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:20260422T214743Z UID:GPL/1 DESCRIPTION:Title: Nonc ommutative Weil conjectures\nby Gonçalo Tabuada (FCT / UNL\, Portugal ) as part of Geometry and Physics @ Lisbon\n\n\nAbstract\nThe Weil conject ures (proved by Deligne in the 70's) played a key role in the development of modern algebraic geometry. In this talk\, making use of some recent top ological "technology"\, I will extended the Weil conjectures from the real m of algebraic geometry to the broad noncommutative setting of differentia l graded categories. Moreover\, I will prove the noncommutative Weil conje ctures in some interesting cases.\n LOCATION:https://researchseminars.org/talk/GPL/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Davide Masoero (GFMUL\, Lisbon) DTSTART:20201023T131500Z DTEND:20201023T141500Z DTSTAMP:20260422T214743Z UID:GPL/2 DESCRIPTION:Title: The Painlevé I equation and the A2 quiver\nby Davide Masoero (GFMUL\, Lis bon) as part of Geometry and Physics @ Lisbon\n\n\nAbstract\nWe study a se cond-order linear differential equation known as the deformed cubic oscill ator\, whose isomonodromic deformations are controlled by the first Painle vé equation. We use the generalised monodromy map for this equation to gi ve solutions to the Bridgeland's Riemann-Hilbert problem arising from the Donaldson-Thomas theory of the A2 quiver.\n\nThe talk is partially based o n a work in collaboration with Tom Bridgeland (https://arxiv.org/abs/2006. 10648)\n\nMore information and sponsors:\nhttp://cmafcio.campus.ciencias.u lisboa.pt/node/170\n LOCATION:https://researchseminars.org/talk/GPL/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Giordano Cotti (FCUL\, Lisbon) DTSTART:20201216T140000Z DTEND:20201216T150000Z DTSTAMP:20260422T214743Z UID:GPL/3 DESCRIPTION:Title: Quan tum differential equations\, isomonodromic deformations\, and derived cate gories\nby Giordano Cotti (FCUL\, Lisbon) as part of Geometry and Phys ics @ Lisbon\n\n\nAbstract\nThe quantum differential equation (qDE) is a r ich object attached to a smooth projective variety X. It is an ordinary di fferential equation in the complex domain which encodes information of the enumerative geometry of X\, more precisely its Gromov-Witten theory. Furt hermore\, the asymptotic and monodromy of its solutions conjecturally rule s also the topology and complex geometry of X. \n\nThese differential equa tions were introduced in the middle of the creative impetus for mathematic ally rigorous foundations of Topological Field Theories\, Supersymmetric Q uantum Field Theories and related Mirror Symmetry phenomena. Special menti on has to be given to the relation between qDE's and Dubrovin-Frobenius ma nifolds\, the latter being identifiable with the space of isomonodromic de formation parameters of the former. \n\nThe study of qDE’s represents a challenging active area in both contemporary geometry and mathematical ph ysics: it is continuously inspiring the introduction of new mathematical t ools\, ranging from algebraic geometry\, the realm of integrable systems\, the analysis of ODE’s\, to the theory of integral transforms and specia l functions.\n\nThis talk will be a gentle introduction to the analytical study of qDE’s\, their relationship with derived categories of coherent sheaves (in both non-equivariant and equivariant settings)\, and a theory of integral representations for its solutions. The talk will be a survey o f the results of the speaker in this research area.\n LOCATION:https://researchseminars.org/talk/GPL/3/ END:VEVENT BEGIN:VEVENT SUMMARY:André Oliveira (Univ. Porto) DTSTART:20210122T140000Z DTEND:20210122T150000Z DTSTAMP:20260422T214743Z 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\nConsider t he moduli space M(G) of G-Higgs bundles on a compact Riemann surface X\, f or a real semisimple Lie group G. Hitchin components in the split real for m case and maximal components in the Hermitian case were\, for several yea rs\, the only known source of examples of higher Teichmüller components of M(G). These components (which are not fully distinguished by topologica l invariants) are important because the corresponding representations of t he fundamental group of X have special properties\, generalizing Teichmü ller space\, such as being discrete and faithful. Recently\, the existence of new such higher Teichmüller components was proved for G = SO(p\,q) w hich\, in general\, is not neither split nor Hermitian.\n\nIn this talk I will explain the new Lie theoretic notion of magical nilpotent\, which giv es rise to the classification of groups for which such components exist. I t turns out that this classification agrees with the one of Guichard and W ienhard for groups admitting a positive structure. We provide a parametriz ation of higher Teichmüller components\, generalizing the Hitchin sectio n for split real forms and the Cayley correspondence for maximal component s 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://researchseminars.org/talk/GPL/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Giordano Cotti (GFMUL\, Lisbon) DTSTART:20210209T100000Z DTEND:20210209T120000Z DTSTAMP:20260422T214743Z UID:GPL/5 DESCRIPTION:Title: Frob enius manifolds\, irregular singularities\, and isomonodromy deformations\ , Lecture I\nby Giordano Cotti (GFMUL\, Lisbon) as part of Geometry an d Physics @ Lisbon\n\n\nAbstract\nLecture I - Introduction to Frobenius ma nifolds\n\nThe aim of the course is to give a self-contained introduction to the analytic theory of Frobenius manifolds\, ordinary differential equa tions with rational coefficients in complex domains\, and their isomonodro mic deformations. Applications to enumerative geometry will also be discus sed. In the final part of the mini-course\, more recent results in this re search 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 le ctures will stay available for a later view).\n\nThe public has the possib ility to ask questions to the speaker through the live-chat\, that will be read by a moderator.\n\nFor more information\, including the syllabus\, t he abstract of each lecture and the recommended literature\, visit: https: //irregular.rd.ciencias.ulisboa.pt/frobenius-manifolds-irregular-singulari ties-and-isomonodromy-deformations/\n\nThe course is a part of the FCT Res earch Project "Irregular connections on algebraic curves and quantum field theory" (PTDC/MAT-PUR/30234/2017) \nhttps://irregular.rd.ciencias.ulisboa .pt\n\nGroup of Mathematical Physics of Lisbon University\n LOCATION:https://researchseminars.org/talk/GPL/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Giordano Cotti (GFMUL\, Lisbon) DTSTART:20210211T100000Z DTEND:20210211T120000Z DTSTAMP:20260422T214743Z UID:GPL/6 DESCRIPTION:Title: Frob enius manifolds\, irregular singularities\, and isomonodromy deformations\ , Lecture II\nby Giordano Cotti (GFMUL\, Lisbon) as part of Geometry a nd Physics @ Lisbon\n\n\nAbstract\nLecture II - Examples of Frobenius mani folds\n\nThe aim of the course is to give a self-contained introduction to the analytic theory of Frobenius manifolds\, ordinary differential equati ons with rational coefficients in complex domains\, and their isomonodromi c deformations. Applications to enumerative geometry will also be discusse d. In the final part of the mini-course\, more recent results in this rese arch area will be presented.\n\nThe course will consist of 5 lectures\, wh ich will be shown live on YouTube\, at the url shown below (where the lect ures will stay available for a later view).\n\nThe public has the possibil ity to ask questions to the speaker through the live-chat\, that will be r ead by a moderator.\n\nFor more information\, including the syllabus\, the abstract of each lecture and the recommended literature\, visit: https:// irregular.rd.ciencias.ulisboa.pt/frobenius-manifolds-irregular-singulariti es-and-isomonodromy-deformations/\n\nThe course is a part of the FCT Resea rch Project "Irregular connections on algebraic curves and quantum field t heory" (PTDC/MAT-PUR/30234/2017) \nhttps://irregular.rd.ciencias.ulisboa.p t\n\nGroup of Mathematical Physics of Lisbon University\n LOCATION:https://researchseminars.org/talk/GPL/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Giordano Cotti (GFMUL\, Lisbon) DTSTART:20210216T100000Z DTEND:20210216T120000Z DTSTAMP:20260422T214743Z UID:GPL/7 DESCRIPTION:Title: Frob enius manifolds\, irregular singularities\, and isomonodromy deformations\ , Lecture III\nby Giordano Cotti (GFMUL\, Lisbon) as part of Geometry and Physics @ Lisbon\n\n\nAbstract\nLecture III - Analytic theory of Frobe nius manifolds\, Part I\n\nThe aim of the course is to give a self-contain ed introduction to the analytic theory of Frobenius manifolds\, ordinary d ifferential equations with rational coefficients in complex domains\, and their isomonodromic deformations. Applications to enumerative geometry wil l also be discussed. In the final part of the mini-course\, more recent re sults 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 bel ow (where the lectures will stay available for a later view).\n\nThe publi c has the possibility to ask questions to the speaker through the live-cha t\, that will be read by a moderator.\n\nFor more information\, including the syllabus\, the abstract of each lecture and the recommended literature \, visit: https://irregular.rd.ciencias.ulisboa.pt/frobenius-manifolds-irr egular-singularities-and-isomonodromy-deformations/\n\nThe course is a par t of the FCT Research Project "Irregular connections on algebraic curves a nd quantum field theory" (PTDC/MAT-PUR/30234/2017) \nhttps://irregular.rd. ciencias.ulisboa.pt\n\nGroup of Mathematical Physics of Lisbon University\ n LOCATION:https://researchseminars.org/talk/GPL/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Giordano Cotti (GFMUL\, Lisbon) DTSTART:20210218T100000Z DTEND:20210218T120000Z DTSTAMP:20260422T214743Z UID:GPL/8 DESCRIPTION:Title: Frob enius manifolds\, irregular singularities\, and isomonodromy deformations\ , Lecture IV\nby Giordano Cotti (GFMUL\, Lisbon) as part of Geometry a nd Physics @ Lisbon\n\n\nAbstract\nLecture IV - Analytic theory of Frobeni us manifolds\, Part II\n\nThe aim of the course is to give a self-containe d introduction to the analytic theory of Frobenius manifolds\, ordinary di fferential equations with rational coefficients in complex domains\, and t heir isomonodromic deformations. Applications to enumerative geometry will also be discussed. In the final part of the mini-course\, more recent res ults in this research area will be presented.\n\nThe course will consist o f 5 lectures\, which will be shown live on YouTube\, at the url shown belo w (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 t he syllabus\, the abstract of each lecture and the recommended literature\ , visit: \nhttps://irregular.rd.ciencias.ulisboa.pt/frobenius-manifolds-ir regular-singularities-and-isomonodromy-deformations/\n\nThe course is a pa rt of the FCT Research Project "Irregular connections on algebraic curves and quantum field theory" (PTDC/MAT-PUR/30234/2017) \nhttps://irregular.rd .ciencias.ulisboa.pt\n\nGroup of Mathematical Physics of Lisbon University \n LOCATION:https://researchseminars.org/talk/GPL/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Giordano Cotti (GFMUL\, Lisbon) DTSTART:20210219T100000Z DTEND:20210219T120000Z DTSTAMP:20260422T214743Z UID:GPL/9 DESCRIPTION:Title: Frob enius manifolds\, irregular singularities\, and isomonodromy deformations\ , Lecture V\nby Giordano Cotti (GFMUL\, Lisbon) as part of Geometry an d Physics @ Lisbon\n\n\nAbstract\nLecture V - Some recent results and work in progress\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://researchseminars.org/talk/GPL/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Thomas Krämer (Humboldt Universität zu Berlin) DTSTART:20210219T140000Z DTEND:20210219T150000Z DTSTAMP:20260422T214743Z UID:GPL/10 DESCRIPTION:Title: Sem icontinuity of Gauss maps and the Schottky problem\nby Thomas Krämer (Humboldt Universität zu Berlin) as part of Geometry and Physics @ Lisbon \n\n\nAbstract\nWe show that the degree of the Gauss map for subvarieties of abelian varieties is semicontinuous in families\, and we discuss its ju mp loci. In the case of theta divisors this gives a finite stratification of the moduli space of ppav's whose strata include the Torelli locus and t he Prym locus. More generally we obtain semicontinuity results for the int ersection cohomology of algebraic varieties with a finite morphism to an a belian variety\, leading to a topological interpretation for various jump loci in algebraic geometry. \n\nThis is joint work with Giulio Codogni.\n LOCATION:https://researchseminars.org/talk/GPL/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Ricardo Campos (CNRS/University of Montpellier) DTSTART:20210319T150000Z DTEND:20210319T160000Z DTSTAMP:20260422T214743Z UID:GPL/11 DESCRIPTION:Title: Con figuration 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 configurat ion space of n points on it: the subspace of X^n in which two points canno t share the same position. Despite their apparent simplicity such configur ation spaces are remarkably complicated\; the homology of these spaces 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 algebra ic models for the rational homotopy type of configuration spaces of points .\n LOCATION:https://researchseminars.org/talk/GPL/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Pierre Schapira (Sorbonne University) DTSTART:20210416T140000Z DTEND:20210416T150000Z DTSTAMP:20260422T214743Z UID:GPL/12 DESCRIPTION:Title: Eul er calculus of constructible functions and applications\nby Pierre Sch apira (Sorbonne University) as part of Geometry and Physics @ Lisbon\n\n\n Abstract\nIn this elementary talk\, we will recall the classical notions o f subanalytic sets\, constructible sheaves and constructible functions on a real analytic manifold and explain how to treat such objects “up to in finity’”. \n\nNext\, we will describe the Euler calculus of constructi ble functions\, in which integration is purely topological\, with applicat ions to tomography. Finally we will show how the gamma-topology on a vecto r space allows one to embed the space of constructible functions in that o f distributions.\n LOCATION:https://researchseminars.org/talk/GPL/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Stéphane Guillermou (CNRS\, Univ. Grenoble) DTSTART:20210514T140000Z DTEND:20210514T150000Z DTSTAMP:20260422T214743Z UID:GPL/13 DESCRIPTION:Title: Sta ble Gauss map of nearby Lagrangians\nby Stéphane Guillermou (CNRS\, U niv. Grenoble) as part of Geometry and Physics @ Lisbon\n\n\nAbstract\nThe stable Gauss map of a Lagrangian $L$ in a cotangent $T^*M$ is a map $g\\c olon L \\to U/O$ obtained by stabilization of the usual Gauss map from $L$ to the Lagrangian Grassmannian of $T^*M$. Arnold's conjecture on nearby Lagrangians implies in particular that $g$ is homotopic to a constant map. We will see the weaker result that the map induced by $g$ on the homotopy groups is trivial.\n\nThis is joint work with Mohammed Abouzaid\, Sylvain Courte and Thomas\n LOCATION:https://researchseminars.org/talk/GPL/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Sean Lawton (George Mason Univ.) DTSTART:20210614T130000Z DTEND:20210614T140000Z DTSTAMP:20260422T214743Z UID:GPL/14 DESCRIPTION:Title: Fla wed Groups\nby Sean Lawton (George Mason Univ.) as part of Geometry an d Physics @ Lisbon\n\n\nAbstract\nA group is flawed if its moduli space of G-representations is\nhomotopic to its moduli space of K-representations for all reductive\naffine algebraic groups G with maximal compact subgroup K. In this talk\nwe discuss this definition\, and associated examples\, theorems\, and\nconjectures. This work is in collaboration with Carlos Flo rentino.\n LOCATION:https://researchseminars.org/talk/GPL/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Sean Lawton (George Mason Univ.) DTSTART:20210621T130000Z DTEND:20210621T140000Z DTSTAMP:20260422T214743Z UID:GPL/15 DESCRIPTION:Title: Poi sson maps between character varieties\nby Sean Lawton (George Mason Un iv.) as part of Geometry and Physics @ Lisbon\n\n\nAbstract\nWe explore in duced mappings between character varieties by\nmappings between surfaces. It is shown that these mappings are generally\nPoisson. We also explicitly calculate the Poisson bi-vector in a new\ncase. This work is in collabor ation with Indranil Biswas\, Jacques\nHurtubise\, and Lisa C. Jeffrey.\n LOCATION:https://researchseminars.org/talk/GPL/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Giosuè Muratore (Univ. Lisbon) DTSTART:20211029T140000Z DTEND:20211029T150000Z DTSTAMP:20260422T214743Z UID:GPL/16 DESCRIPTION:Title: Enu meration of rational contact curves via torus actions\nby Giosuè Mura tore (Univ. Lisbon) as part of Geometry and Physics @ Lisbon\n\n\nAbstract \nComplex projective spaces of odd dimension have a unique contact structu re. So\, in these spaces we have contact (Legendrian) rational curves. We are interested in enumeration of such curves. We prove that some Gromov-Wi tten numbers associated with rational contact curves in projective space w ith arbitrary incidence conditions are enumerative. Also\, we use the Bott formula on the Kontsevich space to find the exact value of those numbers. \n LOCATION:https://researchseminars.org/talk/GPL/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Giosuè Muratore (FCUL\, Lisbon) DTSTART:20220615T123000Z DTEND:20220615T140000Z DTSTAMP:20260422T214743Z UID:GPL/17 DESCRIPTION:Title: Int roduction to Gromov-Witten invariants\, I\nby Giosuè Muratore (FCUL\, Lisbon) as part of Geometry and Physics @ Lisbon\n\nLecture held in Sala 6.2.33.\n\nAbstract\nThe goal of this crash course is to introduce the bas ic notions of moduli space of stable maps\nand Gromov-Witten invariants. I n 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 following topics\, time permitting.
\n(1) Basic defin itions.
\n(2) The case of genus 0: boundary divisors and examples.
\ n(3) Gromov-Witten invariants.
\n(4) Quantum cohomology.
\n(5) Konts evich-Atiyah-Bott formula.\n LOCATION:https://researchseminars.org/talk/GPL/17/ END:VEVENT BEGIN:VEVENT SUMMARY:Giosuè Muratore (FCUL\, Lisbon) DTSTART:20220617T103000Z DTEND:20220617T120000Z DTSTAMP:20260422T214743Z UID:GPL/18 DESCRIPTION:Title: Int roduction to Gromov-Witten invariants\, II\nby Giosuè Muratore (FCUL\ , Lisbon) as part of Geometry and Physics @ Lisbon\n\n\nAbstract\nThe 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\nDescri ption:\nThe course is split in 5 main parts. We will cover the following t opics\, time permitting.
\n(1) Basic definitions.
\n(2) The case of genus 0: boundary divisors and examples.
\n(3) Gromov-Witten invariants .
\n(4) Quantum cohomology.
\n(5) Kontsevich-Atiyah-Bott formula.\n\ nIf time permits\, we will give some enumerative applications.\n\nMain Ref erences:\n\n[CK99] D. A. Cox and S. Katz\, Mirror symmetry and algebraic g eometry\, AMS\, 1999.
\n[FP97] W. Fulton and R. Pandharipande\, Notes o n stable maps and quantum cohomology\, Algebraic geometry—Santa Cruz 199 5\, Proc. Sympos. Pure Math.\, 62\, AMS\, 1997.
\n[HTK+03] K. Hori\, R. Thomas\, S. Katz\, C. Vafa\, R. Pandharipande\, A. Klemm\, R. Vakil\, and E. Zaslow\, Mirror symmetry\, vol. 1\, AMS\, 2003.\n LOCATION:https://researchseminars.org/talk/GPL/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Giosuè Muratore (FCUL\, Lisbon) DTSTART:20220622T103000Z DTEND:20220622T120000Z DTSTAMP:20260422T214743Z UID:GPL/19 DESCRIPTION:Title: Int roduction to Gromov-Witten invariants\, III\nby Giosuè Muratore (FCUL \, Lisbon) as part of Geometry and Physics @ Lisbon\n\n\nAbstract\nThe goa l of this crash course is to introduce the basic notions of moduli space o f stable maps\nand Gromov-Witten invariants. In particular when the stable maps have rational domain and the\ntarget is a projective space.\n\nDescr iption:\nThe course is split in 5 main parts. We will cover the following topics\, time permitting.
\n(1) Basic definitions.
\n(2) The case of genus 0: boundary divisors and examples.
\n(3) Gromov-Witten invariant s.
\n(4) Quantum cohomology.
\n(5) Kontsevich-Atiyah-Bott formula.\n \nIf time permits\, we will give some enumerative applications.\n\nMain Re ferences:\n\n[CK99] D. A. Cox and S. Katz\, Mirror symmetry and algebraic geometry\, AMS\, 1999.
\n[FP97] W. Fulton and R. Pandharipande\, Notes on stable maps and quantum cohomology\, Algebraic geometry—Santa Cruz 19 95\, Proc. Sympos. Pure Math.\, 62\, AMS\, 1997.
\n[HTK+03] K. Hori\, R . Thomas\, S. Katz\, C. Vafa\, R. Pandharipande\, A. Klemm\, R. Vakil\, an d E. Zaslow\, Mirror symmetry\, vol. 1\, AMS\, 2003.\n LOCATION:https://researchseminars.org/talk/GPL/19/ END:VEVENT BEGIN:VEVENT SUMMARY:Giosuè Muratore (FCUL\, Lisbon) DTSTART:20220624T103000Z DTEND:20220624T120000Z DTSTAMP:20260422T214743Z UID:GPL/20 DESCRIPTION:Title: Int roduction to Gromov-Witten invariants\, IV\nby Giosuè Muratore (FCUL\ , Lisbon) as part of Geometry and Physics @ Lisbon\n\n\nAbstract\nThe 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\nDescri ption:\nThe course is split in 5 main parts. We will cover the following t opics\, time permitting.
\n(1) Basic definitions.
\n(2) The case of genus 0: boundary divisors and examples.
\n(3) Gromov-Witten invariants .
\n(4) Quantum cohomology.
\n(5) Kontsevich-Atiyah-Bott formula.\n\ nIf time permits\, we will give some enumerative applications.\n\nMain Ref erences:\n\n[CK99] D. A. Cox and S. Katz\, Mirror symmetry and algebraic g eometry\, AMS\, 1999.
\n[FP97] W. Fulton and R. Pandharipande\, Notes o n stable maps and quantum cohomology\, Algebraic geometry—Santa Cruz 199 5\, Proc. Sympos. Pure Math.\, 62\, AMS\, 1997.
\n[HTK+03] K. Hori\, R. Thomas\, S. Katz\, C. Vafa\, R. Pandharipande\, A. Klemm\, R. Vakil\, and E. Zaslow\, Mirror symmetry\, vol. 1\, AMS\, 2003.\n LOCATION:https://researchseminars.org/talk/GPL/20/ END:VEVENT BEGIN:VEVENT SUMMARY:Herwig Hauser (Univ. Vienna) DTSTART:20230202T110000Z DTEND:20230202T123000Z DTSTAMP:20260422T214743Z UID:GPL/21 DESCRIPTION:Title: Mod uli of n points on the projective line\nby Herwig Hauser (Univ. Vienna ) as part of Geometry and Physics @ Lisbon\n\nLecture held in 6.2.33 (Semi nar Room\, Math\, FCUL).\n\nAbstract\nThis mini-course addresses Master an d Doctoral students as well as Postdoc and Senior researchers in mathemati cs.\nObjective: The problem of constructing normal forms and moduli spaces for various geometric objects goes back (at least\, and\namong many other s) to the Italian geometers (Enriques\, Chisini\, Severi\, ...). A highlig ht was reached in the 1960 and 70es when\nDeligne\, Mumford and Knudsen in vestigated and constructed the moduli space of stable curves of genus $g$. These spectacular\nworks had a huge impact\, though the techniques from a lgebraic geometry they applied were quite challenging. In the course\, we\ nwish to offer a gentle and hopefully fascinating introduction to these re sults\, restricting always to curves of genus zero\, that is\,\ntransversa l unions of projective lines ${\\mathbb P}^1$. This case is already a rich source of ideas and methods.\n\nContents: We start by discussing the conc ept of (coarse and fine) moduli spaces\, universal families and the philos ophical\nbackground thereof: why is it natural to study such questions\, a nd why the given axiomatic framework is the correct one? Once\nwe have bec ome familiar with these foundations (seeing many examples on the way)\, we will concentrate on n points in ${\\mathbb P}^1$ and\nthe action of $PGL_ 2$ on them by Mobius transformations. This is part of classical projective geometry and very beautiful. As long as the $n$ points are pairwise disti nct\, things are easy\, and a moduli space is easily constructed. Things b ecome tricky as the points start to move and thus become closer to each ot her until they collide and coalesce. What are the limiting configurations of the points one has to expect in this variation? This question has a lon g history - Grothendieck proposed in SGA1 a convincing answer: $n$-pointed stable curves.\n\nWe will take at the beginning a different approach by p roposing an alternative version of limit. Namely\, we embed the space of $ n$\ndistinct points in a large projective space and then take limits there in via the Zariski-closure. This opens the door to the theory of\nphylogen etic trees: they are certain finite graphs with leaves and inner vertices as a tree in a forest. Their geometric combinatorics\nwill become the guid ing principle to design many proofs for our moduli spaces. Working with ph ylogenetic trees can be a very\npleasing occupation\, we will draw\, glue\ , cut and compose these trees and thus get surprising constructions and in sights.\nAt that point a miracle happens: The stable curves of Grothendiec k\, Deligne\, Mumford\, Knudsen pop up on their own. We don’t\neven have to define them - they are just there. So the circle closes up\, and our j ourney is now able to reprove many of the classical\nresults in an easy go ing and appealing manner.\nThe course is based on a recent research cooper ation with Jiayue Qi and Josef Schicho from the University of Linz within the\nproject P34765 of the Austrian Science Fund FWF.\n\nHerwig Hauser\, F aculty of Mathematics\, University of Vienna herwig.hauser@univie.ac.at\n LOCATION:https://researchseminars.org/talk/GPL/21/ END:VEVENT BEGIN:VEVENT SUMMARY:Herwig Hauser (Univ. Vienna) DTSTART:20230203T110000Z DTEND:20230203T123000Z DTSTAMP:20260422T214743Z UID:GPL/22 DESCRIPTION:Title: Mod uli of n points on the projective line\nby Herwig Hauser (Univ. Vienna ) as part of Geometry and Physics @ Lisbon\n\nLecture held in 6.2.33 (Semi nar Room\, Math\, FCUL).\n\nAbstract\nThis mini-course addresses Master an d Doctoral students as well as Postdoc and Senior researchers in mathemati cs.\nObjective: The problem of constructing normal forms and moduli spaces for various geometric objects goes back (at least\, and\namong many other s) to the Italian geometers (Enriques\, Chisini\, Severi\, ...). A highlig ht was reached in the 1960 and 70es when\nDeligne\, Mumford and Knudsen in vestigated and constructed the moduli space of stable curves of genus $g$. These spectacular\nworks had a huge impact\, though the techniques from a lgebraic geometry they applied were quite challenging. In the course\, we\ nwish to offer a gentle and hopefully fascinating introduction to these re sults\, restricting always to curves of genus zero\, that is\,\ntransversa l unions of projective lines ${\\mathbb P}^1$. This case is already a rich source of ideas and methods.\n\nContents: We start by discussing the conc ept of (coarse and fine) moduli spaces\, universal families and the philos ophical\nbackground thereof: why is it natural to study such questions\, a nd why the given axiomatic framework is the correct one? Once\nwe have bec ome familiar with these foundations (seeing many examples on the way)\, we will concentrate on n points in ${\\mathbb P}^1$ and\nthe action of $PGL_ 2$ on them by Mobius transformations. This is part of classical projective geometry and very beautiful. As long as the $n$ points are pairwise disti nct\, things are easy\, and a moduli space is easily constructed. Things b ecome tricky as the points start to move and thus become closer to each ot her until they collide and coalesce. What are the limiting configurations of the points one has to expect in this variation? This question has a lon g history - Grothendieck proposed in SGA1 a convincing answer: $n$-pointed stable curves.\n\nWe will take at the beginning a different approach by p roposing an alternative version of limit. Namely\, we embed the space of $ n$\ndistinct points in a large projective space and then take limits there in via the Zariski-closure. This opens the door to the theory of\nphylogen etic trees: they are certain finite graphs with leaves and inner vertices as a tree in a forest. Their geometric combinatorics\nwill become the guid ing principle to design many proofs for our moduli spaces. Working with ph ylogenetic trees can be a very\npleasing occupation\, we will draw\, glue\ , cut and compose these trees and thus get surprising constructions and in sights.\nAt that point a miracle happens: The stable curves of Grothendiec k\, Deligne\, Mumford\, Knudsen pop up on their own. We don’t\neven have to define them - they are just there. So the circle closes up\, and our j ourney is now able to reprove many of the classical\nresults in an easy go ing and appealing manner.\nThe course is based on a recent research cooper ation with Jiayue Qi and Josef Schicho from the University of Linz within the\nproject P34765 of the Austrian Science Fund FWF.\n\nHerwig Hauser\, F aculty of Mathematics\, University of Vienna herwig.hauser@univie.ac.at\n LOCATION:https://researchseminars.org/talk/GPL/22/ END:VEVENT BEGIN:VEVENT SUMMARY:Herwig Hauser (Univ. Vienna) DTSTART:20230209T110000Z DTEND:20230209T123000Z DTSTAMP:20260422T214743Z UID:GPL/23 DESCRIPTION:Title: Mod uli of n points on the projective line\nby Herwig Hauser (Univ. Vienna ) as part of Geometry and Physics @ Lisbon\n\nLecture held in 6.2.33 (Semi nar Room\, Math\, FCUL).\n\nAbstract\nThis mini-course addresses Master an d Doctoral students as well as Postdoc and Senior researchers in mathemati cs.\nObjective: The problem of constructing normal forms and moduli spaces for various geometric objects goes back (at least\, and\namong many other s) to the Italian geometers (Enriques\, Chisini\, Severi\, ...). A highlig ht was reached in the 1960 and 70es when\nDeligne\, Mumford and Knudsen in vestigated and constructed the moduli space of stable curves of genus $g$. These spectacular\nworks had a huge impact\, though the techniques from a lgebraic geometry they applied were quite challenging. In the course\, we\ nwish to offer a gentle and hopefully fascinating introduction to these re sults\, restricting always to curves of genus zero\, that is\,\ntransversa l unions of projective lines ${\\mathbb P}^1$. This case is already a rich source of ideas and methods.\n\nContents: We start by discussing the conc ept of (coarse and fine) moduli spaces\, universal families and the philos ophical\nbackground thereof: why is it natural to study such questions\, a nd why the given axiomatic framework is the correct one? Once\nwe have bec ome familiar with these foundations (seeing many examples on the way)\, we will concentrate on n points in ${\\mathbb P}^1$ and\nthe action of $PGL_ 2$ on them by Mobius transformations. This is part of classical projective geometry and very beautiful. As long as the $n$ points are pairwise disti nct\, things are easy\, and a moduli space is easily constructed. Things b ecome tricky as the points start to move and thus become closer to each ot her until they collide and coalesce. What are the limiting configurations of the points one has to expect in this variation? This question has a lon g history - Grothendieck proposed in SGA1 a convincing answer: $n$-pointed stable curves.\n\nWe will take at the beginning a different approach by p roposing an alternative version of limit. Namely\, we embed the space of $ n$\ndistinct points in a large projective space and then take limits there in via the Zariski-closure. This opens the door to the theory of\nphylogen etic trees: they are certain finite graphs with leaves and inner vertices as a tree in a forest. Their geometric combinatorics\nwill become the guid ing principle to design many proofs for our moduli spaces. Working with ph ylogenetic trees can be a very\npleasing occupation\, we will draw\, glue\ , cut and compose these trees and thus get surprising constructions and in sights.\nAt that point a miracle happens: The stable curves of Grothendiec k\, Deligne\, Mumford\, Knudsen pop up on their own. We don’t\neven have to define them - they are just there. So the circle closes up\, and our j ourney is now able to reprove many of the classical\nresults in an easy go ing and appealing manner.\nThe course is based on a recent research cooper ation with Jiayue Qi and Josef Schicho from the University of Linz within the\nproject P34765 of the Austrian Science Fund FWF.\n\nHerwig Hauser\, F aculty of Mathematics\, University of Vienna herwig.hauser@univie.ac.at\n LOCATION:https://researchseminars.org/talk/GPL/23/ END:VEVENT BEGIN:VEVENT SUMMARY:Herwig Hauser (Univ. Vienna) DTSTART:20230210T110000Z DTEND:20230210T123000Z DTSTAMP:20260422T214743Z UID:GPL/24 DESCRIPTION:Title: Mod uli of n points on the projective line\nby Herwig Hauser (Univ. Vienna ) as part of Geometry and Physics @ Lisbon\n\nLecture held in 6.2.33 (Semi nar Room\, Math\, FCUL).\n\nAbstract\nThis mini-course addresses Master an d Doctoral students as well as Postdoc and Senior researchers in mathemati cs.\nObjective: The problem of constructing normal forms and moduli spaces for various geometric objects goes back (at least\, and\namong many other s) to the Italian geometers (Enriques\, Chisini\, Severi\, ...). A highlig ht was reached in the 1960 and 70es when\nDeligne\, Mumford and Knudsen in vestigated and constructed the moduli space of stable curves of genus $g$. These spectacular\nworks had a huge impact\, though the techniques from a lgebraic geometry they applied were quite challenging. In the course\, we\ nwish to offer a gentle and hopefully fascinating introduction to these re sults\, restricting always to curves of genus zero\, that is\,\ntransversa l unions of projective lines ${\\mathbb P}^1$. This case is already a rich source of ideas and methods.\n\nContents: We start by discussing the conc ept of (coarse and fine) moduli spaces\, universal families and the philos ophical\nbackground thereof: why is it natural to study such questions\, a nd why the given axiomatic framework is the correct one? Once\nwe have bec ome familiar with these foundations (seeing many examples on the way)\, we will concentrate on n points in ${\\mathbb P}^1$ and\nthe action of $PGL_ 2$ on them by Mobius transformations. This is part of classical projective geometry and very beautiful. As long as the $n$ points are pairwise disti nct\, things are easy\, and a moduli space is easily constructed. Things b ecome tricky as the points start to move and thus become closer to each ot her until they collide and coalesce. What are the limiting configurations of the points one has to expect in this variation? This question has a lon g history - Grothendieck proposed in SGA1 a convincing answer: $n$-pointed stable curves.\n\nWe will take at the beginning a different approach by p roposing an alternative version of limit. Namely\, we embed the space of $ n$\ndistinct points in a large projective space and then take limits there in via the Zariski-closure. This opens the door to the theory of\nphylogen etic trees: they are certain finite graphs with leaves and inner vertices as a tree in a forest. Their geometric combinatorics\nwill become the guid ing principle to design many proofs for our moduli spaces. Working with ph ylogenetic trees can be a very\npleasing occupation\, we will draw\, glue\ , cut and compose these trees and thus get surprising constructions and in sights.\nAt that point a miracle happens: The stable curves of Grothendiec k\, Deligne\, Mumford\, Knudsen pop up on their own. We don’t\neven have to define them - they are just there. So the circle closes up\, and our j ourney is now able to reprove many of the classical\nresults in an easy go ing and appealing manner.\nThe course is based on a recent research cooper ation with Jiayue Qi and Josef Schicho from the University of Linz within the\nproject P34765 of the Austrian Science Fund FWF.\n\nHerwig Hauser\, F aculty of Mathematics\, University of Vienna herwig.hauser@univie.ac.at\n LOCATION:https://researchseminars.org/talk/GPL/24/ END:VEVENT BEGIN:VEVENT SUMMARY:Herwig Hauser (Univ. Vienna) DTSTART:20230213T110000Z DTEND:20230213T123000Z DTSTAMP:20260422T214743Z UID:GPL/25 DESCRIPTION:Title: Mod uli of n points on the projective line\nby Herwig Hauser (Univ. Vienna ) as part of Geometry and Physics @ Lisbon\n\nLecture held in 6.2.33 (Semi nar Room\, Math\, FCUL).\n\nAbstract\nThis mini-course addresses Master an d Doctoral students as well as Postdoc and Senior researchers in mathemati cs.\nObjective: The problem of constructing normal forms and moduli spaces for various geometric objects goes back (at least\, and\namong many other s) to the Italian geometers (Enriques\, Chisini\, Severi\, ...). A highlig ht was reached in the 1960 and 70es when\nDeligne\, Mumford and Knudsen in vestigated and constructed the moduli space of stable curves of genus $g$. These spectacular\nworks had a huge impact\, though the techniques from a lgebraic geometry they applied were quite challenging. In the course\, we\ nwish to offer a gentle and hopefully fascinating introduction to these re sults\, restricting always to curves of genus zero\, that is\,\ntransversa l unions of projective lines ${\\mathbb P}^1$. This case is already a rich source of ideas and methods.\n\nContents: We start by discussing the conc ept of (coarse and fine) moduli spaces\, universal families and the philos ophical\nbackground thereof: why is it natural to study such questions\, a nd why the given axiomatic framework is the correct one? Once\nwe have bec ome familiar with these foundations (seeing many examples on the way)\, we will concentrate on n points in ${\\mathbb P}^1$ and\nthe action of $PGL_ 2$ on them by Mobius transformations. This is part of classical projective geometry and very beautiful. As long as the $n$ points are pairwise disti nct\, things are easy\, and a moduli space is easily constructed. Things b ecome tricky as the points start to move and thus become closer to each ot her until they collide and coalesce. What are the limiting configurations of the points one has to expect in this variation? This question has a lon g history - Grothendieck proposed in SGA1 a convincing answer: $n$-pointed stable curves.\n\nWe will take at the beginning a different approach by p roposing an alternative version of limit. Namely\, we embed the space of $ n$\ndistinct points in a large projective space and then take limits there in via the Zariski-closure. This opens the door to the theory of\nphylogen etic trees: they are certain finite graphs with leaves and inner vertices as a tree in a forest. Their geometric combinatorics\nwill become the guid ing principle to design many proofs for our moduli spaces. Working with ph ylogenetic trees can be a very\npleasing occupation\, we will draw\, glue\ , cut and compose these trees and thus get surprising constructions and in sights.\nAt that point a miracle happens: The stable curves of Grothendiec k\, Deligne\, Mumford\, Knudsen pop up on their own. We don’t\neven have to define them - they are just there. So the circle closes up\, and our j ourney is now able to reprove many of the classical\nresults in an easy go ing and appealing manner.\nThe course is based on a recent research cooper ation with Jiayue Qi and Josef Schicho from the University of Linz within the\nproject P34765 of the Austrian Science Fund FWF.\n\nHerwig Hauser\, F aculty of Mathematics\, University of Vienna herwig.hauser@univie.ac.at\n LOCATION:https://researchseminars.org/talk/GPL/25/ END:VEVENT BEGIN:VEVENT SUMMARY:Davide Guzzetti (SISSA\, Italy) DTSTART:20221206T110000Z DTEND:20221206T120000Z DTSTAMP:20260422T214743Z UID:GPL/26 DESCRIPTION:Title: Int roduction to isomonodromy deformations and applications\nby Davide Guz zetti (SISSA\, Italy) as part of Geometry and Physics @ Lisbon\n\nLecture held in 6.2.33 (Seminar Room\, Math\, FCUL).\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/GPL/26/ END:VEVENT BEGIN:VEVENT SUMMARY:Jean Douçot (GFM\, Universidade de Lisboa) DTSTART:20230130T110000Z DTEND:20230130T120000Z DTSTAMP:20260422T214743Z UID:GPL/27 DESCRIPTION:Title: som onodromic deformations and generalised braid groups\nby Jean Douçot ( GFM\, Universidade de Lisboa) as part of Geometry and Physics @ Lisbon\n\n Lecture held in 6.2.33 (Seminar Room\, Math\, FCUL).\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/GPL/27/ END:VEVENT BEGIN:VEVENT SUMMARY:Gonçalo Oliveira (IST\, Universidade de Lisboa) DTSTART:20230228T110000Z DTEND:20230228T120000Z DTSTAMP:20260422T214743Z UID:GPL/28 DESCRIPTION:Title: Fro m electrostatics to geodesics in K3 surfaces\nby Gonçalo Oliveira (IS T\, Universidade de Lisboa) as part of Geometry and Physics @ Lisbon\n\nLe cture held in 6.2.33 (Seminar Room\, Math\, FCUL).\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/GPL/28/ END:VEVENT BEGIN:VEVENT SUMMARY:Xavier Blot (GFM\, Universidade de Lisboa) DTSTART:20230328T100000Z DTEND:20230328T110000Z DTSTAMP:20260422T214743Z UID:GPL/29 DESCRIPTION:Title: The quantum Witten-Kontsevich series\nby Xavier Blot (GFM\, 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://researchseminars.org/talk/GPL/29/ END:VEVENT BEGIN:VEVENT SUMMARY:Leonardo Santilli (Yau Mathematical Sciences Center) DTSTART:20230418T100000Z DTEND:20230418T110000Z DTSTAMP:20260422T214743Z UID:GPL/30 DESCRIPTION:Title: Qui vers counting monster potentials\nby Leonardo Santilli (Yau Mathematic al Sciences Center) as part of Geometry and Physics @ Lisbon\n\nLecture he ld in 6.2.33 (Seminar Room\, Math\, FCUL).\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/GPL/30/ END:VEVENT BEGIN:VEVENT SUMMARY:Giosuè Muratore (CMAFcIO\, Universidade de Lisboa) DTSTART:20230511T100000Z DTEND:20230511T110000Z DTSTAMP:20260422T214743Z UID:GPL/31 DESCRIPTION:Title: Enu meration of rational contact curves: the irreducible case\nby Giosuè Muratore (CMAFcIO\, Universidade de Lisboa) 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://researchseminars.org/talk/GPL/31/ END:VEVENT BEGIN:VEVENT SUMMARY:Wilhelm Schlag (Yale University) DTSTART:20230516T100000Z DTEND:20230516T110000Z DTSTAMP:20260422T214743Z UID:GPL/32 DESCRIPTION:Title: Lya punov exponents\, Schrödinger cocycles\, and Avila’s global theory\ nby Wilhelm Schlag (Yale University) as part of Geometry and Physics @ Lis bon\n\nLecture held in 6.2.33 (Seminar Room\, Math\, FCUL).\nAbstract: TBA \n LOCATION:https://researchseminars.org/talk/GPL/32/ END:VEVENT BEGIN:VEVENT SUMMARY:Vicente Muñoz (Univ. Complutense\, Madrid) DTSTART:20230706T100000Z DTEND:20230706T110000Z DTSTAMP:20260422T214743Z UID:GPL/33 DESCRIPTION:Title: A S male-Barden manifold admitting K-contact but no Sasakian structure\nby Vicente Muñoz (Univ. Complutense\, Madrid) as part of Geometry and Physi cs @ Lisbon\n\nLecture held in 6.2.33 (Seminar Room\, Math\, FCUL).\nAbstr act: TBA\n LOCATION:https://researchseminars.org/talk/GPL/33/ END:VEVENT BEGIN:VEVENT SUMMARY:Luca Scala (UFRJ\, Brasil & Univ. Lusófona) DTSTART:20230704T100000Z DTEND:20230704T110000Z DTSTAMP:20260422T214743Z UID:GPL/34 DESCRIPTION:Title: Coh omology of tautological boundles on Hilbert schemes of point and related p roblems\nby Luca Scala (UFRJ\, Brasil & Univ. Lusófona) as part of Ge ometry and Physics @ Lisbon\n\nLecture held in 6.2.33 (Seminar Room\, Math \, FCUL).\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/GPL/34/ END:VEVENT BEGIN:VEVENT SUMMARY:Azizeh Nozad (IPM\, Iran) DTSTART:20230622T100000Z DTEND:20230622T110000Z DTSTAMP:20260422T214743Z UID:GPL/35 DESCRIPTION:Title: Ser re polynomials of character varieties of free groups\nby Azizeh Nozad (IPM\, Iran) as part of Geometry and Physics @ Lisbon\n\nLecture held in 6 .2.33 (Seminar Room\, Math\, FCUL).\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/GPL/35/ END:VEVENT BEGIN:VEVENT SUMMARY:Vadim Lebovici (Univ. Paris-Sud & E.N.S.) DTSTART:20230620T100000Z DTEND:20230620T110000Z DTSTAMP:20260422T214743Z UID:GPL/36 DESCRIPTION:Title: Eul er calculus and its applications\nby Vadim Lebovici (Univ. Paris-Sud & E.N.S.) as part of Geometry and Physics @ Lisbon\n\nLecture held in 6.2.3 3 (Seminar Room\, Math\, FCUL).\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/GPL/36/ END:VEVENT BEGIN:VEVENT SUMMARY:Miguel Moreira (MIT) DTSTART:20240110T110000Z DTEND:20240110T120000Z DTSTAMP:20260422T214743Z UID:GPL/37 DESCRIPTION:Title: The cohomology ring of moduli spaces of 1-dimensional sheaves on $\\mathbb P^ 2$\nby Miguel Moreira (MIT) as part of Geometry and Physics @ Lisbon\n \nLecture held in 6.2.33 (Seminar Room\, Math\, FCUL).\n\nAbstract\nIn thi s talk I will go over some recent results and conjectures concerning the c ohomology (and in particular its ring structure) of the moduli spaces of s table 1-dimensional sheaves on the projective plane. The cohomology of suc h moduli spaces\, together with its perverse filtration\, is conjectured t o 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 cohomol ogy rings of moduli spaces of sheaves supported in curves up to degree 5\, and how that can be used to verify this prediction in such degrees. If ti me allows\, I will explain a new conjectural description of the perverse f iltration which we have also verified up to degree 5. This is based on joi nt work with Y. Kononov\, W. Lim and W. Pi.\n LOCATION:https://researchseminars.org/talk/GPL/37/ END:VEVENT BEGIN:VEVENT SUMMARY:Ángel González-Prieto (Univ. Complutense Madrid) DTSTART:20240618T100000Z DTEND:20240618T110000Z DTSTAMP:20260422T214743Z UID:GPL/38 DESCRIPTION:Title: Cha racter Varieties of Knots\nby Ángel González-Prieto (Univ. Compluten se Madrid) as part of Geometry and Physics @ Lisbon\n\nLecture held in 6.2 .33 (Seminar Room\, Math\, FCUL).\n\nAbstract\nKnot invariants\, such as t he Jones polynomial and the Reshetikhin-Turaev invariants\, are ubiquitous in the study of 3-manifold geometry. Among these invariants\, one stands out: the fundamental group of the complement of the knot\, also known as t he knot group. Particularly interesting is the study of the space of repre sentations of these knot groups\, referred to as the character varieties o f knots. Even the simplest properties of these character varieties have le d to profound results in hyperbolic geometry. However\, general methods to uncover the deep geometric features of these spaces are still lacking.\n\ nIn this talk\, we will discuss various aspects of these character varieti es from both geometric and algebraic perspectives. Even for character vari eties of torus knots\, intriguing features emerge that allow us to compare their geometry in both the complex and real cases. Time permitting\, we w ill also explore how Topological Quantum Field Theories can be employed to provide unexpected generalized skein relations for the arithmetic of char acter varieties of knots over finite groups.\n LOCATION:https://researchseminars.org/talk/GPL/38/ END:VEVENT BEGIN:VEVENT SUMMARY:Sean Lawton (George Mason Univ.) DTSTART:20240619T100000Z DTEND:20240619T110000Z DTSTAMP:20260422T214743Z UID:GPL/39 DESCRIPTION:Title: The SU(2\,1)-character variety of the 1-holed torus\nby Sean Lawton (Geor ge Mason Univ.) as part of Geometry and Physics @ Lisbon\n\nLecture held i n 6.2.33 (Seminar Room\, Math\, FCUL).\n\nAbstract\nWe sketch the proof th at the SU(2\,1)-character variety of the 1-holed torus is homotopic to a p roduct of circles. We then discuss the mapping class group dynamics on th is character variety. In particular\, we describe an open domain of disco ntinuity. This work represents collaborative work with Sara Maloni and Fr édéric Palesi. See arXiv:2402.10838 for more information.\n LOCATION:https://researchseminars.org/talk/GPL/39/ END:VEVENT BEGIN:VEVENT SUMMARY:Andrew P. Turner (Virginia Tech (USA)) DTSTART:20241106T160000Z DTEND:20241106T170000Z DTSTAMP:20260422T214743Z UID:GPL/40 DESCRIPTION:Title: Hig gsing on SU(N) Symmetric Matter and its F-theory Realization\nby Andre w P. Turner (Virginia Tech (USA)) as part of Geometry and Physics @ Lisbon \n\nLecture held in 6.2.33 (Seminar Room\, Math\, FCUL).\n\nAbstract\nF-th eory is a powerful framework for studying string compactifications that en codes many of the details of the physical theory in the geometry of a sing ular elliptically fibered Calabi–Yau manifold. In the first part of this talk\, I will provide an introduction to F-theory\, discussing the motiva tion for this construction and the mathematical techniques used to analyze F-theory vacua. I will then describe recent work on the explicit realizat ion within F-theory of the Higgsing of an SU(N) gauge theory on symmetric matter\, primarily exploiting heterotic/F-theory duality. The new models a nalyzed in this work provide explicit counterexamples to several long-stan ding assumptions about the physical interpretation of the Mordell–Weil g roup of the elliptic fibration.\n LOCATION:https://researchseminars.org/talk/GPL/40/ END:VEVENT BEGIN:VEVENT SUMMARY:Giosuè Muratore (CEMS.UL\, Lisbon) DTSTART:20250110T150000Z DTEND:20250110T160000Z DTSTAMP:20260422T214743Z UID:GPL/41 DESCRIPTION:Title: Cou nts of lines with tangency conditions in A1-homotopy\nby Giosuè Murat ore (CEMS.UL\, Lisbon) as part of Geometry and Physics @ Lisbon\n\nLecture held in 6.2.33 (Seminar Room\, Math\, FCUL).\n\nAbstract\nA¹-homotopy th eory\, introduced by Morel and Voevodsky\, provides a powerful motivic fra mework that bridges algebraic geometry and the methods of classical topolo gy. By extending the toolkit of algebraic geometry with concepts from homo topy theory\, this approach has opened the door to a wide range of applica tions across the field. In this talk\, we will outline the fundamental ide as behind A¹-homotopy theory and explore its relevance in enumerative geo metry\, highlighting recent developments and results.\n LOCATION:https://researchseminars.org/talk/GPL/41/ END:VEVENT BEGIN:VEVENT SUMMARY:Alejandro Calleja (Univ. Complutense\, Madrid) DTSTART:20250217T110000Z DTEND:20250217T120000Z DTSTAMP:20260422T214743Z UID:GPL/42 DESCRIPTION:Title: Cha racter Varieties in Knot Theory\nby Alejandro Calleja (Univ. Compluten se\, Madrid) as part of Geometry and Physics @ Lisbon\n\nLecture held 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 mod uli space of representations ρ : π1(S^3 − K) → G of the knot group i nto G. The importance of these varieties lies in the fact that their 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-polynomia l\, exposing the techniques used to study them\, as well as the main known results\, focusing especially on the case of torus knots. In this context \, being able to distinguish when two representations are isomorphic becom es crucial. For facing this problem\, we will introduce the configuration space of orbits\, a variety formed by tuples of pairwise non-isomorphic re presentations.\n LOCATION:https://researchseminars.org/talk/GPL/42/ END:VEVENT BEGIN:VEVENT SUMMARY:Marcos Petrúcio Cavalcante (Univ. Fed. de Alagoas) DTSTART:20250225T133000Z DTEND:20250225T143000Z DTSTAMP:20260422T214743Z UID:GPL/43 DESCRIPTION:Title: Sta bility of extremal domains\nby Marcos Petrúcio Cavalcante (Univ. Fed. de Alagoas) as part of Geometry and Physics @ Lisbon\n\nLecture held in 6 .2.33 (Seminar Room\, Math\, FCUL).\n\nAbstract\nA domain in a Riemannian manifold is said to be extremal if it is a critical point of the first eig envalue functional under volume-preserving variations. From this variation al characterization\, we derive a natural notion of stability. In this tal k\, we classify the stable extremal domains in the 2-sphere and in higher- dimensional spheres when the boundary is minimal. Additionally\, we establ ish topological bounds for stable domains in general compact Riemannian su rfaces\, assuming either nonnegative total Gaussian curvature or small vol ume. This is joint work with Ivaldo Nunes (UFMA).\n LOCATION:https://researchseminars.org/talk/GPL/43/ END:VEVENT BEGIN:VEVENT SUMMARY:Markus Kiderlen (Aarhus University) DTSTART:20250226T140000Z DTEND:20250226T160000Z DTSTAMP:20260422T214743Z UID:GPL/44 DESCRIPTION:Title: Cro fton-type Formulae in Rotational Integral Geometry\nby Markus Kiderlen (Aarhus University) as part of Geometry and Physics @ Lisbon\n\nLecture h eld in 6.2.33 (Seminar Room\, Math\, FCUL).\n\nAbstract\nThe purpose of th is talk is to give an introduction to rotational integral geometry and exe mplify a number of its core results and their applications. Integral geome try\, introduced by Blaschke in the 1930s\, is the theory of invariant me asures on geometric spaces (often Grassmannians) and its application to de termine geometric probabilities.\n\nWe will start by recalling the kinemat ic Crofton formula\, which allows us to retrieve certain geometric charact eristics (such as volume\, surface area and other intrinsic volumes) of a compact convex set $K$ in $\\mathbb R^n$ from intersections with invariant ly integrated $k$-dimensional affine subspaces\, where $k=0\,\\ldots\,n-1$ is fixed.\n\nMotivated by applications from biology\, we suggest a number of variants of Crofton's formula\, where the intersecting affine spaces a re constrained to contain the origin -- and hence are just linear subspace s -- or even all contain a fixed lower-dimensional axis. Corresponding rot ational Crofton formulae will be established and explained. We also show that the set of these formulae is complete in that they retrieve all possi ble intrinsic volumes of $K$. Proofs rely on old and new Blaschke-Petkants chin theorems\, which we also will outline.\n\nJoint work with Emil Dare a nd Eva B. Vedel Jensen.\n LOCATION:https://researchseminars.org/talk/GPL/44/ END:VEVENT BEGIN:VEVENT SUMMARY:Fabrizio Del Monte (University of Birmingham\, UK) DTSTART:20250416T130000Z DTEND:20250416T140000Z DTSTAMP:20260422T214743Z UID:GPL/45 DESCRIPTION:Title: Mon odromies\, Clusters\, and the WKB Approximation for q-Difference Equations \nby Fabrizio Del Monte (University of Birmingham\, UK) as part of Geo metry and Physics @ Lisbon\n\nLecture held in 6.2.33 (Seminar Room\, Math\ , FCUL).\n\nAbstract\nThe study of monodromies of differential equations h as been a rich area of mathematical physics\, interconnected with various fields in mathematics and physics. Recent discoveries reveal that monodrom y varieties naturally possess the structure of cluster varieties\, signifi cantly enhancing our understanding of their connections to string theory a nd Donaldson–Thomas invariants. A key technique in these developments is the (exact) WKB approximation. In string theory\, q-difference equations (qDEs) naturally appear as an "M-theory completion" of differential equati ons\, though defining monodromy in this context remains an active research area. In this seminar\, I will discuss how the WKB approximation\, tradit ionally formulated for second-order ODEs\, can be effectively generalized to second-order q-difference equations\, providing a natural characterizat ion of their monodromies. Central to this approach is the WKB Stokes diagr am\, known in the physics literature as the exponential network\, which of fers a framework for defining cluster coordinates for monodromies of qDEs. \n\nI will illustrate this formalism through explicit examples\, including the q-difference Mathieu equation. Remarkably\, its monodromy around the origin—known in topological string theory as the quantum mirror map—ta kes the form of the Hamiltonian of a cluster integrable system in terms of these cluster coordinates.\n LOCATION:https://researchseminars.org/talk/GPL/45/ END:VEVENT BEGIN:VEVENT SUMMARY:Tomás Inácio (Fac. Ciências ULisboa) DTSTART:20250514T133000Z DTEND:20250514T143000Z DTSTAMP:20260422T214743Z UID:GPL/46 DESCRIPTION:Title: A H itchhiker’s Guide to Joyce Structures\nby Tomás Inácio (Fac. Ciên cias ULisboa) as part of Geometry and Physics @ Lisbon\n\nLecture held in 6.2.33 (Seminar Room\, Math\, FCUL).\n\nAbstract\nJoyce structures were in troduced by Tom Bridgeland in the context of stability conditions and were constructed in close analogy to Frobenius structures introduced in Topolo gical Field Theories. The main motivation behind them was the similarity b etween the Iso-Stokes condition and the Kontsevich-Soibelman Wall Crossing Formula. Since then\, Joyce structures have exhibited not only a rich ana lytical side but also an extremely interesting geometric structure.\n\nIn this seminar\, I will introduce these works\, starting with the definition and motivation of Joyce structures and then moving to the formulation of the Riemann-Hilbert-Birkhoff problem. After discussing an explicit solutio n\, I will conclude by exploring the geometric side and interpreting all t he concepts in this new setting. Given the variety of topics\, I will make an effort to provide specific examples.\n LOCATION:https://researchseminars.org/talk/GPL/46/ END:VEVENT BEGIN:VEVENT SUMMARY:Ariel Pacetti (Universidade de Aveiro) DTSTART:20250604T133000Z DTEND:20250604T143000Z DTSTAMP:20260422T214743Z UID:GPL/47 DESCRIPTION:Title: Lan glands Program and Applications\nby Ariel Pacetti (Universidade de Ave iro) as part of Geometry and Physics @ Lisbon\n\nLecture held in 6.2.33 (S eminar Room\, Math\, FCUL).\n\nAbstract\nThe goal of this general audience talk is to introduce the L-function attached to a projective variety and state some of its expected properties. A way to prove such properties is t o relate the L-function to objects of a more analytic nature (namely autom orphic forms). During the talk we will study some baby examples of the cor respondence\, and state some recent results (as well as some open problems ). At last we will explain how the theory is well suited for the study of solutions to Diophantine equations (we will include a 5 minutes proof of F ermat's last theorem).\n LOCATION:https://researchseminars.org/talk/GPL/47/ END:VEVENT BEGIN:VEVENT SUMMARY:Jean-Pierre Bourguignon (IHÉS (Nicolaas Kuiper Honorary Professor )) DTSTART:20250625T140000Z DTEND:20250625T150000Z DTSTAMP:20260422T214743Z UID:GPL/48 DESCRIPTION:Title: Rev isiting the scalar curvature\nby Jean-Pierre Bourguignon (IHÉS (Nicol aas Kuiper Honorary Professor)) as part of Geometry and Physics @ Lisbon\n \nLecture held in 6.2.33 (Seminar Room\, Math\, FCUL).\n\nAbstract\nThe sc alar curvature is the weakest invariant involving the curvature of a Riema nnian metric. On surfaces\, where the concept of curvature was first devel oped by Carl-Friedrich GAUSS\, the curvature reduces to it\, but in higher dimensions this scalar function misses a lot of information about the cur vature 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 generated a h uge amount of literature because of an a priori totally unexpected deep i nterplay of the existence of a metric with positive scalar curvature with the topology of manifolds.\n\nThis has mobilised many radically new approa ches\, involving in particular spinors and a deeper understanding of a num ber of topological or differentiable invariants or constructions. \n\nTher e are still a number of open problems connected to prescribing the scalar curvature on a manifold\, and some will be presented.\n LOCATION:https://researchseminars.org/talk/GPL/48/ END:VEVENT BEGIN:VEVENT SUMMARY:Daniel Holmes (IST\, Austria) DTSTART:20260304T140000Z DTEND:20260304T150000Z DTSTAMP:20260422T214743Z UID:GPL/49 DESCRIPTION:Title: Equ ivariant Gromov-Witten theory and GKM spaces\nby Daniel Holmes (IST\, Austria) as part of Geometry and Physics @ Lisbon\n\nLecture held in 6.2.3 3 (Seminar Room\, Math\, FCUL).\n\nAbstract\nAn important class of example s in algebraic and symplectic geometry is given by GKM spaces\, which are torus-equivariant spaces with finitely many fixed points and complex-one-d imensional orbits. This class includes smooth toric varieties\, homogeneou s spaces\, smooth Schubert varieties\, as well as many non-algebraic examp les like the twisted flag manifold of Eschenburg/Tolman/Woodward.\n\nAt th e intersection of geometry\, algebra\, and combinatorics lies a fruitful t wo-way interaction between Gromov-Witten theory and GKM theory established by equivariant localization. In one direction\, GKM theory provides a set ting where Gromov-Witten invariants become explicitly computable\, which w e have implemented in a software package (joint work with Giosuè Muratore ). In the other direction\, the axiomatic behavior of Gromov-Witten invari ants is strong enough to imply structural properties of GKM spaces. I will present recent results in both directions.\n LOCATION:https://researchseminars.org/talk/GPL/49/ END:VEVENT BEGIN:VEVENT SUMMARY:Thiago Paiva (Beijing University) DTSTART:20260318T140000Z DTEND:20260318T150000Z DTSTAMP:20260422T214743Z UID:GPL/50 DESCRIPTION:Title: A s impler braid description for all links in the 3-sphere\nby Thiago Paiv a (Beijing University) as part of Geometry and Physics @ Lisbon\n\nLecture held in 6.2.33 (Seminar Room\, Math\, FCUL).\n\nAbstract\nBy Alexander's theorem\, every link in the 3-sphere can be represented as the closure of a braid. Lorenz links and twisted torus links are two families that have b een extensively studied and are well-described in terms of braids. In this talk\, we will present a natural generalization of Lorenz links and twist ed torus links that produces all links in the 3-sphere. This provides a si mpler braid description for all links in the 3-sphere.\n\nPassword for the livestream "functor"\n LOCATION:https://researchseminars.org/talk/GPL/50/ END:VEVENT BEGIN:VEVENT SUMMARY:Bruno de Oliveira (University of Miami) DTSTART:20260325T143000Z DTEND:20260325T153000Z DTSTAMP:20260422T214743Z UID:GPL/51 DESCRIPTION:Title: On surfaces of general type with extremal cotangent dimension\nby Bruno d e 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 th is talk we give a brief survey on the cotangent dimension for surfaces. Th en we present several results describing general conditions that guarantee that a surface has maximal cotangent dimension\, i.e. it is big. We focus on an approach via fibrations whose orbifold base is of Campana general t ype. Finally\, we address minimal cotangent dimension\, i.e. absence of sy mmetric differentials\, for surfaces of general type. Here\, the approach uses double covers and symmetric logarithmic differentials. We give specia l attention to the class of surfaces named Horikawa surfaces. This talk de scribes joint work with D. Brotbek and E. Rousseau.\n LOCATION:https://researchseminars.org/talk/GPL/51/ END:VEVENT BEGIN:VEVENT SUMMARY:Juan Numpaque Roa (University of Porto) DTSTART:20260422T130000Z DTEND:20260422T140000Z DTSTAMP:20260422T214743Z UID:GPL/52 DESCRIPTION:Title: Ten sor products of quiver bundles\nby Juan Numpaque Roa (University of Po rto) as part of Geometry and Physics @ Lisbon\n\nLecture held in 6.2.33 (S eminar Room\, Math\, FCUL).\n\nAbstract\nIn this talk I will discuss on a notion of tensor product of (twisted) quiver representations with relation s in the category of $O_X$-modules. As a first application of our notion\, we see that tensor products of polystable quiver bundles are polystable a nd later we use this to both deduce a quiver version of the classic Segre embedding and to identify distinguished closed subschemes of GL(n\,$\\math bb C$)-character varieties of free abelian groups.\n LOCATION:https://researchseminars.org/talk/GPL/52/ END:VEVENT END:VCALENDAR