BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Gonçalo Tabuada (FCT / UNL\, Portugal) DTSTART:20200724T123000Z DTEND:20200724T133000Z DTSTAMP:20260415T002631Z UID:GPL/1 DESCRIPTION:Title: Noncommutative Weil conjectures\nby Gonçalo Tabuada (FCT / UNL\, P ortugal) as part of Geometry and Physics @ Lisbon\n\n\nAbstract\nThe Weil conjectures (proved by Deligne in the 70's) played a key role in the devel opment of modern algebraic geometry. In this talk\, making use of some rec ent topological "technology"\, I will extended the Weil conjectures from t he realm of algebraic geometry to the broad noncommutative setting of diff erential graded categories. Moreover\, I will prove the noncommutative Wei l conjectures in some interesting cases.\n LOCATION:https://stable.researchseminars.org/talk/GPL/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Davide Masoero (GFMUL\, Lisbon) DTSTART:20201023T131500Z DTEND:20201023T141500Z DTSTAMP:20260415T002631Z UID:GPL/2 DESCRIPTION:Title: The Painlevé I equation and the A2 quiver\nby Davide Masoero (GFMU L\, Lisbon) as part of Geometry and Physics @ Lisbon\n\n\nAbstract\nWe stu dy a second-order linear differential equation known as the deformed cubic oscillator\, whose isomonodromic deformations are controlled by the first Painlevé equation. We use the generalised monodromy map for this equatio n to give solutions to the Bridgeland's Riemann-Hilbert problem arising fr om the Donaldson-Thomas theory of the A2 quiver.\n\nThe talk is partially based on a work in collaboration with Tom Bridgeland (https://arxiv.org/ab s/2006.10648)\n\nMore information and sponsors:\nhttp://cmafcio.campus.cie ncias.ulisboa.pt/node/170\n LOCATION:https://stable.researchseminars.org/talk/GPL/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Giordano Cotti (FCUL\, Lisbon) DTSTART:20201216T140000Z DTEND:20201216T150000Z DTSTAMP:20260415T002631Z UID:GPL/3 DESCRIPTION:Title: Quantum differential equations\, isomonodromic deformations\, and deriv ed categories\nby Giordano Cotti (FCUL\, Lisbon) as part of Geometry a nd Physics @ Lisbon\n\n\nAbstract\nThe quantum differential equation (qDE) is a rich object attached to a smooth projective variety X. It is an ordi nary differential equation in the complex domain which encodes information of the enumerative geometry of X\, more precisely its Gromov-Witten theor y. Furthermore\, the asymptotic and monodromy of its solutions conjectural ly rules also the topology and complex geometry of X. \n\nThese differenti al equations were introduced in the middle of the creative impetus for mat hematically rigorous foundations of Topological Field Theories\, Supersymm etric Quantum Field Theories and related Mirror Symmetry phenomena. Specia l mention has to be given to the relation between qDE's and Dubrovin-Frobe nius manifolds\, the latter being identifiable with the space of isomonodr omic deformation parameters of the former. \n\nThe study of qDE’s repre sents a challenging active area in both contemporary geometry and mathemat ical physics: it is continuously inspiring the introduction of new mathema tical tools\, ranging from algebraic geometry\, the realm of integrable sy stems\, the analysis of ODE’s\, to the theory of integral transforms and special functions.\n\nThis talk will be a gentle introduction to the anal ytical study of qDE’s\, their relationship with derived categories of co herent sheaves (in both non-equivariant and equivariant settings)\, and a theory of integral representations for its solutions. The talk will be a s urvey of the results of the speaker in this research area.\n LOCATION:https://stable.researchseminars.org/talk/GPL/3/ END:VEVENT BEGIN:VEVENT SUMMARY:André Oliveira (Univ. Porto) DTSTART:20210122T140000Z DTEND:20210122T150000Z DTSTAMP:20260415T002631Z UID:GPL/4 DESCRIPTION:Title: Lie algebras and higher Teichmüller components\nby André Oliveira (Univ. Porto) as part of Geometry and Physics @ Lisbon\n\n\nAbstract\nCon sider the moduli space M(G) of G-Higgs bundles on a compact Riemann surfac e X\, for a real semisimple Lie group G. Hitchin components in the split r eal form case and maximal components in the Hermitian case were\, for seve ral years\, the only known source of examples of higher Teichmüller comp onents of M(G). These components (which are not fully distinguished by top ological invariants) are important because the corresponding representatio ns of the fundamental group of X have special properties\, generalizing Te ichmüller space\, such as being discrete and faithful. Recently\, the ex istence of new such higher Teichmüller components was proved for G = SO( p\,q) which\, in general\, is not neither split nor Hermitian.\n\nIn this talk I will explain the new Lie theoretic notion of magical nilpotent\, wh ich gives rise to the classification of groups for which such components e xist. It turns out that this classification agrees with the one of Guichar d and Wienhard for groups admitting a positive structure. We provide a par ametrization of higher Teichmüller components\, generalizing the Hitchin section for split real forms and the Cayley correspondence for maximal co mponents in the Hermitian (tube type) case.\n\nThis is joint work with S. Bradlow\, B. Collier\, O. García-Prada and P. Gothen.\n LOCATION:https://stable.researchseminars.org/talk/GPL/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Giordano Cotti (GFMUL\, Lisbon) DTSTART:20210209T100000Z DTEND:20210209T120000Z DTSTAMP:20260415T002631Z UID:GPL/5 DESCRIPTION:Title: Frobenius manifolds\, irregular singularities\, and isomonodromy deform ations\, Lecture I\nby Giordano Cotti (GFMUL\, Lisbon) as part of Geom etry and Physics @ Lisbon\n\n\nAbstract\nLecture I - Introduction to Frobe nius manifolds\n\nThe aim of the course is to give a self-contained introd uction to the analytic theory of Frobenius manifolds\, ordinary differenti al equations with rational coefficients in complex domains\, and their iso monodromic deformations. Applications to enumerative geometry will also be discussed. In the final part of the mini-course\, more recent results in this research area will be presented.\n\nThe course will consist of 5 lect ures\, which will be shown live on YouTube\, at the url shown below (where the lectures will stay available for a later view).\n\nThe public has the possibility to ask questions to the speaker through the live-chat\, that will be read by a moderator.\n\nFor more information\, including the sylla bus\, the abstract of each lecture and the recommended literature\, visit: https://irregular.rd.ciencias.ulisboa.pt/frobenius-manifolds-irregular-si ngularities-and-isomonodromy-deformations/\n\nThe course is a part of the FCT Research Project "Irregular connections on algebraic curves and quantu m field theory" (PTDC/MAT-PUR/30234/2017) \nhttps://irregular.rd.ciencias. ulisboa.pt\n\nGroup of Mathematical Physics of Lisbon University\n LOCATION:https://stable.researchseminars.org/talk/GPL/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Giordano Cotti (GFMUL\, Lisbon) DTSTART:20210211T100000Z DTEND:20210211T120000Z DTSTAMP:20260415T002631Z UID:GPL/6 DESCRIPTION:Title: Frobenius manifolds\, irregular singularities\, and isomonodromy deform ations\, Lecture II\nby Giordano Cotti (GFMUL\, Lisbon) as part of Geo metry and Physics @ Lisbon\n\n\nAbstract\nLecture II - Examples of Frobeni us manifolds\n\nThe aim of the course is to give a self-contained introduc tion to the analytic theory of Frobenius manifolds\, ordinary differential equations with rational coefficients in complex domains\, and their isomo nodromic deformations. Applications to enumerative geometry will also be d iscussed. In the final part of the mini-course\, more recent results in th is research area will be presented.\n\nThe course will consist of 5 lectur es\, which will be shown live on YouTube\, at the url shown below (where t he lectures will stay available for a later view).\n\nThe public has the p ossibility to ask questions to the speaker through the live-chat\, that wi ll be read by a moderator.\n\nFor more information\, including the syllabu s\, the abstract of each lecture and the recommended literature\, visit: h ttps://irregular.rd.ciencias.ulisboa.pt/frobenius-manifolds-irregular-sing ularities-and-isomonodromy-deformations/\n\nThe course is a part of the FC T Research Project "Irregular connections on algebraic curves and quantum field theory" (PTDC/MAT-PUR/30234/2017) \nhttps://irregular.rd.ciencias.ul isboa.pt\n\nGroup of Mathematical Physics of Lisbon University\n LOCATION:https://stable.researchseminars.org/talk/GPL/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Giordano Cotti (GFMUL\, Lisbon) DTSTART:20210216T100000Z DTEND:20210216T120000Z DTSTAMP:20260415T002631Z UID:GPL/7 DESCRIPTION:Title: Frobenius manifolds\, irregular singularities\, and isomonodromy deform ations\, Lecture III\nby Giordano Cotti (GFMUL\, Lisbon) as part of Ge ometry and Physics @ Lisbon\n\n\nAbstract\nLecture III - Analytic theory o f Frobenius manifolds\, Part I\n\nThe aim of the course is to give a self- contained introduction to the analytic theory of Frobenius manifolds\, ord inary differential equations with rational coefficients in complex domains \, and their isomonodromic deformations. Applications to enumerative geome try will also be discussed. In the final part of the mini-course\, more re cent results in this research area will be presented.\n\nThe course will c onsist of 5 lectures\, which will be shown live on YouTube\, at the url sh own below (where the lectures will stay available for a later view).\n\nTh e public has the possibility to ask questions to the speaker through the l ive-chat\, that will be read by a moderator.\n\nFor more information\, inc luding the syllabus\, the abstract of each lecture and the recommended lit erature\, visit: https://irregular.rd.ciencias.ulisboa.pt/frobenius-manifo lds-irregular-singularities-and-isomonodromy-deformations/\n\nThe course i s a part of the FCT Research Project "Irregular connections on algebraic c urves and quantum field theory" (PTDC/MAT-PUR/30234/2017) \nhttps://irregu lar.rd.ciencias.ulisboa.pt\n\nGroup of Mathematical Physics of Lisbon Univ ersity\n LOCATION:https://stable.researchseminars.org/talk/GPL/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Giordano Cotti (GFMUL\, Lisbon) DTSTART:20210218T100000Z DTEND:20210218T120000Z DTSTAMP:20260415T002631Z UID:GPL/8 DESCRIPTION:Title: Frobenius manifolds\, irregular singularities\, and isomonodromy deform ations\, Lecture IV\nby Giordano Cotti (GFMUL\, Lisbon) as part of Geo metry and Physics @ Lisbon\n\n\nAbstract\nLecture IV - Analytic theory of Frobenius manifolds\, Part II\n\nThe aim of the course is to give a self-c ontained introduction to the analytic theory of Frobenius manifolds\, ordi nary differential equations with rational coefficients in complex domains\ , and their isomonodromic deformations. Applications to enumerative geomet ry will also be discussed. In the final part of the mini-course\, more rec ent results in this research area will be presented.\n\nThe course will co nsist of 5 lectures\, which will be shown live on YouTube\, at the url sho wn below (where the lectures will stay available for a later view).\n\nThe public has the possibility to ask questions to the speaker through the li ve-chat\, that will be read by a moderator.\n\nFor more information\, incl uding the syllabus\, the abstract of each lecture and the recommended lite rature\, visit: \nhttps://irregular.rd.ciencias.ulisboa.pt/frobenius-manif olds-irregular-singularities-and-isomonodromy-deformations/\n\nThe course is a part of the FCT Research Project "Irregular connections on algebraic curves and quantum field theory" (PTDC/MAT-PUR/30234/2017) \nhttps://irreg ular.rd.ciencias.ulisboa.pt\n\nGroup of Mathematical Physics of Lisbon Uni versity\n LOCATION:https://stable.researchseminars.org/talk/GPL/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Giordano Cotti (GFMUL\, Lisbon) DTSTART:20210219T100000Z DTEND:20210219T120000Z DTSTAMP:20260415T002631Z UID:GPL/9 DESCRIPTION:Title: Frobenius manifolds\, irregular singularities\, and isomonodromy deform ations\, Lecture V\nby Giordano Cotti (GFMUL\, Lisbon) as part of Geom etry and Physics @ Lisbon\n\n\nAbstract\nLecture V - Some recent results a nd work in progress\n\nThe aim of the course is to give a self-contained i ntroduction to the analytic theory of Frobenius manifolds\, ordinary diffe rential equations with rational coefficients in complex domains\, and thei r isomonodromic deformations. Applications to enumerative geometry will al so be discussed. In the final part of the mini-course\, more recent result s in this research area will be presented.\n\nThe course will consist of 5 lectures\, which will be shown live on YouTube\, at the url shown below ( where the lectures will stay available for a later view).\n\nThe public ha s the possibility to ask questions to the speaker through the live-chat\, that will be read by a moderator.\n\nFor more information\, including the syllabus\, the abstract of each lecture and the recommended literature\, v isit: https://irregular.rd.ciencias.ulisboa.pt/frobenius-manifolds-irregul ar-singularities-and-isomonodromy-deformations/\n\nThe course is a part of the FCT Research Project "Irregular connections on algebraic curves and q uantum field theory" (PTDC/MAT-PUR/30234/2017) \nhttps://irregular.rd.cien cias.ulisboa.pt\n\nGroup of Mathematical Physics of Lisbon University\n LOCATION:https://stable.researchseminars.org/talk/GPL/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Thomas Krämer (Humboldt Universität zu Berlin) DTSTART:20210219T140000Z DTEND:20210219T150000Z DTSTAMP:20260415T002631Z UID:GPL/10 DESCRIPTION:Title: Semicontinuity of Gauss maps and the Schottky problem\nby Thomas K rämer (Humboldt Universität zu Berlin) as part of Geometry and Physics @ Lisbon\n\n\nAbstract\nWe show that the degree of the Gauss map for subvar ieties of abelian varieties is semicontinuous in families\, and we discuss its jump loci. In the case of theta divisors this gives a finite stratifi cation of the moduli space of ppav's whose strata include the Torelli locu s and the Prym locus. More generally we obtain semicontinuity results for the intersection cohomology of algebraic varieties with a finite morphism to an abelian variety\, leading to a topological interpretation for variou s jump loci in algebraic geometry. \n\nThis is joint work with Giulio Codo gni.\n LOCATION:https://stable.researchseminars.org/talk/GPL/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Ricardo Campos (CNRS/University of Montpellier) DTSTART:20210319T150000Z DTEND:20210319T160000Z DTSTAMP:20260415T002631Z UID:GPL/11 DESCRIPTION:Title: Configuration spaces of points and their homotopy type\nby Ricardo Campos (CNRS/University of Montpellier) as part of Geometry and Physics @ Lisbon\n\n\nAbstract\nGiven a topological space X\, one can study the con figuration space of n points on it: the subspace of X^n in which two point s cannot share the same position. Despite their apparent simplicity such c onfiguration spaces are remarkably complicated\; the homology of these spa ces is reasonably unknown\, let alone their homotopy type. This classical problem in algebraic topology has much impact in more modern mathematics\, namely in understanding how manifolds can embed in other manifolds\, such as in knot theory. In this talk I will give a gentle introduction to this topic and explain how using ideas going back to Kontsevich we can obtain algebraic models for the rational homotopy type of configuration spaces of points.\n LOCATION:https://stable.researchseminars.org/talk/GPL/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Pierre Schapira (Sorbonne University) DTSTART:20210416T140000Z DTEND:20210416T150000Z DTSTAMP:20260415T002631Z UID:GPL/12 DESCRIPTION:Title: Euler calculus of constructible functions and applications\nby Pie rre Schapira (Sorbonne University) as part of Geometry and Physics @ Lisbo n\n\n\nAbstract\nIn this elementary talk\, we will recall the classical no tions of subanalytic sets\, constructible sheaves and constructible functi ons on a real analytic manifold and explain how to treat such objects “u p to infinity’”. \n\nNext\, we will describe the Euler calculus of con structible functions\, in which integration is purely topological\, with a pplications to tomography. Finally we will show how the gamma-topology on a vector space allows one to embed the space of constructible functions in that of distributions.\n LOCATION:https://stable.researchseminars.org/talk/GPL/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Stéphane Guillermou (CNRS\, Univ. Grenoble) DTSTART:20210514T140000Z DTEND:20210514T150000Z DTSTAMP:20260415T002631Z UID:GPL/13 DESCRIPTION:Title: Stable Gauss map of nearby Lagrangians\nby Stéphane Guillermou (C NRS\, Univ. Grenoble) as part of Geometry and Physics @ Lisbon\n\n\nAbstra ct\nThe stable Gauss map of a Lagrangian $L$ in a cotangent $T^*M$ is a ma p $g\\colon L \\to U/O$ obtained by stabilization of the usual Gauss map f rom $L$ to the Lagrangian Grassmannian of $T^*M$. Arnold's conjecture on nearby Lagrangians implies in particular that $g$ is homotopic to a consta nt map. We will see the weaker result that the map induced by $g$ on the h omotopy groups is trivial.\n\nThis is joint work with Mohammed Abouzaid\, Sylvain Courte and Thomas\n LOCATION:https://stable.researchseminars.org/talk/GPL/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Sean Lawton (George Mason Univ.) DTSTART:20210614T130000Z DTEND:20210614T140000Z DTSTAMP:20260415T002631Z UID:GPL/14 DESCRIPTION:Title: Flawed Groups\nby Sean Lawton (George Mason Univ.) as part of Geom etry and Physics @ Lisbon\n\n\nAbstract\nA group is flawed if its moduli s pace of G-representations is\nhomotopic to its moduli space of K-represent ations for all reductive\naffine algebraic groups G with maximal compact s ubgroup K. In this talk\nwe discuss this definition\, and associated exam ples\, theorems\, and\nconjectures. This work is in collaboration with Car los Florentino.\n LOCATION:https://stable.researchseminars.org/talk/GPL/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Sean Lawton (George Mason Univ.) DTSTART:20210621T130000Z DTEND:20210621T140000Z DTSTAMP:20260415T002631Z UID:GPL/15 DESCRIPTION:Title: Poisson maps between character varieties\nby Sean Lawton (George M ason Univ.) as part of Geometry and Physics @ Lisbon\n\n\nAbstract\nWe exp lore induced mappings between character varieties by\nmappings between sur faces. It is shown that these mappings are generally\nPoisson. We also exp licitly calculate the Poisson bi-vector in a new\ncase. This work is in c ollaboration with Indranil Biswas\, Jacques\nHurtubise\, and Lisa C. Jeffr ey.\n LOCATION:https://stable.researchseminars.org/talk/GPL/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Giosuè Muratore (Univ. Lisbon) DTSTART:20211029T140000Z DTEND:20211029T150000Z DTSTAMP:20260415T002631Z UID:GPL/16 DESCRIPTION:Title: Enumeration of rational contact curves via torus actions\nby Giosu è Muratore (Univ. Lisbon) as part of Geometry and Physics @ Lisbon\n\n\nA bstract\nComplex projective spaces of odd dimension have a unique contact structure. So\, in these spaces we have contact (Legendrian) rational curv es. We are interested in enumeration of such curves. We prove that some Gr omov-Witten numbers associated with rational contact curves in projective space with arbitrary incidence conditions are enumerative. Also\, we use t he Bott formula on the Kontsevich space to find the exact value of those n umbers.\n LOCATION:https://stable.researchseminars.org/talk/GPL/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Giosuè Muratore (FCUL\, Lisbon) DTSTART:20220615T123000Z DTEND:20220615T140000Z DTSTAMP:20260415T002631Z UID:GPL/17 DESCRIPTION:Title: Introduction to Gromov-Witten invariants\, I\nby Giosuè Muratore (FCUL\, Lisbon) as part of Geometry and Physics @ Lisbon\n\nLecture held i n Sala 6.2.33.\n\nAbstract\nThe goal of this crash course is to introduce the basic notions of moduli space of stable maps\nand Gromov-Witten invari ants. In particular when the stable maps have rational domain and the\ntar get is a projective space.\n\nDescription:\nThe course is split in 5 main parts. We will cover the following topics\, time permitting.
\n(1) Basi c definitions.
\n(2) The case of genus 0: boundary divisors and example s.
\n(3) Gromov-Witten invariants.
\n(4) Quantum cohomology.
\n(5 ) Kontsevich-Atiyah-Bott formula.\n LOCATION:https://stable.researchseminars.org/talk/GPL/17/ END:VEVENT BEGIN:VEVENT SUMMARY:Giosuè Muratore (FCUL\, Lisbon) DTSTART:20220617T103000Z DTEND:20220617T120000Z DTSTAMP:20260415T002631Z UID:GPL/18 DESCRIPTION:Title: Introduction to Gromov-Witten invariants\, II\nby Giosuè Muratore (FCUL\, Lisbon) as part of Geometry and Physics @ Lisbon\n\n\nAbstract\nT he goal of this crash course is to introduce the basic notions of moduli s pace of stable maps\nand Gromov-Witten invariants. In particular when the stable maps have rational domain and the\ntarget is a projective space.\n\ nDescription:\nThe course is split in 5 main parts. We will cover the foll owing topics\, time permitting.
\n(1) Basic definitions.
\n(2) The c ase of genus 0: boundary divisors and examples.
\n(3) Gromov-Witten inv ariants.
\n(4) Quantum cohomology.
\n(5) Kontsevich-Atiyah-Bott form ula.\n\nIf time permits\, we will give some enumerative applications.\n\nM ain References:\n\n[CK99] D. A. Cox and S. Katz\, Mirror symmetry and alge braic geometry\, AMS\, 1999.
\n[FP97] W. Fulton and R. Pandharipande\, Notes on stable maps and quantum cohomology\, Algebraic geometry—Santa C ruz 1995\, Proc. Sympos. Pure Math.\, 62\, AMS\, 1997.
\n[HTK+03] K. Ho ri\, R. Thomas\, S. Katz\, C. Vafa\, R. Pandharipande\, A. Klemm\, R. Vaki l\, and E. Zaslow\, Mirror symmetry\, vol. 1\, AMS\, 2003.\n LOCATION:https://stable.researchseminars.org/talk/GPL/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Giosuè Muratore (FCUL\, Lisbon) DTSTART:20220622T103000Z DTEND:20220622T120000Z DTSTAMP:20260415T002631Z UID:GPL/19 DESCRIPTION:Title: Introduction to Gromov-Witten invariants\, III\nby Giosuè Murator e (FCUL\, Lisbon) as part of Geometry and Physics @ Lisbon\n\n\nAbstract\n The goal of this crash course is to introduce the basic notions of moduli space of stable maps\nand Gromov-Witten invariants. In particular when the stable maps have rational domain and the\ntarget is a projective space.\n \nDescription:\nThe course is split in 5 main parts. We will cover the fol lowing topics\, time permitting.
\n(1) Basic definitions.
\n(2) The case of genus 0: boundary divisors and examples.
\n(3) Gromov-Witten in variants.
\n(4) Quantum cohomology.
\n(5) Kontsevich-Atiyah-Bott for mula.\n\nIf time permits\, we will give some enumerative applications.\n\n Main References:\n\n[CK99] D. A. Cox and S. Katz\, Mirror symmetry and alg ebraic geometry\, AMS\, 1999.
\n[FP97] W. Fulton and R. Pandharipande\, Notes on stable maps and quantum cohomology\, Algebraic geometry—Santa Cruz 1995\, Proc. Sympos. Pure Math.\, 62\, AMS\, 1997.
\n[HTK+03] K. H ori\, R. Thomas\, S. Katz\, C. Vafa\, R. Pandharipande\, A. Klemm\, R. Vak il\, and E. Zaslow\, Mirror symmetry\, vol. 1\, AMS\, 2003.\n LOCATION:https://stable.researchseminars.org/talk/GPL/19/ END:VEVENT BEGIN:VEVENT SUMMARY:Giosuè Muratore (FCUL\, Lisbon) DTSTART:20220624T103000Z DTEND:20220624T120000Z DTSTAMP:20260415T002631Z UID:GPL/20 DESCRIPTION:Title: Introduction to Gromov-Witten invariants\, IV\nby Giosuè Muratore (FCUL\, Lisbon) as part of Geometry and Physics @ Lisbon\n\n\nAbstract\nT he goal of this crash course is to introduce the basic notions of moduli s pace of stable maps\nand Gromov-Witten invariants. In particular when the stable maps have rational domain and the\ntarget is a projective space.\n\ nDescription:\nThe course is split in 5 main parts. We will cover the foll owing topics\, time permitting.
\n(1) Basic definitions.
\n(2) The c ase of genus 0: boundary divisors and examples.
\n(3) Gromov-Witten inv ariants.
\n(4) Quantum cohomology.
\n(5) Kontsevich-Atiyah-Bott form ula.\n\nIf time permits\, we will give some enumerative applications.\n\nM ain References:\n\n[CK99] D. A. Cox and S. Katz\, Mirror symmetry and alge braic geometry\, AMS\, 1999.
\n[FP97] W. Fulton and R. Pandharipande\, Notes on stable maps and quantum cohomology\, Algebraic geometry—Santa C ruz 1995\, Proc. Sympos. Pure Math.\, 62\, AMS\, 1997.
\n[HTK+03] K. Ho ri\, R. Thomas\, S. Katz\, C. Vafa\, R. Pandharipande\, A. Klemm\, R. Vaki l\, and E. Zaslow\, Mirror symmetry\, vol. 1\, AMS\, 2003.\n LOCATION:https://stable.researchseminars.org/talk/GPL/20/ END:VEVENT BEGIN:VEVENT SUMMARY:Herwig Hauser (Univ. Vienna) DTSTART:20230202T110000Z DTEND:20230202T123000Z DTSTAMP:20260415T002631Z UID:GPL/21 DESCRIPTION:Title: Moduli of n points on the projective line\nby Herwig Hauser (Univ. Vienna) as part of Geometry and Physics @ Lisbon\n\nLecture held in 6.2.3 3 (Seminar Room\, Math\, FCUL).\n\nAbstract\nThis mini-course addresses Ma ster and Doctoral students as well as Postdoc and Senior researchers in ma thematics.\nObjective: The problem of constructing normal forms and moduli spaces for various geometric objects goes back (at least\, and\namong man y others) to the Italian geometers (Enriques\, Chisini\, Severi\, ...). A highlight was reached in the 1960 and 70es when\nDeligne\, Mumford and Knu dsen investigated and constructed the moduli space of stable curves of gen us $g$. These spectacular\nworks had a huge impact\, though the techniques from algebraic geometry they applied were quite challenging. In the cours e\, we\nwish to offer a gentle and hopefully fascinating introduction to t hese results\, restricting always to curves of genus zero\, that is\,\ntra nsversal unions of projective lines ${\\mathbb P}^1$. This case is already a rich source of ideas and methods.\n\nContents: We start by discussing t he concept of (coarse and fine) moduli spaces\, universal families and the philosophical\nbackground thereof: why is it natural to study such questi ons\, and why the given axiomatic framework is the correct one? Once\nwe h ave become familiar with these foundations (seeing many examples on the wa y)\, we will concentrate on n points in ${\\mathbb P}^1$ and\nthe action o f $PGL_2$ on them by Mobius transformations. This is part of classical pro jective geometry and very beautiful. As long as the $n$ points are pairwis e distinct\, things are easy\, and a moduli space is easily constructed. T hings become tricky as the points start to move and thus become closer to each other until they collide and coalesce. What are the limiting configur ations of the points one has to expect in this variation? This question ha s a long history - Grothendieck proposed in SGA1 a convincing answer: $n$- pointed stable curves.\n\nWe will take at the beginning a different approa ch by proposing an alternative version of limit. Namely\, we embed the spa ce of $n$\ndistinct points in a large projective space and then take limit s therein via the Zariski-closure. This opens the door to the theory of\np hylogenetic trees: they are certain finite graphs with leaves and inner ve rtices as a tree in a forest. Their geometric combinatorics\nwill become t he guiding principle to design many proofs for our moduli spaces. Working with phylogenetic trees can be a very\npleasing occupation\, we will draw\ , glue\, cut and compose these trees and thus get surprising constructions and insights.\nAt that point a miracle happens: The stable curves of Grot hendieck\, Deligne\, Mumford\, Knudsen pop up on their own. We don’t\nev en have to define them - they are just there. So the circle closes up\, an d our journey is now able to reprove many of the classical\nresults in an easy going and appealing manner.\nThe course is based on a recent research cooperation with Jiayue Qi and Josef Schicho from the University of Linz within the\nproject P34765 of the Austrian Science Fund FWF.\n\nHerwig Hau ser\, Faculty of Mathematics\, University of Vienna herwig.hauser@univie.a c.at\n LOCATION:https://stable.researchseminars.org/talk/GPL/21/ END:VEVENT BEGIN:VEVENT SUMMARY:Herwig Hauser (Univ. Vienna) DTSTART:20230203T110000Z DTEND:20230203T123000Z DTSTAMP:20260415T002631Z UID:GPL/22 DESCRIPTION:Title: Moduli of n points on the projective line\nby Herwig Hauser (Univ. Vienna) as part of Geometry and Physics @ Lisbon\n\nLecture held in 6.2.3 3 (Seminar Room\, Math\, FCUL).\n\nAbstract\nThis mini-course addresses Ma ster and Doctoral students as well as Postdoc and Senior researchers in ma thematics.\nObjective: The problem of constructing normal forms and moduli spaces for various geometric objects goes back (at least\, and\namong man y others) to the Italian geometers (Enriques\, Chisini\, Severi\, ...). A highlight was reached in the 1960 and 70es when\nDeligne\, Mumford and Knu dsen investigated and constructed the moduli space of stable curves of gen us $g$. These spectacular\nworks had a huge impact\, though the techniques from algebraic geometry they applied were quite challenging. In the cours e\, we\nwish to offer a gentle and hopefully fascinating introduction to t hese results\, restricting always to curves of genus zero\, that is\,\ntra nsversal unions of projective lines ${\\mathbb P}^1$. This case is already a rich source of ideas and methods.\n\nContents: We start by discussing t he concept of (coarse and fine) moduli spaces\, universal families and the philosophical\nbackground thereof: why is it natural to study such questi ons\, and why the given axiomatic framework is the correct one? Once\nwe h ave become familiar with these foundations (seeing many examples on the wa y)\, we will concentrate on n points in ${\\mathbb P}^1$ and\nthe action o f $PGL_2$ on them by Mobius transformations. This is part of classical pro jective geometry and very beautiful. As long as the $n$ points are pairwis e distinct\, things are easy\, and a moduli space is easily constructed. T hings become tricky as the points start to move and thus become closer to each other until they collide and coalesce. What are the limiting configur ations of the points one has to expect in this variation? This question ha s a long history - Grothendieck proposed in SGA1 a convincing answer: $n$- pointed stable curves.\n\nWe will take at the beginning a different approa ch by proposing an alternative version of limit. Namely\, we embed the spa ce of $n$\ndistinct points in a large projective space and then take limit s therein via the Zariski-closure. This opens the door to the theory of\np hylogenetic trees: they are certain finite graphs with leaves and inner ve rtices as a tree in a forest. Their geometric combinatorics\nwill become t he guiding principle to design many proofs for our moduli spaces. Working with phylogenetic trees can be a very\npleasing occupation\, we will draw\ , glue\, cut and compose these trees and thus get surprising constructions and insights.\nAt that point a miracle happens: The stable curves of Grot hendieck\, Deligne\, Mumford\, Knudsen pop up on their own. We don’t\nev en have to define them - they are just there. So the circle closes up\, an d our journey is now able to reprove many of the classical\nresults in an easy going and appealing manner.\nThe course is based on a recent research cooperation with Jiayue Qi and Josef Schicho from the University of Linz within the\nproject P34765 of the Austrian Science Fund FWF.\n\nHerwig Hau ser\, Faculty of Mathematics\, University of Vienna herwig.hauser@univie.a c.at\n LOCATION:https://stable.researchseminars.org/talk/GPL/22/ END:VEVENT BEGIN:VEVENT SUMMARY:Herwig Hauser (Univ. Vienna) DTSTART:20230209T110000Z DTEND:20230209T123000Z DTSTAMP:20260415T002631Z UID:GPL/23 DESCRIPTION:Title: Moduli of n points on the projective line\nby Herwig Hauser (Univ. Vienna) as part of Geometry and Physics @ Lisbon\n\nLecture held in 6.2.3 3 (Seminar Room\, Math\, FCUL).\n\nAbstract\nThis mini-course addresses Ma ster and Doctoral students as well as Postdoc and Senior researchers in ma thematics.\nObjective: The problem of constructing normal forms and moduli spaces for various geometric objects goes back (at least\, and\namong man y others) to the Italian geometers (Enriques\, Chisini\, Severi\, ...). A highlight was reached in the 1960 and 70es when\nDeligne\, Mumford and Knu dsen investigated and constructed the moduli space of stable curves of gen us $g$. These spectacular\nworks had a huge impact\, though the techniques from algebraic geometry they applied were quite challenging. In the cours e\, we\nwish to offer a gentle and hopefully fascinating introduction to t hese results\, restricting always to curves of genus zero\, that is\,\ntra nsversal unions of projective lines ${\\mathbb P}^1$. This case is already a rich source of ideas and methods.\n\nContents: We start by discussing t he concept of (coarse and fine) moduli spaces\, universal families and the philosophical\nbackground thereof: why is it natural to study such questi ons\, and why the given axiomatic framework is the correct one? Once\nwe h ave become familiar with these foundations (seeing many examples on the wa y)\, we will concentrate on n points in ${\\mathbb P}^1$ and\nthe action o f $PGL_2$ on them by Mobius transformations. This is part of classical pro jective geometry and very beautiful. As long as the $n$ points are pairwis e distinct\, things are easy\, and a moduli space is easily constructed. T hings become tricky as the points start to move and thus become closer to each other until they collide and coalesce. What are the limiting configur ations of the points one has to expect in this variation? This question ha s a long history - Grothendieck proposed in SGA1 a convincing answer: $n$- pointed stable curves.\n\nWe will take at the beginning a different approa ch by proposing an alternative version of limit. Namely\, we embed the spa ce of $n$\ndistinct points in a large projective space and then take limit s therein via the Zariski-closure. This opens the door to the theory of\np hylogenetic trees: they are certain finite graphs with leaves and inner ve rtices as a tree in a forest. Their geometric combinatorics\nwill become t he guiding principle to design many proofs for our moduli spaces. Working with phylogenetic trees can be a very\npleasing occupation\, we will draw\ , glue\, cut and compose these trees and thus get surprising constructions and insights.\nAt that point a miracle happens: The stable curves of Grot hendieck\, Deligne\, Mumford\, Knudsen pop up on their own. We don’t\nev en have to define them - they are just there. So the circle closes up\, an d our journey is now able to reprove many of the classical\nresults in an easy going and appealing manner.\nThe course is based on a recent research cooperation with Jiayue Qi and Josef Schicho from the University of Linz within the\nproject P34765 of the Austrian Science Fund FWF.\n\nHerwig Hau ser\, Faculty of Mathematics\, University of Vienna herwig.hauser@univie.a c.at\n LOCATION:https://stable.researchseminars.org/talk/GPL/23/ END:VEVENT BEGIN:VEVENT SUMMARY:Herwig Hauser (Univ. Vienna) DTSTART:20230210T110000Z DTEND:20230210T123000Z DTSTAMP:20260415T002631Z UID:GPL/24 DESCRIPTION:Title: Moduli of n points on the projective line\nby Herwig Hauser (Univ. Vienna) as part of Geometry and Physics @ Lisbon\n\nLecture held in 6.2.3 3 (Seminar Room\, Math\, FCUL).\n\nAbstract\nThis mini-course addresses Ma ster and Doctoral students as well as Postdoc and Senior researchers in ma thematics.\nObjective: The problem of constructing normal forms and moduli spaces for various geometric objects goes back (at least\, and\namong man y others) to the Italian geometers (Enriques\, Chisini\, Severi\, ...). A highlight was reached in the 1960 and 70es when\nDeligne\, Mumford and Knu dsen investigated and constructed the moduli space of stable curves of gen us $g$. These spectacular\nworks had a huge impact\, though the techniques from algebraic geometry they applied were quite challenging. In the cours e\, we\nwish to offer a gentle and hopefully fascinating introduction to t hese results\, restricting always to curves of genus zero\, that is\,\ntra nsversal unions of projective lines ${\\mathbb P}^1$. This case is already a rich source of ideas and methods.\n\nContents: We start by discussing t he concept of (coarse and fine) moduli spaces\, universal families and the philosophical\nbackground thereof: why is it natural to study such questi ons\, and why the given axiomatic framework is the correct one? Once\nwe h ave become familiar with these foundations (seeing many examples on the wa y)\, we will concentrate on n points in ${\\mathbb P}^1$ and\nthe action o f $PGL_2$ on them by Mobius transformations. This is part of classical pro jective geometry and very beautiful. As long as the $n$ points are pairwis e distinct\, things are easy\, and a moduli space is easily constructed. T hings become tricky as the points start to move and thus become closer to each other until they collide and coalesce. What are the limiting configur ations of the points one has to expect in this variation? This question ha s a long history - Grothendieck proposed in SGA1 a convincing answer: $n$- pointed stable curves.\n\nWe will take at the beginning a different approa ch by proposing an alternative version of limit. Namely\, we embed the spa ce of $n$\ndistinct points in a large projective space and then take limit s therein via the Zariski-closure. This opens the door to the theory of\np hylogenetic trees: they are certain finite graphs with leaves and inner ve rtices as a tree in a forest. Their geometric combinatorics\nwill become t he guiding principle to design many proofs for our moduli spaces. Working with phylogenetic trees can be a very\npleasing occupation\, we will draw\ , glue\, cut and compose these trees and thus get surprising constructions and insights.\nAt that point a miracle happens: The stable curves of Grot hendieck\, Deligne\, Mumford\, Knudsen pop up on their own. We don’t\nev en have to define them - they are just there. So the circle closes up\, an d our journey is now able to reprove many of the classical\nresults in an easy going and appealing manner.\nThe course is based on a recent research cooperation with Jiayue Qi and Josef Schicho from the University of Linz within the\nproject P34765 of the Austrian Science Fund FWF.\n\nHerwig Hau ser\, Faculty of Mathematics\, University of Vienna herwig.hauser@univie.a c.at\n LOCATION:https://stable.researchseminars.org/talk/GPL/24/ END:VEVENT BEGIN:VEVENT SUMMARY:Herwig Hauser (Univ. Vienna) DTSTART:20230213T110000Z DTEND:20230213T123000Z DTSTAMP:20260415T002631Z UID:GPL/25 DESCRIPTION:Title: Moduli of n points on the projective line\nby Herwig Hauser (Univ. Vienna) as part of Geometry and Physics @ Lisbon\n\nLecture held in 6.2.3 3 (Seminar Room\, Math\, FCUL).\n\nAbstract\nThis mini-course addresses Ma ster and Doctoral students as well as Postdoc and Senior researchers in ma thematics.\nObjective: The problem of constructing normal forms and moduli spaces for various geometric objects goes back (at least\, and\namong man y others) to the Italian geometers (Enriques\, Chisini\, Severi\, ...). A highlight was reached in the 1960 and 70es when\nDeligne\, Mumford and Knu dsen investigated and constructed the moduli space of stable curves of gen us $g$. These spectacular\nworks had a huge impact\, though the techniques from algebraic geometry they applied were quite challenging. In the cours e\, we\nwish to offer a gentle and hopefully fascinating introduction to t hese results\, restricting always to curves of genus zero\, that is\,\ntra nsversal unions of projective lines ${\\mathbb P}^1$. This case is already a rich source of ideas and methods.\n\nContents: We start by discussing t he concept of (coarse and fine) moduli spaces\, universal families and the philosophical\nbackground thereof: why is it natural to study such questi ons\, and why the given axiomatic framework is the correct one? Once\nwe h ave become familiar with these foundations (seeing many examples on the wa y)\, we will concentrate on n points in ${\\mathbb P}^1$ and\nthe action o f $PGL_2$ on them by Mobius transformations. This is part of classical pro jective geometry and very beautiful. As long as the $n$ points are pairwis e distinct\, things are easy\, and a moduli space is easily constructed. T hings become tricky as the points start to move and thus become closer to each other until they collide and coalesce. What are the limiting configur ations of the points one has to expect in this variation? This question ha s a long history - Grothendieck proposed in SGA1 a convincing answer: $n$- pointed stable curves.\n\nWe will take at the beginning a different approa ch by proposing an alternative version of limit. Namely\, we embed the spa ce of $n$\ndistinct points in a large projective space and then take limit s therein via the Zariski-closure. This opens the door to the theory of\np hylogenetic trees: they are certain finite graphs with leaves and inner ve rtices as a tree in a forest. Their geometric combinatorics\nwill become t he guiding principle to design many proofs for our moduli spaces. Working with phylogenetic trees can be a very\npleasing occupation\, we will draw\ , glue\, cut and compose these trees and thus get surprising constructions and insights.\nAt that point a miracle happens: The stable curves of Grot hendieck\, Deligne\, Mumford\, Knudsen pop up on their own. We don’t\nev en have to define them - they are just there. So the circle closes up\, an d our journey is now able to reprove many of the classical\nresults in an easy going and appealing manner.\nThe course is based on a recent research cooperation with Jiayue Qi and Josef Schicho from the University of Linz within the\nproject P34765 of the Austrian Science Fund FWF.\n\nHerwig Hau ser\, Faculty of Mathematics\, University of Vienna herwig.hauser@univie.a c.at\n LOCATION:https://stable.researchseminars.org/talk/GPL/25/ END:VEVENT BEGIN:VEVENT SUMMARY:Davide Guzzetti (SISSA\, Italy) DTSTART:20221206T110000Z DTEND:20221206T120000Z DTSTAMP:20260415T002631Z UID:GPL/26 DESCRIPTION:Title: Introduction to isomonodromy deformations and applications\nby Dav ide Guzzetti (SISSA\, Italy) as part of Geometry and Physics @ Lisbon\n\nL ecture held in 6.2.33 (Seminar Room\, Math\, FCUL).\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/GPL/26/ END:VEVENT BEGIN:VEVENT SUMMARY:Jean Douçot (GFM\, Universidade de Lisboa) DTSTART:20230130T110000Z DTEND:20230130T120000Z DTSTAMP:20260415T002631Z UID:GPL/27 DESCRIPTION:Title: somonodromic deformations and generalised braid groups\nby Jean Do uçot (GFM\, Universidade de Lisboa) as part of Geometry and Physics @ Lis bon\n\nLecture held in 6.2.33 (Seminar Room\, Math\, FCUL).\nAbstract: TBA \n LOCATION:https://stable.researchseminars.org/talk/GPL/27/ END:VEVENT BEGIN:VEVENT SUMMARY:Gonçalo Oliveira (IST\, Universidade de Lisboa) DTSTART:20230228T110000Z DTEND:20230228T120000Z DTSTAMP:20260415T002631Z UID:GPL/28 DESCRIPTION:Title: From electrostatics to geodesics in K3 surfaces\nby Gonçalo Olive ira (IST\, Universidade de Lisboa) as part of Geometry and Physics @ Lisbo n\n\nLecture held in 6.2.33 (Seminar Room\, Math\, FCUL).\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/GPL/28/ END:VEVENT BEGIN:VEVENT SUMMARY:Xavier Blot (GFM\, Universidade de Lisboa) DTSTART:20230328T100000Z DTEND:20230328T110000Z DTSTAMP:20260415T002631Z UID:GPL/29 DESCRIPTION:Title: The quantum Witten-Kontsevich series\nby Xavier Blot (GFM\, Univer sidade de Lisboa) as part of Geometry and Physics @ Lisbon\n\nLecture held in 6.2.33 (Seminar Room\, Math\, FCUL).\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/GPL/29/ END:VEVENT BEGIN:VEVENT SUMMARY:Leonardo Santilli (Yau Mathematical Sciences Center) DTSTART:20230418T100000Z DTEND:20230418T110000Z DTSTAMP:20260415T002631Z UID:GPL/30 DESCRIPTION:Title: Quivers counting monster potentials\nby Leonardo Santilli (Yau Mat hematical Sciences Center) as part of Geometry and Physics @ Lisbon\n\nLec ture held in 6.2.33 (Seminar Room\, Math\, FCUL).\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/GPL/30/ END:VEVENT BEGIN:VEVENT SUMMARY:Giosuè Muratore (CMAFcIO\, Universidade de Lisboa) DTSTART:20230511T100000Z DTEND:20230511T110000Z DTSTAMP:20260415T002631Z UID:GPL/31 DESCRIPTION:Title: Enumeration of rational contact curves: the irreducible case\nby G iosuè Muratore (CMAFcIO\, Universidade de Lisboa) as part of Geometry and Physics @ Lisbon\n\nLecture held in 6.2.33 (Seminar Room\, Math\, FCUL).\ nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/GPL/31/ END:VEVENT BEGIN:VEVENT SUMMARY:Wilhelm Schlag (Yale University) DTSTART:20230516T100000Z DTEND:20230516T110000Z DTSTAMP:20260415T002631Z UID:GPL/32 DESCRIPTION:Title: Lyapunov exponents\, Schrödinger cocycles\, and Avila’s global theo ry\nby Wilhelm Schlag (Yale University) as part of Geometry and Physic s @ Lisbon\n\nLecture held in 6.2.33 (Seminar Room\, Math\, FCUL).\nAbstra ct: TBA\n LOCATION:https://stable.researchseminars.org/talk/GPL/32/ END:VEVENT BEGIN:VEVENT SUMMARY:Vicente Muñoz (Univ. Complutense\, Madrid) DTSTART:20230706T100000Z DTEND:20230706T110000Z DTSTAMP:20260415T002631Z UID:GPL/33 DESCRIPTION:Title: A Smale-Barden manifold admitting K-contact but no Sasakian structure< /a>\nby Vicente Muñoz (Univ. Complutense\, Madrid) as part of Geometry an d Physics @ Lisbon\n\nLecture held in 6.2.33 (Seminar Room\, Math\, FCUL). \nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/GPL/33/ END:VEVENT BEGIN:VEVENT SUMMARY:Luca Scala (UFRJ\, Brasil & Univ. Lusófona) DTSTART:20230704T100000Z DTEND:20230704T110000Z DTSTAMP:20260415T002631Z UID:GPL/34 DESCRIPTION:Title: Cohomology of tautological boundles on Hilbert schemes of point and re lated problems\nby Luca Scala (UFRJ\, Brasil & Univ. Lusófona) as par t of Geometry and Physics @ Lisbon\n\nLecture held in 6.2.33 (Seminar Room \, Math\, FCUL).\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/GPL/34/ END:VEVENT BEGIN:VEVENT SUMMARY:Azizeh Nozad (IPM\, Iran) DTSTART:20230622T100000Z DTEND:20230622T110000Z DTSTAMP:20260415T002631Z UID:GPL/35 DESCRIPTION:Title: Serre polynomials of character varieties of free groups\nby Azizeh Nozad (IPM\, Iran) as part of Geometry and Physics @ Lisbon\n\nLecture he ld in 6.2.33 (Seminar Room\, Math\, FCUL).\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/GPL/35/ END:VEVENT BEGIN:VEVENT SUMMARY:Vadim Lebovici (Univ. Paris-Sud & E.N.S.) DTSTART:20230620T100000Z DTEND:20230620T110000Z DTSTAMP:20260415T002631Z UID:GPL/36 DESCRIPTION:Title: Euler calculus and its applications\nby Vadim Lebovici (Univ. Pari s-Sud & E.N.S.) as part of Geometry and Physics @ Lisbon\n\nLecture held i n 6.2.33 (Seminar Room\, Math\, FCUL).\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/GPL/36/ END:VEVENT BEGIN:VEVENT SUMMARY:Miguel Moreira (MIT) DTSTART:20240110T110000Z DTEND:20240110T120000Z DTSTAMP:20260415T002631Z UID:GPL/37 DESCRIPTION:Title: The cohomology ring of moduli spaces of 1-dimensional sheaves on $\\ma thbb P^2$\nby Miguel Moreira (MIT) as part of Geometry and Physics @ L isbon\n\nLecture held in 6.2.33 (Seminar Room\, Math\, FCUL).\n\nAbstract\ nIn this talk I will go over some recent results and conjectures concernin g the cohomology (and in particular its ring structure) of the moduli spac es of stable 1-dimensional sheaves on the projective plane. The cohomology of such moduli spaces\, together with its perverse filtration\, is conjec tured to be related to curve counting on the total space of the canonical bundle of $\\mathbb P^2$. I will explain a strategy to fully describe the cohomology rings of moduli spaces of sheaves supported in curves up to deg ree 5\, and how that can be used to verify this prediction in such degrees . If time allows\, I will explain a new conjectural description of the per verse filtration which we have also verified up to degree 5. This is based on joint work with Y. Kononov\, W. Lim and W. Pi.\n LOCATION:https://stable.researchseminars.org/talk/GPL/37/ END:VEVENT BEGIN:VEVENT SUMMARY:Ángel González-Prieto (Univ. Complutense Madrid) DTSTART:20240618T100000Z DTEND:20240618T110000Z DTSTAMP:20260415T002631Z UID:GPL/38 DESCRIPTION:Title: Character Varieties of Knots\nby Ángel González-Prieto (Univ. Co mplutense Madrid) as part of Geometry and Physics @ Lisbon\n\nLecture held in 6.2.33 (Seminar Room\, Math\, FCUL).\n\nAbstract\nKnot invariants\, su ch as the Jones polynomial and the Reshetikhin-Turaev invariants\, are ubi quitous in the study of 3-manifold geometry. Among these invariants\, one stands out: the fundamental group of the complement of the knot\, also kno wn as the knot group. Particularly interesting is the study of the space o f representations of these knot groups\, referred to as the character vari eties of knots. Even the simplest properties of these character varieties have led to profound results in hyperbolic geometry. However\, general met hods to uncover the deep geometric features of these spaces are still lack ing.\n\nIn this talk\, we will discuss various aspects of these character varieties from both geometric and algebraic perspectives. Even for charact er varieties of torus knots\, intriguing features emerge that allow us to compare their geometry in both the complex and real cases. Time permitting \, we will also explore how Topological Quantum Field Theories can be empl oyed to provide unexpected generalized skein relations for the arithmetic of character varieties of knots over finite groups.\n LOCATION:https://stable.researchseminars.org/talk/GPL/38/ END:VEVENT BEGIN:VEVENT SUMMARY:Sean Lawton (George Mason Univ.) DTSTART:20240619T100000Z DTEND:20240619T110000Z DTSTAMP:20260415T002631Z UID:GPL/39 DESCRIPTION:Title: The SU(2\,1)-character variety of the 1-holed torus\nby Sean Lawto n (George Mason Univ.) as part of Geometry and Physics @ Lisbon\n\nLecture held in 6.2.33 (Seminar Room\, Math\, FCUL).\n\nAbstract\nWe sketch the p roof that the SU(2\,1)-character variety of the 1-holed torus is homotopic to a product of circles. We then discuss the mapping class group dynamic s on this character variety. In particular\, we describe an open domain o f discontinuity. This work represents collaborative work with Sara Maloni and Frédéric Palesi. See arXiv:2402.10838 for more information.\n LOCATION:https://stable.researchseminars.org/talk/GPL/39/ END:VEVENT BEGIN:VEVENT SUMMARY:Andrew P. Turner (Virginia Tech (USA)) DTSTART:20241106T160000Z DTEND:20241106T170000Z DTSTAMP:20260415T002631Z UID:GPL/40 DESCRIPTION:Title: Higgsing on SU(N) Symmetric Matter and its F-theory Realization\nb y Andrew P. Turner (Virginia Tech (USA)) as part of Geometry and Physics @ Lisbon\n\nLecture held in 6.2.33 (Seminar Room\, Math\, FCUL).\n\nAbstrac t\nF-theory is a powerful framework for studying string compactifications that encodes many of the details of the physical theory in the geometry of a singular elliptically fibered Calabi–Yau manifold. In the first part of this talk\, I will provide an introduction to F-theory\, discussing the motivation for this construction and the mathematical techniques used to analyze F-theory vacua. I will then describe recent work on the explicit r ealization within F-theory of the Higgsing of an SU(N) gauge theory on sym metric matter\, primarily exploiting heterotic/F-theory duality. The new m odels analyzed in this work provide explicit counterexamples to several lo ng-standing assumptions about the physical interpretation of the Mordell –Weil group of the elliptic fibration.\n LOCATION:https://stable.researchseminars.org/talk/GPL/40/ END:VEVENT BEGIN:VEVENT SUMMARY:Giosuè Muratore (CEMS.UL\, Lisbon) DTSTART:20250110T150000Z DTEND:20250110T160000Z DTSTAMP:20260415T002631Z UID:GPL/41 DESCRIPTION:Title: Counts of lines with tangency conditions in A1-homotopy\nby Giosu è Muratore (CEMS.UL\, Lisbon) as part of Geometry and Physics @ Lisbon\n\ nLecture held in 6.2.33 (Seminar Room\, Math\, FCUL).\n\nAbstract\nA¹-hom otopy theory\, introduced by Morel and Voevodsky\, provides a powerful mot ivic framework that bridges algebraic geometry and the methods of classica l topology. By extending the toolkit of algebraic geometry with concepts f rom homotopy theory\, this approach has opened the door to a wide range of applications across the field. In this talk\, we will outline the fundame ntal ideas behind A¹-homotopy theory and explore its relevance in enumera tive geometry\, highlighting recent developments and results.\n LOCATION:https://stable.researchseminars.org/talk/GPL/41/ END:VEVENT BEGIN:VEVENT SUMMARY:Alejandro Calleja (Univ. Complutense\, Madrid) DTSTART:20250217T110000Z DTEND:20250217T120000Z DTSTAMP:20260415T002631Z UID:GPL/42 DESCRIPTION:Title: Character Varieties in Knot Theory\nby Alejandro Calleja (Univ. Co mplutense\, Madrid) as part of Geometry and Physics @ Lisbon\n\nLecture he ld in 6.2.33 (Seminar Room\, Math\, FCUL).\n\nAbstract\nGiven an algebraic group G and a knot K ⊂ S^3\, we define the G-character variety of K as the moduli space of representations ρ : π1(S^3 − K) → G of the knot group into G. The importance of these varieties lies in the fact that thei r study provides in a natural way many knot invariants.\n\nIn this talk\, we will introduce one of the most important of these invariants\, the E-po lynomial\, exposing the techniques used to study them\, as well as the mai n known results\, focusing especially on the case of torus knots. In this context\, being able to distinguish when two representations are isomorphi c becomes crucial. For facing this problem\, we will introduce the configu ration space of orbits\, a variety formed by tuples of pairwise non-isomor phic representations.\n LOCATION:https://stable.researchseminars.org/talk/GPL/42/ END:VEVENT BEGIN:VEVENT SUMMARY:Marcos Petrúcio Cavalcante (Univ. Fed. de Alagoas) DTSTART:20250225T133000Z DTEND:20250225T143000Z DTSTAMP:20260415T002631Z UID:GPL/43 DESCRIPTION:Title: Stability of extremal domains\nby Marcos Petrúcio Cavalcante (Uni v. Fed. de Alagoas) as part of Geometry and Physics @ Lisbon\n\nLecture he ld in 6.2.33 (Seminar Room\, Math\, FCUL).\n\nAbstract\nA domain in a Riem annian manifold is said to be extremal if it is a critical point of the fi rst eigenvalue functional under volume-preserving variations. From this va riational characterization\, we derive a natural notion of stability. In t his talk\, we classify the stable extremal domains in the 2-sphere and in higher-dimensional spheres when the boundary is minimal. Additionally\, we establish topological bounds for stable domains in general compact Rieman nian surfaces\, assuming either nonnegative total Gaussian curvature or sm all volume. This is joint work with Ivaldo Nunes (UFMA).\n LOCATION:https://stable.researchseminars.org/talk/GPL/43/ END:VEVENT BEGIN:VEVENT SUMMARY:Markus Kiderlen (Aarhus University) DTSTART:20250226T140000Z DTEND:20250226T160000Z DTSTAMP:20260415T002631Z UID:GPL/44 DESCRIPTION:Title: Crofton-type Formulae in Rotational Integral Geometry\nby Markus K iderlen (Aarhus University) as part of Geometry and Physics @ Lisbon\n\nLe cture held in 6.2.33 (Seminar Room\, Math\, FCUL).\n\nAbstract\nThe purpos e of this talk is to give an introduction to rotational integral geometry and exemplify a number of its core results and their applications. Integra l geometry\, introduced by Blaschke in the 1930s\, is the theory of invar iant measures on geometric spaces (often Grassmannians) and its applicatio n to determine geometric probabilities.\n\nWe will start by recalling the kinematic Crofton formula\, which allows us to retrieve certain geometric characteristics (such as volume\, surface area and other intrinsic volumes ) of a compact convex set $K$ in $\\mathbb R^n$ from intersections with in variantly integrated $k$-dimensional affine subspaces\, where $k=0\,\\ldot s\,n-1$ is fixed.\n\nMotivated by applications from biology\, we suggest a number of variants of Crofton's formula\, where the intersecting affine s paces are constrained to contain the origin -- and hence are just linear s ubspaces -- or even all contain a fixed lower-dimensional axis. Correspond ing rotational Crofton formulae will be established and explained. We als o show that the set of these formulae is complete in that they retrieve al l possible intrinsic volumes of $K$. Proofs rely on old and new Blaschke-P etkantschin theorems\, which we also will outline.\n\nJoint work with Emil Dare and Eva B. Vedel Jensen.\n LOCATION:https://stable.researchseminars.org/talk/GPL/44/ END:VEVENT BEGIN:VEVENT SUMMARY:Fabrizio Del Monte (University of Birmingham\, UK) DTSTART:20250416T130000Z DTEND:20250416T140000Z DTSTAMP:20260415T002631Z UID:GPL/45 DESCRIPTION:Title: Monodromies\, Clusters\, and the WKB Approximation for q-Difference Eq uations\nby Fabrizio Del Monte (University of Birmingham\, UK) as part of Geometry and Physics @ Lisbon\n\nLecture held in 6.2.33 (Seminar Room\ , Math\, FCUL).\n\nAbstract\nThe study of monodromies of differential equa tions has been a rich area of mathematical physics\, interconnected with v arious fields in mathematics and physics. Recent discoveries reveal that m onodromy varieties naturally possess the structure of cluster varieties\, significantly enhancing our understanding of their connections to string t heory and Donaldson–Thomas invariants. A key technique in these developm ents is the (exact) WKB approximation. In string theory\, q-difference equ ations (qDEs) naturally appear as an "M-theory completion" of differential equations\, though defining monodromy in this context remains an active r esearch area. In this seminar\, I will discuss how the WKB approximation\, traditionally formulated for second-order ODEs\, can be effectively gener alized to second-order q-difference equations\, providing a natural charac terization of their monodromies. Central to this approach is the WKB Stoke s diagram\, known in the physics literature as the exponential network\, w hich offers a framework for defining cluster coordinates for monodromies o f qDEs.\n\nI will illustrate this formalism through explicit examples\, in cluding the q-difference Mathieu equation. Remarkably\, its monodromy arou nd the origin—known in topological string theory as the quantum mirror m ap—takes the form of the Hamiltonian of a cluster integrable system in t erms of these cluster coordinates.\n LOCATION:https://stable.researchseminars.org/talk/GPL/45/ END:VEVENT BEGIN:VEVENT SUMMARY:Tomás Inácio (Fac. Ciências ULisboa) DTSTART:20250514T133000Z DTEND:20250514T143000Z DTSTAMP:20260415T002631Z UID:GPL/46 DESCRIPTION:Title: A Hitchhiker’s Guide to Joyce Structures\nby Tomás Inácio (Fac . Ciências ULisboa) as part of Geometry and Physics @ Lisbon\n\nLecture h eld in 6.2.33 (Seminar Room\, Math\, FCUL).\n\nAbstract\nJoyce structures were introduced by Tom Bridgeland in the context of stability conditions a nd were constructed in close analogy to Frobenius structures introduced in Topological Field Theories. The main motivation behind them was the simil arity between the Iso-Stokes condition and the Kontsevich-Soibelman Wall C rossing Formula. Since then\, Joyce structures have exhibited not only a r ich analytical side but also an extremely interesting geometric structure. \n\nIn this seminar\, I will introduce these works\, starting with the def inition and motivation of Joyce structures and then moving to the formulat ion of the Riemann-Hilbert-Birkhoff problem. After discussing an explicit solution\, I will conclude by exploring the geometric side and interpretin g all the concepts in this new setting. Given the variety of topics\, I wi ll make an effort to provide specific examples.\n LOCATION:https://stable.researchseminars.org/talk/GPL/46/ END:VEVENT BEGIN:VEVENT SUMMARY:Ariel Pacetti (Universidade de Aveiro) DTSTART:20250604T133000Z DTEND:20250604T143000Z DTSTAMP:20260415T002631Z UID:GPL/47 DESCRIPTION:Title: Langlands Program and Applications\nby Ariel Pacetti (Universidade de Aveiro) as part of Geometry and Physics @ Lisbon\n\nLecture held in 6. 2.33 (Seminar Room\, Math\, FCUL).\n\nAbstract\nThe goal of this general a udience talk is to introduce the L-function attached to a projective varie ty and state some of its expected properties. A way to prove such properti es is to relate the L-function to objects of a more analytic nature (namel y automorphic forms). During the talk we will study some baby examples of the correspondence\, and state some recent results (as well as some open p roblems). At last we will explain how the theory is well suited for the st udy of solutions to Diophantine equations (we will include a 5 minutes pro of of Fermat's last theorem).\n LOCATION:https://stable.researchseminars.org/talk/GPL/47/ END:VEVENT BEGIN:VEVENT SUMMARY:Jean-Pierre Bourguignon (IHÉS (Nicolaas Kuiper Honorary Professor )) DTSTART:20250625T140000Z DTEND:20250625T150000Z DTSTAMP:20260415T002631Z UID:GPL/48 DESCRIPTION:Title: Revisiting the scalar curvature\nby Jean-Pierre Bourguignon (IHÉS (Nicolaas Kuiper Honorary Professor)) as part of Geometry and Physics @ L isbon\n\nLecture held in 6.2.33 (Seminar Room\, Math\, FCUL).\n\nAbstract\ nThe scalar curvature is the weakest invariant involving the curvature of a Riemannian metric. On surfaces\, where the concept of curvature was firs t developed by Carl-Friedrich GAUSS\, the curvature reduces to it\, but in higher dimensions this scalar function misses a lot of information about the curvature which is a 4-tensor field (it has 20 components in dimension 4). \n\nStill\, in the last 60 years problems connected to it have genera ted a huge amount of literature because of an a priori totally unexpected deep interplay of the existence of a metric with positive scalar curvatur e with the topology of manifolds.\n\nThis has mobilised many radically new approaches\, involving in particular spinors and a deeper understanding o f a number of topological or differentiable invariants or constructions. \ n\nThere are still a number of open problems connected to prescribing the scalar curvature on a manifold\, and some will be presented.\n LOCATION:https://stable.researchseminars.org/talk/GPL/48/ END:VEVENT BEGIN:VEVENT SUMMARY:Daniel Holmes (IST\, Austria) DTSTART:20260304T140000Z DTEND:20260304T150000Z DTSTAMP:20260415T002631Z UID:GPL/49 DESCRIPTION:Title: Equivariant Gromov-Witten theory and GKM spaces\nby Daniel Holmes (IST\, Austria) as part of Geometry and Physics @ Lisbon\n\nLecture held i n 6.2.33 (Seminar Room\, Math\, FCUL).\n\nAbstract\nAn important class of examples in algebraic and symplectic geometry is given by GKM spaces\, whi ch are torus-equivariant spaces with finitely many fixed points and comple x-one-dimensional orbits. This class includes smooth toric varieties\, hom ogeneous spaces\, smooth Schubert varieties\, as well as many non-algebrai c examples like the twisted flag manifold of Eschenburg/Tolman/Woodward.\n \nAt the intersection of geometry\, algebra\, and combinatorics lies a fru itful two-way interaction between Gromov-Witten theory and GKM theory esta blished by equivariant localization. In one direction\, GKM theory provide s a setting where Gromov-Witten invariants become explicitly computable\, which we have implemented in a software package (joint work with Giosuè M uratore). In the other direction\, the axiomatic behavior of Gromov-Witten invariants is strong enough to imply structural properties of GKM spaces. I will present recent results in both directions.\n LOCATION:https://stable.researchseminars.org/talk/GPL/49/ END:VEVENT BEGIN:VEVENT SUMMARY:Thiago Paiva (Beijing University) DTSTART:20260318T140000Z DTEND:20260318T150000Z DTSTAMP:20260415T002631Z UID:GPL/50 DESCRIPTION:Title: A simpler braid description for all links in the 3-sphere\nby Thia go Paiva (Beijing University) as part of Geometry and Physics @ Lisbon\n\n Lecture held in 6.2.33 (Seminar Room\, Math\, FCUL).\n\nAbstract\nBy Alexa nder's theorem\, every link in the 3-sphere can be represented as the clos ure of a braid. Lorenz links and twisted torus links are two families that have been extensively studied and are well-described in terms of braids. In this talk\, we will present a natural generalization of Lorenz links an d twisted torus links that produces all links in the 3-sphere. This provid es a simpler braid description for all links in the 3-sphere.\n\nPassword for the livestream "functor"\n LOCATION:https://stable.researchseminars.org/talk/GPL/50/ END:VEVENT BEGIN:VEVENT SUMMARY:Bruno de Oliveira (University of Miami) DTSTART:20260325T143000Z DTEND:20260325T153000Z DTSTAMP:20260415T002631Z UID:GPL/51 DESCRIPTION:Title: On surfaces of general type with extremal cotangent dimension\nby Bruno de Oliveira (University of Miami) as part of Geometry and Physics @ Lisbon\n\nLecture held in 6.2.33 (Seminar Room\, Math\, FCUL).\n\nAbstract \nIn this talk we give a brief survey on the cotangent dimension for surfa ces. Then we present several results describing general conditions that gu arantee that a surface has maximal cotangent dimension\, i.e. it is big. W e focus on an approach via fibrations whose orbifold base is of Campana ge neral type. Finally\, we address minimal cotangent dimension\, i.e. absenc e of symmetric differentials\, for surfaces of general type. Here\, the ap proach uses double covers and symmetric logarithmic differentials. We give special attention to the class of surfaces named Horikawa surfaces. This talk describes joint work with D. Brotbek and E. Rousseau.\n LOCATION:https://stable.researchseminars.org/talk/GPL/51/ END:VEVENT BEGIN:VEVENT SUMMARY:Juan Numpaque Roa (University of Porto) DTSTART:20260422T130000Z DTEND:20260422T140000Z DTSTAMP:20260415T002631Z UID:GPL/52 DESCRIPTION:Title: Tensor products of quiver bundles\nby Juan Numpaque Roa (Universit y of Porto) as part of Geometry and Physics @ Lisbon\n\nLecture held in 6. 2.33 (Seminar Room\, Math\, FCUL).\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/GPL/52/ END:VEVENT END:VCALENDAR