat e the symplectic mapping class groups in real dimension four. So far\, all known examples indicate this is true\, even though the symplectic Torelli group is generally much larger than the algebraic one. Yet there are only very few cases people could prove this as a theorem.\n\nWe will define a notion of "positive rational surfaces"\, which is equivalent to the ambien t symplectic manifolds of (symplectic) log Calabi-Yau pairs. We compute th e symplectic Torelli group for the positive rational surfaces and confirm Donaldson's conjecture as a result. We also answer several other questions about the symplectic Torelli groups in dimension $4$.\n LOCATION:https://researchseminars.org/talk/Geolis/115/ END:VEVENT BEGIN:VEVENT SUMMARY:Song Sun (University of California\, Berkeley) DTSTART:20230328T150000Z DTEND:20230328T160000Z DTSTAMP:20260315T011557Z UID:Geolis/116 DESCRIPTION:Title: Complete Calabi-Yau metrics asymptotic to cones\nby Song Sun (Univers ity of California\, Berkeley) as part of Geometria em Lisboa (IST)\n\n\nAb stract\nComplete Calabi-Yau metrics provide singularity models for limits of Kahler-Einstein metrics. We study complete Calabi-Yau metrics with Eucl idean volume growth and quadratic curvature decay. It is known that under these assumptions the metric is always asymptotic to a unique cone at infi nity. Previous work of Donaldson-S. gives a 2-step degeneration to the con e in the algebro-geometric sense\, via a possible intermediate object (a K -semistable cone). We will show that such intermediate K-semistable cone d oes not occur. This is in sharp contrast to the case of local singularitie s. This result together with the work of Conlon-Hein also give a complete algebro-geometric classification of these metrics\, which in particular co nfirms Yau’s compactification conjecture in this setting. I will explain the proof in this talk\, and if time permits I will describe a conjectura l picture in general when the curvature decay condition is removed. Based on joint work with Junsheng Zhang (UC Berkeley).\n LOCATION:https://researchseminars.org/talk/Geolis/116/ END:VEVENT BEGIN:VEVENT SUMMARY:Joé Brendel (School of Mathematical Sciences\, Tel Aviv Universit y) DTSTART:20230418T150000Z DTEND:20230418T160000Z DTSTAMP:20260315T011557Z UID:Geolis/117 DESCRIPTION:Title: Symmetric probes and classification of toric fibres\nby Joé Brendel (School of Mathematical Sciences\, Tel Aviv University) as part of Geometr ia em Lisboa (IST)\n\n\nAbstract\nToric symplectic manifolds contain an in teresting and well-studied family of Lagrangian tori\, called toric fibres . In this talk\, we address the natural question of which toric fibres are equivalent under Hamiltonian diffeomorphisms of the ambient space. On one hand\, we use a symmetric version of McDuff's probes to construct such eq uivalences and on the other hand\, we give certain obstructions coming fro m Chekanov's classification of product tori in symplectic vector spaces co mbined with a lifting trick from toric geometry. We will discuss many four -dimensional examples in which a full classification can be achieved.\n LOCATION:https://researchseminars.org/talk/Geolis/117/ END:VEVENT BEGIN:VEVENT SUMMARY:Umut Varolgunes (Bogazici University) DTSTART:20230314T160000Z DTEND:20230314T170000Z DTSTAMP:20260315T011557Z UID:Geolis/118 DESCRIPTION:Title: Heaviness and SH-visibility\nby Umut Varolgunes (Bogazici University) as part of Geometria em Lisboa (IST)\n\n\nAbstract\nConsider a compact su bset K of a closed symplectic manifold M. We say that K is SH-visible if i ts relative symplectic cohomology does not vanish over the Novikov field. With Cheuk Yu Mak and Yuhan Sun\, we recently proved that SH-visibility is equivalent to K being heavy as defined by Entov-Polterovich. l will recal l these notions and explain the proof. If time permits I will also discuss some consequences.\n LOCATION:https://researchseminars.org/talk/Geolis/118/ END:VEVENT BEGIN:VEVENT SUMMARY:Claude LeBrun (Stony Brook University) DTSTART:20230316T153000Z DTEND:20230316T163000Z DTSTAMP:20260315T011557Z UID:Geolis/119 DESCRIPTION:Title: Einstein Manifolds\, Self-Dual Weyl Curvature\, and Conformally Kähler G eometry\nby Claude LeBrun (Stony Brook University) as part of Geometri a em Lisboa (IST)\n\n\nAbstract\nThere are certain compact 4-manifolds\, s uch as real and complex hyperbolic 4-manifolds\, 4-tori\, and K3\, where w e completely understand the moduli space of Einstein metrics. But there ar e vast numbers of other 4-manifolds where we know that Einstein metrics ex ist\, but cannot currently determine whether or not there might also exist other Einstein metrics on them that are utterly different from the ones w e currently know.\n\nIn this lecture\, I will present two quite different characterizations of the known Einstein metrics on del Pezzo surfaces. The se results imply\, in particular\, that the known Einstein metrics exactly sweep out a single connected component of the Einstein moduli space. I wi ll then briefly indicate the role these results play in current avenues of research.\n LOCATION:https://researchseminars.org/talk/Geolis/119/ END:VEVENT BEGIN:VEVENT SUMMARY:Žan Grad (Instituto Superior Técnico) DTSTART:20230509T150000Z DTEND:20230509T160000Z DTSTAMP:20260315T011557Z UID:Geolis/120 DESCRIPTION:Title: Lie categories\nby Žan Grad (Instituto Superior Técnico) as part of Geometria em Lisboa (IST)\n\n\nAbstract\nWhat does it mean for a category to be endowed with a compatible differentiable structure? In this talk\, we will discuss the interplay of a categorical structure with that of a sm ooth manifold\, and show how to describe such categories infinitesimally\, similarly as to how we construct the Lie algebra of a Lie group. We will generalise the notion of rank from linear algebra to morphisms of Lie cate gories\, and introduce the notion of an extension of a Lie category to a g roupoid. Examples of Lie categories arising in differential geometry and i n physics will be highlighted.\n LOCATION:https://researchseminars.org/talk/Geolis/120/ END:VEVENT BEGIN:VEVENT SUMMARY:Jörg Teschner (DESY\, Theory Group) DTSTART:20230516T150000Z DTEND:20230516T160000Z DTSTAMP:20260315T011557Z UID:Geolis/121 DESCRIPTION:Title: Separation of variables and analytic Langlands correspondence\nby Jö rg Teschner (DESY\, Theory Group) as part of Geometria em Lisboa (IST)\n\n \nAbstract\nFamous results of N. Hitchin establish existence of an integra ble structure of the Hitchin moduli spaces. The goal of this talk will be to discuss a more explicit approach known in the integrable models literat ure as separation of variables\, how it can be applied to the quantisation of the Hitchin system\, and how the result is related to the analytic Lan glands correspondence studied by Etingof\, Frenkel and Kazhdan.\n\nPartly based on arXiv:1707.07873\n LOCATION:https://researchseminars.org/talk/Geolis/121/ END:VEVENT BEGIN:VEVENT SUMMARY:Valery Alexeev (University of Georgia) DTSTART:20230516T133000Z DTEND:20230516T143000Z DTSTAMP:20260315T011557Z UID:Geolis/122 DESCRIPTION:Title: Compact moduli of K3 surfaces and tropical spheres with 24 singular point s\nby Valery Alexeev (University of Georgia) as part of Geometria em L isboa (IST)\n\n\nAbstract\nI will talk about geometric compactifications o f moduli spaces of K3 surfaces\, similar in spirit to the Deligne-Mumford moduli spaces of stable curves. Constructions borrow ideas from the tropic al and integral-affine geometry and mirror symmetry. The main result is th at in many common situations there exists a geometric compactification whi ch is toroidal\, and many of these compactifications can be described expl icitly using tropical spheres with 24 singular points. Much of this talk i s based on the joint work with Philip Engel.\n LOCATION:https://researchseminars.org/talk/Geolis/122/ END:VEVENT BEGIN:VEVENT SUMMARY:Bruno de Oliveira (University of Miami) DTSTART:20230620T150000Z DTEND:20230620T160000Z DTSTAMP:20260315T011557Z UID:Geolis/123 DESCRIPTION:Title: On the geography of surfaces with big cotangent bundle\nby Bruno de O liveira (University of Miami) as part of Geometria em Lisboa (IST)\n\n\nAb stract\nBigness of the cotangent bundle is a negativity property of the cu rvature which has important complex analytic consequences\, such as on the Kobayashi hyperbolicity properties and the GGL-conjecture for surfaces. W e present a birational criterion for a surface to have big cotangent bundl e that takes in account the singularities present in the minimal model and describe how it improves upon other criterions. The criterion allows cert ain geographic regions of surfaces of general type to have big cotangent b undle\, that other criterions can not reach. In this spirit\, we produce t he examples with the lowest slope $c_1^2/c_2$ having big cotangent bundle that are currently known.\n LOCATION:https://researchseminars.org/talk/Geolis/123/ END:VEVENT BEGIN:VEVENT SUMMARY:Alex Waldron (University of Wisconsin - Madison) DTSTART:20230606T150000Z DTEND:20230606T160000Z DTSTAMP:20260315T011557Z UID:Geolis/124 DESCRIPTION:Title: Strong gap theorems via Yang-Mills flow\nby Alex Waldron (University of Wisconsin - Madison) as part of Geometria em Lisboa (IST)\n\n\nAbstract \nGiven a principal bundle over a compact Riemannian 4-manifold or special -holonomy manifold\, it is natural to ask whether a uniform gap exists bet ween the instanton energy and that of any non-minimal Yang-Mills connectio n. This question is quite open in general\, although positive results exis t in the literature. We'll review several of these gap theorems and streng then them to statements of the following type: the space of all connection s below a certain energy deformation retracts (under Yang-Mills flow) onto the space of instantons. As applications\, we recover a theorem of Taubes on path-connectedness of instanton moduli spaces on the 4-sphere\, and ob tain a method to construct instantons on quaternion-Kähler manifolds with positive scalar curvature.\n\nThe talk is based on joint work in progress with Anuk Dayaprema (UW-Madison).\n LOCATION:https://researchseminars.org/talk/Geolis/124/ END:VEVENT BEGIN:VEVENT SUMMARY:Brayan Ferreira (Universidade Federal do Espírito Santo) DTSTART:20231003T150000Z DTEND:20231003T160000Z DTSTAMP:20260315T011557Z UID:Geolis/125 DESCRIPTION:Title: Symplectic embeddings into disk cotangent bundles of spheres\nby Bray an Ferreira (Universidade Federal do Espírito Santo) as part of Geometria em Lisboa (IST)\n\n\nAbstract\nThe question whether a symplectic manifold embeds into another is central in symplectic topology. Since Gromov nonsq ueezing theorem\, it is known that this is a different problem from volume preserving embedding. There are several nice results about symplectic emb eddings between open subsets of $\\mathbb R^{2n}$ showing that even for th ose examples the question can be completely nontrivial. The problem is sub stantially more well understood when the manifolds are toric domains and h ave dimension $4$\, mostly because of obstructions coming from embedded co ntact homology (ECH). In this talk we are going to discuss symplectic embe dding problems in which the target manifold is the disk cotangent bundle o f a two-dimensional sphere\, i.e.\, the set consisting of the covectors wi th norm less than $1$ over a Riemannian sphere. We shall talk about some t ools such as ECH capacities and action angle coordinates. Much of this tal k is based on joint works with Vinicius Ramos and Alejandro Vicente.\n LOCATION:https://researchseminars.org/talk/Geolis/125/ END:VEVENT BEGIN:VEVENT SUMMARY:Manuel Krannich (Karlsruhe Institute of Technology) DTSTART:20231010T150000Z DTEND:20231010T160000Z DTSTAMP:20260315T011557Z UID:Geolis/126 DESCRIPTION:Title: Exotic tori\, actions by $\\mathrm{SL}_d(\\mathbb Z)$\, and mapping class groups\nby Manuel Krannich (Karlsruhe Institute of Technology) as par t of Geometria em Lisboa (IST)\n\n\nAbstract\nOne of the distinctive featu re of the $d$-dimensional torus $T^d$ is that it admits a faithful smooth action by $\\mathrm{SL}_d(\\mathbb Z)$\, so one might wonder whether such an action (or any nontrivial action) also exists for exotic tori i.e. smoo th $d$-manifolds that are homeomorphic but not diffeomorphic to $T^d$. I w ill discuss this and related questions in the talk\, based on joint work w ith M. Bustamante\, A. Kupers\, and B. Tshishiku.\n LOCATION:https://researchseminars.org/talk/Geolis/126/ END:VEVENT BEGIN:VEVENT SUMMARY:Martin Pinsonnault (University of Western Ontario) DTSTART:20231017T150000Z DTEND:20231017T160000Z DTSTAMP:20260315T011557Z UID:Geolis/127 DESCRIPTION:Title: Embeddings of symplectic balls in $\\mathbb{C}P^2$ and configuration spac es\nby Martin Pinsonnault (University of Western Ontario) as part of G eometria em Lisboa (IST)\n\n\nAbstract\nExistence of symplectic embeddings of $k$ disjoint balls of given capacites $c_1\,\\ldots\, c_k$ into a give n symplectic manifold is a central problem in symplectic topology. However \, beside a few examples\, very little is known about the space of all suc h embeddings. In this talk\, I will discuss the case of rational $4$-manif olds of small Euler numbers\, with a special attention to the minimal mani folds $\\mathbb{C}P^2$ and $S^2\\times S^2$. For rational manifolds\, a ve ry rich and intricate picture emerges that blends symplectic topology\, co mplex geometry\, and algebraic topology.\n LOCATION:https://researchseminars.org/talk/Geolis/127/ END:VEVENT BEGIN:VEVENT SUMMARY:Carlos Florentino (Faculdade de Ciências da Universidade de Lisbo a) DTSTART:20230926T150000Z DTEND:20230926T160000Z DTSTAMP:20260315T011557Z UID:Geolis/128 DESCRIPTION:Title: Symplectic resolutions of moduli spaces of G-Higgs bundles over abelian v arieties\nby Carlos Florentino (Faculdade de Ciências da Universidade de Lisboa) as part of Geometria em Lisboa (IST)\n\n\nAbstract\nFollowing A. Beauville\, a complex algebraic variety $X$ is said to be symplectic if it admits a holomorphic symplectic form $\\omega$ on its smooth locus suc h that\, for every resolution $\\pi: Y \\to X$\, $\\pi^*\\omega$ extends t o a holomorphic $2$-form on $Y$. When this extension is actually non-degen erate (a de facto symplectic form) on $Y$\, we call $\\pi$ a symplectic (o r crepant) resolution.\n\nLet $G$ be a complex reductive group and $A$ an abelian variety of dimension $d$. The aim of this talk is to show that all moduli spaces of $G$-Higgs bundles over $A$ are symplectic varieties\, an d that\, for $G=\\mathrm{GL}(n\,\\mathbb C)$\, the canonical Hilbert-Chow morphism is a symplectic resolution if and only if $d=1$.\n\nMoreover\, us ing a little representation theory\, we can obtain explicit expressions fo r the Poincaré polynomials of all Hilbert-Chow resolutions (either $d=1$\ , all $n$\; or $n=1\,2\,3$ and all $d$). This is joint work with I. Biswas and A. Nozad.\n LOCATION:https://researchseminars.org/talk/Geolis/128/ END:VEVENT BEGIN:VEVENT SUMMARY:Eleonora Di Nezza (Sorbonne Université (IMJ-PRG) and École Norma le Supérieure de Paris (DMA)) DTSTART:20231031T160000Z DTEND:20231031T170000Z DTSTAMP:20260315T011557Z UID:Geolis/129 DESCRIPTION:Title: Singular Kähler-Einstein metrics\nby Eleonora Di Nezza (Sorbonne Uni versité (IMJ-PRG) and École Normale Supérieure de Paris (DMA)) as part of Geometria em Lisboa (IST)\n\n\nAbstract\nStudying metrics with special curvature properties on compact Kähler manifolds is a fundamental problem in Kähler geometry.\nIn this talk\, I will focus on the existence and un iqueness of singular Kähler-Einstein metrics whose singular behavior is p rescribed.\nThese results are based on a series of joint works with T. Dar vas and C. Lu.\n LOCATION:https://researchseminars.org/talk/Geolis/129/ END:VEVENT BEGIN:VEVENT SUMMARY:Cinzia Casagrande (Università di Torino) DTSTART:20231107T160000Z DTEND:20231107T170000Z DTSTAMP:20260315T011557Z UID:Geolis/130 DESCRIPTION:Title: Fano $4$-folds with large Picard number are products of surfaces\nby Cinzia Casagrande (Università di Torino) as part of Geometria em Lisboa ( IST)\n\n\nAbstract\nLet $X$ be a smooth\, complex Fano $4$-fold\, and $\\r ho(X)$ its Picard number. We will discuss the following theorem: if $\\rho (X)>12$\, then $X$ is a product of del Pezzo surfaces. This implies\, in p articular\, that the maximal Picard number of a Fano $4$-fold is $18$. Aft er an introduction and a discussion of examples\, we explain some of the i deas and techniques involved in the proof.\n LOCATION:https://researchseminars.org/talk/Geolis/130/ END:VEVENT BEGIN:VEVENT SUMMARY:Benoit Charbonneau (University of Waterloo) DTSTART:20231107T143000Z DTEND:20231107T153000Z DTSTAMP:20260315T011557Z UID:Geolis/131 DESCRIPTION:Title: Symmetric instantons\nby Benoit Charbonneau (University of Waterloo) as part of Geometria em Lisboa (IST)\n\n\nAbstract\nWith Spencer Whitehead \, we developed a systematic framework to study instantons on $\\mathbb R^ 4$ that are invariant under groups of isometries. In this presentation\, I will describe this framework and some results obtained using it.\n LOCATION:https://researchseminars.org/talk/Geolis/131/ END:VEVENT BEGIN:VEVENT SUMMARY:Maarten Mol (Max Planck Institute for Mathematics) DTSTART:20231121T160000Z DTEND:20231121T170000Z DTSTAMP:20260315T011557Z UID:Geolis/132 DESCRIPTION:Title: Kähler manifolds with a high degree of torus bundle symmetry\nby Maa rten Mol (Max Planck Institute for Mathematics) as part of Geometria em Li sboa (IST)\n\n\nAbstract\nIn this talk I will discuss a natural generaliza tion of symplectic toric manifolds\, for which the symmetry is given by a (symplectic) torus bundle\, rather than a torus. The aim will be to explai n how the Abreu-Guillemin theory of toric Kähler metrics extends to this setting. This is based on an ongoing project with Miguel Abreu and Rui Loj a Fernandes.\n LOCATION:https://researchseminars.org/talk/Geolis/132/ END:VEVENT BEGIN:VEVENT SUMMARY:Sheila Sandon (IRMA-Strasbourg) DTSTART:20240227T160000Z DTEND:20240227T170000Z DTSTAMP:20260315T011557Z UID:Geolis/133 DESCRIPTION:Title: Contact non-squeezing at large scale via generating functions\nby She ila Sandon (IRMA-Strasbourg) as part of Geometria em Lisboa (IST)\n\n\nAbs tract\nThe symplectic non-squeezing theorem\, discovered by Gromov in 1985 \, has been the first result showing a fundamental difference between symp lectic transformations and volume preserving ones. A similar but more subt le phenomenon in contact topology was found by Eliashberg\, Kim and Polter ovich in 2006\, and refined by Fraser in 2016 and Chiu in 2017: in this ca se\nnon-squeezing depends on the size of the domains\, and only appears ab ove a certain quantum scale.\n\nIn my talk I will outline the geometric id eas behind a proof of this general contact non-squeezing theorem that uses generating functions\, a classical method based on finite dimensional Mor se theory. This is a joint work with Maia Fraser and Bingyu Zhang.\n LOCATION:https://researchseminars.org/talk/Geolis/133/ END:VEVENT BEGIN:VEVENT SUMMARY:Naichung Conan Leung (The Chinese University of Hong Kong) DTSTART:20240321T160000Z DTEND:20240321T170000Z DTSTAMP:20260315T011557Z UID:Geolis/134 DESCRIPTION:Title: Quantization of Kähler manifolds\nby Naichung Conan Leung (The Chine se University of Hong Kong) as part of Geometria em Lisboa (IST)\n\n\nAbst ract\nI will explain recent work on relationships among geometric quantiza tion\, deformation quantization\, Berezin-Toeplitz quantization and brane quantization.\n LOCATION:https://researchseminars.org/talk/Geolis/134/ END:VEVENT BEGIN:VEVENT SUMMARY:Levi Lima (Universidade Federal do Ceará) DTSTART:20240206T160000Z DTEND:20240206T170000Z DTSTAMP:20260315T011557Z UID:Geolis/135 DESCRIPTION:Title: Rigidity of non-compact static domains in hyperbolic space via positive m ass theorems\nby Levi Lima (Universidade Federal do Ceará) as part of Geometria em Lisboa (IST)\n\n\nAbstract\nWe introduce a notion of statici ty for non-compact spaces which encompasses several known examples includi ng any domain in hyperbolic space whose boundary is a non-compact totally umbilical hypersurface. For a (time-symmetric) initial data set modeled at infinity on any of these latter examples\, we formulate and prove a posit ive mass theorem in the spin category under natural dominant energy condit ions (both on the interior and along the boundary) whose rigidity statemen t in particular retrieves a recent result by Souam to the effect that no s uch umbilical hypersurface admits a compactly supported deformation keepin g the original lower bound for the mean curvature. A key ingredient in our approach is the consideration of a new boundary condition on spinors whic h somehow interpolates between chirality and MIT bag boundary conditions. Joint work with S. Almaraz (arXiv:2206.09768\, to appear in ASNS Pisa).\n LOCATION:https://researchseminars.org/talk/Geolis/135/ END:VEVENT BEGIN:VEVENT SUMMARY:Filip Živanović (Simons Center for Geometry and Physics at Stony Brook) DTSTART:20231212T160000Z DTEND:20231212T170000Z DTSTAMP:20260315T011557Z UID:Geolis/136 DESCRIPTION:Title: Filtrations on cohomology from Floer theory of contracting $\\mathbb C^*$ -actions\nby Filip Živanović (Simons Center for Geometry and Physics at Stony Brook) as part of Geometria em Lisboa (IST)\n\n\nAbstract\nWe st udy open symplectic manifolds with pseudoholomorphic $\\mathbb C^*$-action s whose $S^1$-part is Hamiltonian\, and construct their associated symplec tic cohomology. From this construction\, we obtain a filtration on quantum /ordinary cohomology that depends on the choice of the $\\mathbb C^*$-acti on. One should think about this filtration as a Floer-theoretic analogue o f the Atiyah-Bott filtration. We construct filtration functional on the Fl oer chain complex\, allowing us to compute the aforementioned filtration v ia Morse-Bott spectral sequence that converges to symplectic cohomology\, which is readily computable in examples. We compare our filtration with kn own ones from algebraic geometry/representation theory literature. Time-al lowing\, I may present the $S^1$-equivariant picture as well. This is join t work with Alexander Ritter.\n LOCATION:https://researchseminars.org/talk/Geolis/136/ END:VEVENT BEGIN:VEVENT SUMMARY:Liat Kessler (University of Haifa) DTSTART:20240116T160000Z DTEND:20240116T170000Z DTSTAMP:20260315T011557Z UID:Geolis/137 DESCRIPTION:Title: Extending cyclic actions to circle actions\nby Liat Kessler (Universi ty of Haifa) as part of Geometria em Lisboa (IST)\n\n\nAbstract\nIt is nat ural to ask whether an action of a finite cyclic group extends to a circle action. Here\, the action is on a symplectic manifold of dimension four. Admitting a circle action implies that a simply connected closed symplecti c four-manifold is either the projective plane or obtained from an $S^2$ b undle over $S^2$ by k blowups. I will show that for k small enough\, any c yclic action that is trivial on homology extends to a circle action\, and present a case in which the action does not extend. I will also discuss ho w we approach this question for a general k. The proofs combine holomorphi c and combinatorial methods. The talk is based on a joint work with River Chiang.\n LOCATION:https://researchseminars.org/talk/Geolis/137/ END:VEVENT BEGIN:VEVENT SUMMARY:Jason Lotay (University of Oxford) DTSTART:20240109T160000Z DTEND:20240109T170000Z DTSTAMP:20260315T011557Z UID:Geolis/138 DESCRIPTION:Title: Translators in Lagrangian mean curvature flow\nby Jason Lotay (Univer sity of Oxford) as part of Geometria em Lisboa (IST)\n\n\nAbstract\nLagran gian mean curvature flow is potentially a powerful tool in solving problem s in symplectic topology. One of the key challenges is the understanding o f formation of singularities\, which is conjectured to have links to J-hol omorphic curves\, stability conditions and the Fukaya category. Unlike the usual mean curvature flow for hypersurfaces\, here one is expected to hav e to tackle singularities modelled on translating solutions to the flow. I will describe joint work with Felix Schulze and Gabor Szekelyhidi which a llows one to recognize a singularity model in Lagrangian mean curvature fl ow as a translator - this is the first such result in any form of mean cur vature flow beyond curves.\n LOCATION:https://researchseminars.org/talk/Geolis/138/ END:VEVENT BEGIN:VEVENT SUMMARY:Rémi Leclercq (Université Paris-Saclay) DTSTART:20231219T160000Z DTEND:20231219T170000Z DTSTAMP:20260315T011557Z UID:Geolis/139 DESCRIPTION:Title: Essential loops of Hamiltonian homeomorphisms\nby Rémi Leclercq (Uni versité Paris-Saclay) as part of Geometria em Lisboa (IST)\n\n\nAbstract\ nIn 1987\, Gromov and Eliashberg showed that if a sequence of diffeomorphi sms preserving a symplectic form C⁰ converges to a diffeomorphism\, the limit also preserves the symplectic form -- even though this is a C¹ cond ition. This result gave rise to the notion of symplectic homeomorphisms\, i.e. elements of the C⁰-closure of the group of symplectomorphisms in th at of homeomorphisms\, and started the study of "continuous symplectic geo metry".\n\nIn this talk\, I will present recent progress in understanding the fundamental group of the C⁰-closure of the group of Hamiltonian diff eomorphisms in that of homeomorphisms. More precisely\, I will explain a s ufficient condition which ensures that certain essential loops of Hamilton ian diffeomorphisms remain essential when seen as "Hamiltonian homeomorphi sms". I will illustrate this method (and its limits) on toric manifolds\, namely complex projective spaces\, rational products of 2-spheres\, and ra tional 1-point blow-ups of CP².\n\nOur condition is based on (explicit) c omputation of the spectral norm of loops of Hamiltonian diffeomorphisms wh ich is of independent interest. For example\, in the case of 1-point blow- ups of CP²\, I will show that the spectral norm exhibits a surprising beh avior which heavily depends on the choice of the symplectic form. This is joint work with Vincent Humilière and Alexandre Jannaud.\n LOCATION:https://researchseminars.org/talk/Geolis/139/ END:VEVENT BEGIN:VEVENT SUMMARY:Yang Li (Massachusetts Institute of Technology) DTSTART:20240123T160000Z DTEND:20240123T170000Z DTSTAMP:20260315T011557Z UID:Geolis/140 DESCRIPTION:Title: On the Thomas-Yau conjecture\nby Yang Li (Massachusetts Institute of Technology) as part of Geometria em Lisboa (IST)\n\n\nAbstract\nThe Thomas -Yau conjecture is an open-ended program to relate special Lagrangians to stability conditions in Floer theory\, but the precise notion of stability is subject to many interpretations. I will focus on the exact case (Stein Calabi-Yau manifolds)\, and deal only with almost calibrated Lagrangians. I will attempt a formulation of Thomas-Yau semistability condition (meant to be less ambitious than Joyce’s program)\, and focus primarily on the symplectic aspects\, and the technique of integration over the moduli spa ce of holomorphic discs.\n LOCATION:https://researchseminars.org/talk/Geolis/140/ END:VEVENT BEGIN:VEVENT SUMMARY:Rita Pardini (Universita' di Pisa) DTSTART:20240220T160000Z DTEND:20240220T170000Z DTSTAMP:20260315T011557Z UID:Geolis/141 DESCRIPTION:Title: Exploring the boundary of the moduli space of stable surfaces: some expli cit examples\nby Rita Pardini (Universita' di Pisa) as part of Geometr ia em Lisboa (IST)\n\n\nAbstract\nI will briefly recall the notion of stab le surfaces and of the corresponding moduli space. Then I will outline a p artial description of the boundary points in the case of surfaces with $K^ 2=1$\, $p_g=2$ (joint work with Stephen Coughlan\, Marco Franciosi\, Julie Rana and Soenke Rollenske\, in various combinations) and\, time permittin g\, in the case of Campedelli and Burniat surfaces (joint work with Valery Alexeev).\n LOCATION:https://researchseminars.org/talk/Geolis/141/ END:VEVENT BEGIN:VEVENT SUMMARY:Shira Tanny (Institute for Advanced Study\, Princeton) DTSTART:20240305T160000Z DTEND:20240305T170000Z DTSTAMP:20260315T011557Z UID:Geolis/142 DESCRIPTION:Title: From Gromov-Witten invariants to dynamics\nby Shira Tanny (Institute for Advanced Study\, Princeton) as part of Geometria em Lisboa (IST)\n\n\n Abstract\nGiven a flow on a manifold\, how to perturb it in order to creat e a periodic orbit passing through a given region? This question was origi nally asked by Poincaré and was initially studied in the 60s. However\, v arious facets of it remain largely open. Recently\, several advances were made in the context of Hamiltonian and contact flows. I will discuss a con nection between this problem and Gromov-Witten invariants\, which are ``co unts" of holomorphic curves. This is based on a joint work with Julian Cha idez.\n LOCATION:https://researchseminars.org/talk/Geolis/142/ END:VEVENT BEGIN:VEVENT SUMMARY:Giordano Cotti (Grupo de Física Matemática\, Universidade de Lis boa) DTSTART:20240130T160000Z DTEND:20240130T170000Z DTSTAMP:20260315T011557Z UID:Geolis/143 DESCRIPTION:Title: Gromov-Witten theory\, quantum differential equations\, and derived categ ories\nby Giordano Cotti (Grupo de Física Matemática\, Universidade de Lisboa) as part of Geometria em Lisboa (IST)\n\n\nAbstract\nEnumerative geometry sinks its roots many centuries back in time. In the last decades \, ideas coming from physics brought innovation to this research area\, wi th both new techniques and the emergence of new rich geometrical structure s. As an example\, Gromov--Witten theory\, focusing on symplectic invarian ts defined as counting numbers of curves on a target space\, led to the no tion of quantum cohomology and quantum differential equations (qDEs).\n\nT he qDEs define a class of ordinary differential equations in the complex d omain\, whose study represents a challenging active area in both contempor ary geometry and mathematical physics. The qDEs define rich invariants att ached to smooth projective varieties. These equations\, indeed\, encapsula te information not only about the enumerative geometry of varieties but ev en (conjecturally) of their topology and complex geometry. The way to disc lose such a huge amount of data is through the study of the asymptotics an d monodromy of their solutions. This talk will be a gentle introduction to the study of qDE's\, their relationship with derived categories of cohere nt sheaves (in both non-equivariant and equivariant settings)\, and a theo ry of integral representations for its solutions. Overall\, the talk will be a survey of the results of the speaker in this research area.\n LOCATION:https://researchseminars.org/talk/Geolis/143/ END:VEVENT BEGIN:VEVENT SUMMARY:Frol Zapolsky (University of Haifa & MISANU) DTSTART:20240227T143000Z DTEND:20240227T153000Z DTSTAMP:20260315T011557Z UID:Geolis/144 DESCRIPTION:Title: Big fiber theorems and symplectic rigidity\nby Frol Zapolsky (Univers ity of Haifa & MISANU) as part of Geometria em Lisboa (IST)\n\n\nAbstract\ nIn many areas of mathematics there are theorems of the following kind: An y map in a suitable class has a big fiber. The classes of maps and the not ions of size vary from field to field. In my talk I'll present several exa mples of this phenomenon. I'll show how Gromov's notion of ideal valued-me asures derived from cohomology can be used to prove some of them. I'll als o introduce objects which are a suitable generalization of ideal-valued me asures in the context of symplectic geometry\, called ideal-valued quasi-m easures\, indicate how they can be constructed using relative symplectic c ohomology\, a tool recently introduced by U. Varolgunes\, and demonstrate how they can be used to obtain new symplectic rigidity results. Based on j oint work with A. Dickstein\, Y. Ganor\, and L. Polterovich.\n LOCATION:https://researchseminars.org/talk/Geolis/144/ END:VEVENT BEGIN:VEVENT SUMMARY:Cristiano Spotti (Aarhus University) DTSTART:20240312T160000Z DTEND:20240312T170000Z DTSTAMP:20260315T011557Z UID:Geolis/145 DESCRIPTION:Title: Algebro geometric aspects of bubbling of Kähler-Einstein metrics\nby Cristiano Spotti (Aarhus University) as part of Geometria em Lisboa (IST) \n\n\nAbstract\nGiven a degenerating family of Kähler-Einstein metrics it is natural to study from a differential geometric perspective the collect ion of all metric limits at all possible scales\, a typical example being the emergence of Kronheimer’s ALE spaces near the formation of orbifold singularities for Einstein 4-manifolds. In this talk\, I will describe\, f ocusing on the discussion of some concrete and elementary examples\, how i t should be possible to use algebro geometric tools to investigate such pr oblem for algebraic families\, leading in the non-collapsing case to an in ductive argument identifying the so-called metric bubble tree at a singula rity (made of a collection of asymptotically conical Calabi-Yau varieties) with a subset of the non-Archimedean Berkovich analytification of the fam ily. Based on joint work with M. de Borbon.\n LOCATION:https://researchseminars.org/talk/Geolis/145/ END:VEVENT BEGIN:VEVENT SUMMARY:Joé Brendel (Université de Neuchâtel) DTSTART:20240402T150000Z DTEND:20240402T160000Z DTSTAMP:20260315T011557Z UID:Geolis/146 DESCRIPTION:Title: Local constructions of exotic Lagrangian tori\nby Joé Brendel (Unive rsité de Neuchâtel) as part of Geometria em Lisboa (IST)\n\n\nAbstract\n Certain simple symplectic manifolds (symplectic vector space\, Milnor fibr es of certain complex surface singularities\,...) contain sets of symplect ically distinct Lagrangian tori which have the following remarkable proper ty: they remain symplectically distinct under embeddings into any reasonab le (i.e. geometrically bounded) symplectic manifold. This leads to a vast extension of the class of spaces in which the existence of exotic tori is known\, especially in dimensions six and above. In this talk we mainly foc us on recent joint work with Johannes Hauber and Joel Schmitz which treats the more intricate case of dimension four.\n LOCATION:https://researchseminars.org/talk/Geolis/146/ END:VEVENT BEGIN:VEVENT SUMMARY:Diogo Oliveira e Silva (Instituto Superior Técnico) DTSTART:20240716T150000Z DTEND:20240716T160000Z DTSTAMP:20260315T011557Z UID:Geolis/147 DESCRIPTION:Title: Sharp extension inequalities on finite fields\nby Diogo Oliveira e Si lva (Instituto Superior Técnico) as part of Geometria em Lisboa (IST)\n\n \nAbstract\nSharp restriction theory and the finite field extension proble m have both received much attention in the last two decades\, but so far t hey have not intersected. In this talk\, we discuss our first results on s harp restriction theory on finite fields. Even though our methods for deal ing with paraboloids and cones borrow some inspiration from their euclidea n counterparts\, new phenomena arise which are related to the underlying a rithmetic and discrete structures. The talk is based on recent joint work with Cristian González-Riquelme.\n LOCATION:https://researchseminars.org/talk/Geolis/147/ END:VEVENT BEGIN:VEVENT SUMMARY:Kiumars Kaveh (University of Pittsburgh) DTSTART:20240618T150000Z DTEND:20240618T160000Z DTSTAMP:20260315T011557Z UID:Geolis/148 DESCRIPTION:Title: A spherical logarithm map\nby Kiumars Kaveh (University of Pittsburgh ) as part of Geometria em Lisboa (IST)\n\n\nAbstract\nThe logarithm map fr om complex algebraic torus to the Euclidean space\, sends an n-tuple of no nzero complex numbers to the logarithms of their absolute values. The imag e of a subvariety in the torus under the logarithm map is called "amoeba" and it contains geometric information about the variety. In this talk we explore the extension of the notion of logarithm map and amoeba to the non -commutative setting\, that is for a spherical homogeneous space G/H where G is a connected complex reductive algebraic group. This is related to Vi ctor Batyrev's question of describing K-orbits in G/H.\nThe talk is based on a join work with Victor Batyrev\, Megumi Harada and Johannes Hofscheier .\n LOCATION:https://researchseminars.org/talk/Geolis/148/ END:VEVENT BEGIN:VEVENT SUMMARY:Leander Stecker (Instituto Superior Técnico) DTSTART:20240430T150000Z DTEND:20240430T160000Z DTSTAMP:20260315T011557Z UID:Geolis/149 DESCRIPTION:Title: Canonical Submersions and 3-$(\\alpha\, \\delta)$-Sasaki geometry*\n by Leander Stecker (Instituto Superior Técnico) as part of Geometria em L isboa (IST)\n\n\nAbstract\nWe introduce the classical results of de Rham a nd Berger on the holonomy of a Riemannian manifold. We compare these to th e situation of parallel skew-torsion\, where we obtain Riemannian submersi ons from reducible holonomy. If time permits I will give an introduction t o 3-$(\\alpha\, \\delta)$-Sasaki manifolds and their submersion onto quate rnionic Kähler manifolds.\n*if time permits\n LOCATION:https://researchseminars.org/talk/Geolis/149/ END:VEVENT BEGIN:VEVENT SUMMARY:Marco Robalo (Institut de Mathematiques de Jussieu-Paris Rive Gauc he) DTSTART:20240507T150000Z DTEND:20240507T160000Z DTSTAMP:20260315T011557Z UID:Geolis/150 DESCRIPTION:Title: Gluing Invariants of Donaldson-Thomas Type\nby Marco Robalo (Institut de Mathematiques de Jussieu-Paris Rive Gauche) as part of Geometria em Li sboa (IST)\n\n\nAbstract\nIn this talk I will explain a general mechanism\ , based on derived symplectic geometry\, to glue the local invariants of s ingularities that appear naturally in Donaldson-Thomas theory. Our mechani sm recovers the categorified vanishing cycles sheaves constructed by Brav- Bussi-Dupont-Joyce\, and provides a new more evolved gluing of Orlov’s c ategories of matrix factorisations\, answering a conjecture of Kontsevich- Soibelman and Y.Toda. This is a joint work with B. Hennion (Orsay) and J. Holstein (Hamburg). The talk will be accessible to a general audience.\n LOCATION:https://researchseminars.org/talk/Geolis/150/ END:VEVENT BEGIN:VEVENT SUMMARY:Alex Waldron (University of Wisconsin -Madison) DTSTART:20240702T150000Z DTEND:20240702T160000Z DTSTAMP:20260315T011557Z UID:Geolis/151 DESCRIPTION:Title: Łojasiewicz inequalities for maps of the 2-sphere\nby Alex Waldron ( University of Wisconsin -Madison) as part of Geometria em Lisboa (IST)\n\n \nAbstract\nInfinite-time convergence of geometric flows\, as even for fin ite-dimensional gradient flows\, is a notoriously subtle problem. The best (or only) bet is to get a ``Łojasiewicz(-Simon) inequality'' stating tha t a power of the gradient dominates the distance to the critical energy va lue. I'll introduce a Łojasiewicz inequality between the tension field an d Dirichlet energy of a map from the 2-sphere to itself\, removing the tec hnical restrictions from an estimate of Topping (Annals '04). The inequali ty guarantees convergence of weak solutions of harmonic map flow from $S^2 $ to $S^2$ assuming that the body map is nonconstant.\n LOCATION:https://researchseminars.org/talk/Geolis/151/ END:VEVENT BEGIN:VEVENT SUMMARY:Pazit Haim-Kislev (Tel-Aviv University) DTSTART:20240528T150000Z DTEND:20240528T160000Z DTSTAMP:20260315T011557Z UID:Geolis/152 DESCRIPTION:Title: On the existence of symplectic barriers\nby Pazit Haim-Kislev (Tel-Av iv University) as part of Geometria em Lisboa (IST)\n\n\nAbstract\nLagrang ian submanifold rigidity has been a fundamental topic in symplectic topolo gy\, contributing to key theories like the Arnold-Givental conjecture and Lagrangian Floer theory. These theories often show that intersections betw een Lagrangian submanifolds are unavoidable via symplectic maps\, exemplif ied by Biran's concept of Lagrangian Barriers (2001).\nConversely\, subman ifolds not containing Lagrangian submanifolds usually exhibit flexibility\ , and can often be symplectically displaced. In this joint work with Richa rd Hind and Yaron Ostrover\, we introduce what appears to be the first ill ustration of Symplectic Barriers\, demonstrating necessary intersections o f symplectic embeddings with symplectic (non-Lagrangian) submanifolds. The key point is that Lagrangian submanifolds are not the sole barriers\, and there exist situations where a symplectic submanifold is not flexible. \ nIn our work\, we also answer a question by Sackel–Song–Varolgunes–Z hu and calculate the optimal symplectic ball embedding in the ball after r emoving a codimension 2 hyperplane with a prescribed Kähler angle.\n LOCATION:https://researchseminars.org/talk/Geolis/152/ END:VEVENT BEGIN:VEVENT SUMMARY:Alejandro Cabrera (Universidade Federal do Rio de Janeiro) DTSTART:20240625T150000Z DTEND:20240625T160000Z DTSTAMP:20260315T011557Z UID:Geolis/153 DESCRIPTION:Title: About an instanton-type PDE for Poisson geometry\nby Alejandro Cabrer a (Universidade Federal do Rio de Janeiro) as part of Geometria em Lisboa (IST)\n\n\nAbstract\nIn this talk\, I will present an instanton-type PDE a ssociated with a Poisson manifold M. After reviewing its role in an underl ying field theory\, we present the main theorem showing existence and clas sification of its solutions. Finally\, we discuss its geometric significan ce leading to a generating function for a symplectic groupoid\, Lie-theore tic\, integration of M.\n LOCATION:https://researchseminars.org/talk/Geolis/153/ END:VEVENT BEGIN:VEVENT SUMMARY:Mingyang Li (University of Berkeley) DTSTART:20240521T150000Z DTEND:20240521T160000Z DTSTAMP:20260315T011557Z UID:Geolis/154 DESCRIPTION:Title: Classification results for Hermitian non-Kähler gravitational instantons \nby Mingyang Li (University of Berkeley) as part of Geometria em Lisb oa (IST)\n\n\nAbstract\nWe will discuss some classification results for He rmitian non-Kähler gravitational instantons. There are three main results : (1) Non-existence of certain Hermitian non-Kähler ALE gravitational ins tantons. (2) Complete classification for Hermitian non-Kähler ALF/AF grav itational instantons. (3) Non-existence of Hermitian non-Kähler gravitati onal instantons under suitable curvature decay condition\, when there is m ore collapsing at infinity (ALG\, ALH\, etc.). These are achieved by a tho rough analysis of the collapsing geometry at infinity and compactification s.\n LOCATION:https://researchseminars.org/talk/Geolis/154/ END:VEVENT BEGIN:VEVENT SUMMARY:Dan Wang (CAMGSD\, Instituto Superior Técnico) DTSTART:20241119T160000Z DTEND:20241119T170000Z DTSTAMP:20260315T011557Z UID:Geolis/155 DESCRIPTION:Title: Dependence of quantum spaces on different polarizations on toric varietie s\nby Dan Wang (CAMGSD\, Instituto Superior Técnico) as part of Geome tria em Lisboa (IST)\n\n\nAbstract\nA crucial problem in geometric quantiz ation is to understand the relationship among quantum spaces associated to different polarizations. Two types of polarizations on toric varieties\, Kähler and real\, have been studied extensively. This talk will focus on the quantum spaces associated with mixed polarizations and explore their r elationships with those associated with Kähler polarizations on toric var ieties.\n LOCATION:https://researchseminars.org/talk/Geolis/155/ END:VEVENT BEGIN:VEVENT SUMMARY:Miguel Moreira (MIT) DTSTART:20250107T160000Z DTEND:20250107T170000Z DTSTAMP:20260315T011557Z UID:Geolis/156 DESCRIPTION:Title: Intersection theory on moduli spaces of parabolic bundles\nby Miguel Moreira (MIT) as part of Geometria em Lisboa (IST)\n\n\nAbstract\nThe geom etry\, topology and intersection theory of moduli spaces of stable vector bundles on curves have been topics of interest for more than 50 years. In the 90s\, Jeffrey and Kirwan managed to prove a formula proposed by Witten for the intersection numbers of tautological classes on such moduli space s. In this talk\, I will explain a different way to calculate those number s and\, more generally\, intersection numbers on moduli of parabolic bundl es. Enriching the problem with a parabolic structure gives access to power ful tools\, such as wall-crossing\, Hecke transforms and Weyl symmetry. If time allows\, I will explain how this approach gives a new proof of (a ge neralization to the parabolic setting of) a vanishing result conjectured b y Newstead and proven by Earl and Kirwan.\n LOCATION:https://researchseminars.org/talk/Geolis/156/ END:VEVENT BEGIN:VEVENT SUMMARY:Dario Di Pinto (CMUC\, University of Lisbon) DTSTART:20241001T150000Z DTEND:20241001T160000Z DTSTAMP:20260315T011557Z UID:Geolis/157 DESCRIPTION:Title: Geometry and topology of anti-quasi-Sasakian manifolds\nby Dario Di P into (CMUC\, University of Lisbon) as part of Geometria em Lisboa (IST)\n\ n\nAbstract\nIn the present talk I will introduce a new class of almost co ntact metric manifolds\, called anti-quasi-Sasakian (aqS for short). They are non-normal almost contact metric manifolds $(M\,\\varphi\,\\xi\,\\eta\ ,g)$\, locally fibering along the 1-dimensional foliation generated by $\\ xi$ onto Kähler manifolds endowed with a closed 2-form of type (2\,0). Va rious examples of anti-quasi-Sasakian manifolds will be provided\, includi ng compact nilmanifolds\, $\\mathbb{S}^1$-bundles and manifolds admitting a $Sp(n)\\times \\{1\\}$-reduction of the structural group of the frame bu ndle. Then\, I will discuss some geometric obstructions to the existence o f aqS structures\, mainly related to curvature and topological properties. In particular\, I will focus on compact manifolds endowed with aqS struct ures of maximal rank\, showing that they cannot be homogeneous and they mu st satisfy some restrictions on the Betti numbers.\n\nThis is based on joi nt works with Giulia Dileo (Bari) and Ivan Yudin (Coimbra).\n\nReferences\ n\n1. D. Di Pinto\, On anti-quasi-Sasakian manifolds of maximal rank J. Ge om. Phys. 200 (2024)\, Paper no. 105174\, 10 pp.\n\n2. D. Di Pinto\, G. Di leo\, Anti-quasi-Sasakian manifolds\, Ann. Global Anal. Geom. 64 (1)\, Art icle no. 5 (2023)\, 35 pp.\n LOCATION:https://researchseminars.org/talk/Geolis/157/ END:VEVENT BEGIN:VEVENT SUMMARY:Francisco Nascimento (Instituto Superior Técnico\, Universidade d e Lisboa) DTSTART:20241203T160000Z DTEND:20241203T170000Z DTSTAMP:20260315T011557Z UID:Geolis/158 DESCRIPTION:Title: Kinematic formulas in convex geometry\nby Francisco Nascimento (Insti tuto Superior Técnico\, Universidade de Lisboa) as part of Geometria em L isboa (IST)\n\n\nAbstract\nWe present a systematic study of kinematic form ulas in convex geometry. We first give a classical presentation of kinemat ic formulas for integration with respect to the rotation group $SO(n)$\, w here Steiner's Formula\, the intrinsic volumes and Hadwiger's Characteriza tion Theorem play a crucial role. Then we will show a new extension to int egration along the general linear group $GL(n)$. Using the bijection of ma trix polar decomposition and a Gaussian measure to integrate along positiv e definite matrices\, a new formula is obtained\, for which the classical $SO(n)$ formula is a particular case. We also reference the unitary group $U(n)$ case and its corresponding extension to the symplectic group $Sp(2n \,\\mathbb{R})$.\n LOCATION:https://researchseminars.org/talk/Geolis/158/ END:VEVENT BEGIN:VEVENT SUMMARY:Saman Habibi Esfahani (Duke University) DTSTART:20241105T160000Z DTEND:20241105T170000Z DTSTAMP:20260315T011557Z UID:Geolis/159 DESCRIPTION:Title: On the Donaldson-Scaduto conjecture\nby Saman Habibi Esfahani (Duke U niversity) as part of Geometria em Lisboa (IST)\n\n\nAbstract\nThis talk i s based on a joint work with Yang Li. Motivated by collapsing Calabi-Yau 3 -folds and G2-manifolds with Lefschetz K3 fibrations in the adiabatic sett ing\, Donaldson and Scaduto conjectured the existence of a special Lagrang ian pair-of-pants in the Calabi-Yau 3-fold $X \\times \\mathbb R^2$\, wher e $X$ is either a hyperkähler K3 surface (global version) or an A2-type A LE hyperkähler 4-manifold (local version). After a brief introduction to the subject\, we discuss the significance of this conjecture in the study of Calabi-Yau 3-folds and G2-manifolds\, and then prove the local version of the conjecture\, which in turn implies the global version for an open s ubset of the moduli of K3 surfaces.\n LOCATION:https://researchseminars.org/talk/Geolis/159/ END:VEVENT BEGIN:VEVENT SUMMARY:Yu-Shen Lin (Boston University) DTSTART:20241112T160000Z DTEND:20241112T170000Z DTSTAMP:20260315T011557Z UID:Geolis/160 DESCRIPTION:Title: Special Lagrangians in Calabi-Yau $3$-folds with a K3-fibration\nby Y u-Shen Lin (Boston University) as part of Geometria em Lisboa (IST)\n\n\nA bstract\nSpecial Lagrangians form an important class of minimal submanifol ds in Calabi-Yau manifolds. In this talk\, we will consider the Calabi-Yau $3$-folds with a K3-fibration and the size of the K3-fibres are small. Mo tivated by tropical geometry\, Donaldson-Scaduto conjectured that special Lagrangian collapse to ``gradient cycles" when the K3-fibres collapse. Thi s phenomenon is similar to holomorphic curves in Calabi-Yau manifolds with collapsing special Lagrangian fibrations converging to tropical curves. S imilar to the realization problem in tropical geometry\, one might expect to reconstruct special Lagrangians from gradient cycles. In this talk\, I will report the first theorem of this kind based on a joint work with Shih -Kai Chiu.\n LOCATION:https://researchseminars.org/talk/Geolis/160/ END:VEVENT BEGIN:VEVENT SUMMARY:Naichung Conan Leung (The Chinese University of Hong Kong) DTSTART:20241217T160000Z DTEND:20241217T170000Z DTSTAMP:20260315T011557Z UID:Geolis/161 DESCRIPTION:Title: 3d mirror symmetry is mirror symmetry\nby Naichung Conan Leung (The C hinese University of Hong Kong) as part of Geometria em Lisboa (IST)\n\n\n Abstract\n3d mirror symmetry is a mysterious duality for certian pairs of hyperkähler manifolds\, or more generally complex symplectic manifolds/st acks. In this talk\, we will describe its relationships with 2d mirror sym metry. This could be regarded as a 3d analog of the paper "Mirror Symmetry is T-Duality" by Strominger\, Yau and Zaslow which described 2d mirror sy mmetry via 1d dualities.\n LOCATION:https://researchseminars.org/talk/Geolis/161/ END:VEVENT BEGIN:VEVENT SUMMARY:Samuel Muñoz-Echániz (University of Cambridge) DTSTART:20250114T160000Z DTEND:20250114T170000Z DTSTAMP:20260315T011557Z UID:Geolis/162 DESCRIPTION:Title: Mapping class groups of h-cobordant manifolds\nby Samuel Muñoz-Echá niz (University of Cambridge) as part of Geometria em Lisboa (IST)\n\n\nAb stract\nA cobordism W between compact manifolds M and M’ is an h-cobordi sm if the inclusions of M and M’ into W are both homotopy equivalences. These sort of cobordisms play an important role in the classification of h igh-dimensional manifolds\, as h-cobordant manifolds are often diffeomorph ic.\n\nWith this in mind\, given two h-cobordant manifolds M and M'\, how different can their diffeomorphism groups Diff(M) and Diff(M') be? The hom otopy groups of these two spaces are the same “up to extensions” in a range of strictly positive degrees. Contrasting this\, I will present exam ples of h-cobordant manifolds in high-dimensions with different mapping cl ass groups. In doing so\, I will review the classical theory of h-cobordis ms and introduce several moduli spaces of manifolds that shed light on thi s question.\n LOCATION:https://researchseminars.org/talk/Geolis/162/ END:VEVENT BEGIN:VEVENT SUMMARY:Nick Sheridan (University of Edinburgh) DTSTART:20250311T150000Z DTEND:20250311T160000Z DTSTAMP:20260315T011557Z UID:Geolis/163 DESCRIPTION:Title: Quantum cohomology as a deformation of symplectic cohomology\nby Nick Sheridan (University of Edinburgh) as part of Geometria em Lisboa (IST)\n \n\nAbstract\nWhen M is a Fano variety and D is an anticanonical divisor i n M\, mirror symmetry suggests that the quantum cohomology of M should be a deformation of the symplectic cohomology of M \\ D. We prove that this h olds under even weaker hypotheses on D (although not in general)\, and exp lain the consequences for mirror symmetry. We also explain how our methods give rise to interesting symplectic rigidity results for subsets of M. Al ong the way we hope to give a brief introduction to Varolgunes' `relative symplectic cohomology'\, which is the key technical tool used to prove our symplectic rigidity results\, but which is of far broader significance in symplectic topology and mirror symmetry as it makes the computation of qu antum cohomology `local'. This is joint work with Strom Borman\, Mohamed E l Alami\, and Umut Varolgunes.\n LOCATION:https://researchseminars.org/talk/Geolis/163/ END:VEVENT BEGIN:VEVENT SUMMARY:Ana Rita Pires (University of Edinburgh) DTSTART:20250218T150000Z DTEND:20250218T160000Z DTSTAMP:20260315T011557Z UID:Geolis/164 DESCRIPTION:Title: Infinite staircases in ball packing problems\nby Ana Rita Pires (Univ ersity of Edinburgh) as part of Geometria em Lisboa (IST)\n\n\nAbstract\nT he symplectic version of the problem of packing K balls into a ball in the densest way possible (in 4 dimensions) can be extended to that of symplec tically embedding an ellipsoid into a ball as small as possible. A classic result due to McDuff and Schlenk asserts that the function that encodes t his problem has a remarkable structure: its graph has infinitely many corn ers\, determined by Fibonacci numbers\, that fit together to form an infin ite staircase.\n\nThis ellipsoid embedding function can be equally defined for other targets\, and this talk will be about other targets for which t he function has and does not have an infinite staircase. Firstly we will s ee how in the case when these targets have lattice moment polygons\, the t argets with infinite staircases seem to be exactly those whose polygon is reflexive (i.e.\, has one interior lattice point). Secondly\, we will look at the family of one-point blowups of CP^2\, where the answer involves se lf-similar behaviour akin to the Cantor set.\n\nThis talk is based on vari ous projects\, joint with Dan Cristofaro-Gardiner\, Tara Holm\, Alessia Ma ndini\, Maria Bertozzi\, Tara Holm\, Emily Maw\, Dusa McDuff\, Grace Mwaky oma\, Morgan Weiler\, and Nicki Magill.\n LOCATION:https://researchseminars.org/talk/Geolis/164/ END:VEVENT BEGIN:VEVENT SUMMARY:Gonçalo Oliveira (Instituto Superior Técnico - University of Lis bon) DTSTART:20250225T150000Z DTEND:20250225T160000Z DTSTAMP:20260315T011557Z UID:Geolis/165 DESCRIPTION:Title: Special Lagrangians and mean curvature flow on Gibbons-Hawking manifolds< /a>\nby Gonçalo Oliveira (Instituto Superior Técnico - University of Lis bon) as part of Geometria em Lisboa (IST)\n\n\nAbstract\nMirror symmetry i s a somewhat mysterious phenomenon that relates the geometry of two distin ct Calabi-Yau manifolds. In the realm of trying to understand this relatio nship several conjectures on the existence of so-called special Lagrangian submanifolds appeared. In this talk\, I will report on joint work with Ja son Lotay on which we prove versions of the Thomas and Thomas-Yau conjectu res regarding the existence of these special Lagrangian submanifolds and t he role of Lagrangian mean curvature flow as a way to find them. I will al so report on some more recent work towards proving more recent conjectures due to Joyce.\n LOCATION:https://researchseminars.org/talk/Geolis/165/ END:VEVENT BEGIN:VEVENT SUMMARY:Ana Cannas (ETH Zurich) DTSTART:20250506T140000Z DTEND:20250506T150000Z DTSTAMP:20260315T011557Z UID:Geolis/166 DESCRIPTION:Title: Real Toric Lagrangians\nby Ana Cannas (ETH Zurich) as part of Geometr ia em Lisboa (IST)\n\n\nAbstract\nWe fix an arbitrary symplectic toric man ifold M. Its real toric lagrangians are the lagrangian submanifolds of M w hose intersection with each torus orbit is clean and an orbit of the subgr oup of elements that square to the identity of the torus (basically that s ubgroup is $\\{ 1 \, -1\\}^n$). In particular\, real toric lagrangians are transverse to the principal torus orbits and retain as much symmetry as p ossible.\n\nThis talk will explain why any two real toric lagrangians in M are related by an equivariant symplectomorphism and\, therefore\, any rea l toric lagrangian must be the real locus for a real structure preserving the moment map. This is joint work with Yael Karshon.\n LOCATION:https://researchseminars.org/talk/Geolis/166/ END:VEVENT BEGIN:VEVENT SUMMARY:Leonardo Macarini (IMPA) DTSTART:20250909T140000Z DTEND:20250909T150000Z DTSTAMP:20260315T011557Z UID:Geolis/167 DESCRIPTION:Title: Existence and localization of closed magnetic geodesics with low energy\nby Leonardo Macarini (IMPA) as part of Geometria em Lisboa (IST)\n\n\n Abstract\nMagnetic flows are generalizations of geodesic flows that descri be the motion of a charged particle in a magnetic field. While every close d Riemannian manifold admits at least one closed geodesic\, the analogous problem for magnetic orbits (also known as magnetic geodesics) is signific antly more challenging and has received considerable attention in recent d ecades. I will present a result establishing that every low energy level o f any magnetic flow admits at least one contractible closed orbit\, assumi ng only that the magnetic strength is not identically zero\, has a compact strict local maximum K\, and that the cohomology class of the magnetic fi eld is spherically rational. Moreover\, this magnetic geodesic can be loca lized within an arbitrarily small neighborhood of K. This is joint work wi th Valerio Assenza and Gabriele Benedetti.\n LOCATION:https://researchseminars.org/talk/Geolis/167/ END:VEVENT BEGIN:VEVENT SUMMARY:Martin Pinsonnault (University of Western Ontario in London) DTSTART:20250605T143000Z DTEND:20250605T153000Z DTSTAMP:20260315T011557Z UID:Geolis/168 DESCRIPTION:Title: Embeddings of more than 8 symplectic balls in $\\mathbb CP^2$\nby Mar tin Pinsonnault (University of Western Ontario in London) as part of Geome tria em Lisboa (IST)\n\n\nAbstract\nWe prove that the space of symplectic embeddings of $n\\geq 1$ standard balls\, each of capacity at most $\\frac {1}{n}$\, into the standard complex projective plane $\\mathbb CP^2$ is ho motopy equivalent to the configuration space of $n$ points in $\\mathbb CP ^2$. Our techniques also suggest that for every $n \\geq 9$\, there may ex ist infinitely many homotopy types of spaces of symplectic ball embeddings .\n LOCATION:https://researchseminars.org/talk/Geolis/168/ END:VEVENT BEGIN:VEVENT SUMMARY:Jarek Kedra (University of Aberdeen) DTSTART:20250624T140000Z DTEND:20250624T150000Z DTSTAMP:20260315T011557Z UID:Geolis/169 DESCRIPTION:Title: Configuration spaces of symplectic balls\nby Jarek Kedra (University of Aberdeen) as part of Geometria em Lisboa (IST)\n\n\nAbstract\nI will re port on the work in progress with S.Anjos and M.Pinsonnault concerning con figuration spaces of symplectic balls in the standard complex projective p lane. A few weeks ago Martin showed that when the balls are small their co nfiguration space is homotopy equivalent to the configuration space of poi nts. I will discuss what is happening if the balls are bigger. I will also try to put it into a more general context of configuration of rigid balls in domains of a Euclidean space.\n LOCATION:https://researchseminars.org/talk/Geolis/169/ END:VEVENT BEGIN:VEVENT SUMMARY:Da Rong Cheng (University of Miami) DTSTART:20250527T140000Z DTEND:20250527T150000Z DTSTAMP:20260315T011557Z UID:Geolis/170 DESCRIPTION:Title: SU(2) Yang-Mills-Higgs functional with self-interaction term on 3-manifol ds\nby Da Rong Cheng (University of Miami) as part of Geometria em Lis boa (IST)\n\n\nAbstract\nI will talk about recent joint work with Daniel F adel (University of São Paulo) and Luiz Lara (Unicamp)\, where we study t he SU(2) Yang-Mills-Higgs functional with positive coupling constant on 3- manifolds. Motivated by the work of Alessandro Pigati and Daniel Stern (20 21) on the U(1)-version of the functional\, we also include a scaling para meter.\n\nWhen the 3-manifold is closed and the parameter is small enough\ , by adapting to our context the min-max method used by Pigati and Stern\, we construct non-trivial critical points satisfying energy upper and lowe r bounds that are natural from the point of view of scaling.\n\nThen\, ove r 3-manifolds with bounded geometry\, we show that\, in the limit as the p arameter tends to zero\, and under the above-mentioned energy upper bound\ , a sequence of critical points exhibits concentration phenomenon at a fin ite collection of points\, while the remaining energy goes into an $L^2$ h armonic 1-form. Moreover\, the concentrated energy at each point is accoun ted for by finitely many "bubbles"\, that is\, non-trivial critical points on $R^3$ with the scaling parameter set to 1.\n LOCATION:https://researchseminars.org/talk/Geolis/170/ END:VEVENT BEGIN:VEVENT SUMMARY:Rui Loja Fernandes (University of Illinois Urbana-Champaign) DTSTART:20250612T093000Z DTEND:20250612T103000Z DTSTAMP:20260315T011557Z UID:Geolis/171 DESCRIPTION:Title: Extremal Kähler Metrics on Toric Lagrangian Fibrations\nby Rui Loja Fernandes (University of Illinois Urbana-Champaign) as part of Geometria e m Lisboa (IST)\n\n\nAbstract\nA toric Lagrangian fibration is a Lagrangian fibration whose singular fibers are all of elliptic type. I will begin by explaining how such fibrations can be viewed as Hamiltonian spaces associ ated with symplectic torus bundles. I will then discuss a generalization t o this class of fibrations of the Abreu–Guillemin–Donaldson theory of extremal Kähler metrics on toric symplectic manifolds. Integral affine ge ometry plays a central role in this generalization\, as the Delzant polyto pe is replaced by a more general domain contained in an integral affine ma nifold. This talk is based on on-going work with Miguel Abreu and Maarten Mol.\n LOCATION:https://researchseminars.org/talk/Geolis/171/ END:VEVENT BEGIN:VEVENT SUMMARY:Alejandro Cabrera (Universidade Federal do Rio de Janeiro) DTSTART:20250715T140000Z DTEND:20250715T150000Z DTSTAMP:20260315T011557Z UID:Geolis/172 DESCRIPTION:Title: Numerical approximation of Hamiltonian flows on Poisson manifolds and gro upoid multiplication\nby Alejandro Cabrera (Universidade Federal do Ri o de Janeiro) as part of Geometria em Lisboa (IST)\n\n\nAbstract\nThe idea is to construct numerical integrator methods for Hamiltonian type of ODE ’s which are defined in an ambient Poisson geometry. The goal is to appr oximate the exact dynamical solutions of this ODE while\, at the same time \, preserve the Poisson structure to a certain controlled degree. This is a non-trivial and long-range generalization of the notion of symplectic me thod in which the Poisson geometry is non-degenerate\, thus\, symplectic. We first outline a first approach to such methods which uses the geometry of so-called approximate symplectic realizations based on recent joint wor k with D. Martín de Diego and M. Vaquero. Finally\, we describe a second approach based on theoretical results coming from Lie-theoretic aspects an d which use an underlying groupoid multiplication\, based on work in progr ess with D. Iglesias and J.C. Marrero.\n LOCATION:https://researchseminars.org/talk/Geolis/172/ END:VEVENT BEGIN:VEVENT SUMMARY:Marcelo Atallah (University of Sheffield) DTSTART:20251007T140000Z DTEND:20251007T150000Z DTSTAMP:20260315T011557Z UID:Geolis/173 DESCRIPTION:Title: C⁰-rigidity of the Hamiltonian diffeomorphism group of symplectic ratio nal surfaces\nby Marcelo Atallah (University of Sheffield) as part of Geometria em Lisboa (IST)\n\n\nAbstract\nA natural question bridging the c elebrated Gromov–Eliashberg theorem and the C⁰-flux conjecture is whet her the identity component of the group of symplectic diffeomorphisms is C ⁰-closed in Symp(M\,ω). Beyond surfaces and the cases in which the Tore lli subgroup of Symp(M\,ω) coincides with the identity component\, little is known. In joint work with Cheuk Yu Mak and Wewei Wu\, we show that\, f or all but a few positive rational surfaces\, the group of Hamiltonian dif feomorphisms is the C⁰-connected component of the identity in Symp(M\,ω )\, thereby giving a positive answer in this setting. Here\, “positive r ational surface” essentially means a k-point blow-up of CP² whose sympl ectic form evaluates positively on the first Chern class.\n LOCATION:https://researchseminars.org/talk/Geolis/173/ END:VEVENT BEGIN:VEVENT SUMMARY:Marta Batoreo (Universidade Federal do Espírito Santo) DTSTART:20250923T140000Z DTEND:20250923T150000Z DTSTAMP:20260315T011557Z UID:Geolis/174 DESCRIPTION:Title: On the number of periodic points of symplectomorphisms on surfaces\nb y Marta Batoreo (Universidade Federal do Espírito Santo) as part of Geome tria em Lisboa (IST)\n\n\nAbstract\nIn this talk I will survey some result s on the existence of periodic points of symplectomorphisms defined on clo sed orientable surfaces of positive genus g. Namely\, I will describe some symplectic flows on such surfaces possessing finitely many periodic point s and describe a non-Hamiltonian variant of the Hofer-Zehnder conjecture f or symplectomorphisms defined on surfaces\; this conjecture provides a qua ntitative threshold on the number of fixed points (possibly counted homolo gically) which forces the existence of infinitely many periodic points. Th is is joint work in progress with Marcelo Atallah and Brayan Ferreira.\n LOCATION:https://researchseminars.org/talk/Geolis/174/ END:VEVENT BEGIN:VEVENT SUMMARY:Mingyang Li (Simons Center for Geometry and Physics) DTSTART:20251028T150000Z DTEND:20251028T160000Z DTSTAMP:20260315T011557Z UID:Geolis/175 DESCRIPTION:Title: Gravitational instantons and harmonic maps\nby Mingyang Li (Simons Ce nter for Geometry and Physics) as part of Geometria em Lisboa (IST)\n\n\nA bstract\nIt is known from general relativity that axisymmetric stationary black holes can be reduced to axisymmetric harmonic maps into the hyperbol ic plane H^2\, while in the Riemannian setting\, 4d Ricci-flat metrics wit h torus symmetry can also be locally reduced to such harmonic maps satisfy ing a tameness condition. We study such harmonic maps. Applications includ e a construction of infinitely many new complete\, asymptotically flat\, R icci-flat 4-manifolds with arbitrarily large b_2. Joint work with Song Sun .\n LOCATION:https://researchseminars.org/talk/Geolis/175/ END:VEVENT BEGIN:VEVENT SUMMARY:Joé Brendel (ETH Zurich) DTSTART:20251118T150000Z DTEND:20251118T160000Z DTSTAMP:20260315T011557Z UID:Geolis/176 DESCRIPTION:Title: Knotted bi-disk embeddings\nby Joé Brendel (ETH Zurich) as part of G eometria em Lisboa (IST)\n\n\nAbstract\nA classical result by McDuff shows that the space of symplectic ball embeddings into many simple symplectic four-manifolds is connected. In this talk\, on the other hand\, we show th at the space of symplectic bi-disk embeddings often has infinitely many co nnected components\, even for simple target spaces like the complex projec tive plane\, or the symplectic ball. This extends earlier results by Gutt- Usher and Dimitroglou-Rizell. The proof uses almost toric fibrations and e xotic Lagrangian tori. Furthermore\, we will discuss natural quantitative questions arising in this context. This talk is based on joint work in pro gress with Grigory Mikhalkin and Felix Schlenk.\n LOCATION:https://researchseminars.org/talk/Geolis/176/ END:VEVENT BEGIN:VEVENT SUMMARY:Tristan Ozuch (Massachusetts Institute of Technology) DTSTART:20251209T150000Z DTEND:20251209T160000Z DTSTAMP:20260315T011557Z UID:Geolis/177 DESCRIPTION:by Tristan Ozuch (Massachusetts Institute of Technology) as pa rt of Geometria em Lisboa (IST)\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/Geolis/177/ END:VEVENT BEGIN:VEVENT SUMMARY:Rui Loja Fernandes (University of Illinois Urbana-Champaign) DTSTART:20260106T150000Z DTEND:20260106T160000Z DTSTAMP:20260315T011557Z UID:Geolis/178 DESCRIPTION:Title: Resolutions of proper actions and toric manifolds\nby Rui Loja Fernan des (University of Illinois Urbana-Champaign) as part of Geometria em Lisb oa (IST)\n\n\nAbstract\nI will define a notion of resolution of a proper a ction. Such resolutions always exist but are not canonical. However\, for so-called polar actions I will describe a canonical construction of a reso lution\, which can be used to show that the leaf space has the structure o f an orbifold. I will illustrate this construction with two examples: (i) the adjoint action\, where it allows one to identify the classical Weyl gr oup with the orbifold fundamental group\; and (ii) toric manifolds\, where the resolution can be described in terms of the real part of the toric ma nifold.\n LOCATION:https://researchseminars.org/talk/Geolis/178/ END:VEVENT BEGIN:VEVENT SUMMARY:Pierre Martinez (Université de Bretagne Occidentale) DTSTART:20260219T140000Z DTEND:20260219T150000Z DTSTAMP:20260315T011557Z UID:Geolis/179 DESCRIPTION:Title: Bigraded cohomology for real algebraic varieties and its arithmetic varia nt\nby Pierre Martinez (Université de Bretagne Occidentale) as part o f Geometria em Lisboa (IST)\n\n\nAbstract\nI will first introduce the bigr aded cohomology for real algebraic varieties developed by Johannes Huisman and Dewi Gleuher. This is a cohomology theory that refines the equivarian t cohomology "à la Kahn-Krasnov" of the complex points of a real variety\ , the latter often being preferred (by the algebraic geometers) in the coh omological study of real algebraic varieties. Since the construction of th is bigraded cohomology and its associated characteristic classes relies on the sheaf exponential morphism\, I will explain how to produce an arithme tic (or algebraic) variant of these cohomology groups\, whose main advanta ge is toeliminate topological or transcendental conditions. I will conclud e by comparing these two versions of bigraded cohomology.\n LOCATION:https://researchseminars.org/talk/Geolis/179/ END:VEVENT END:VCALENDAR