BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Olaf Müller (Humboldt-Universität zu Berlin) DTSTART:20210115T130000Z DTEND:20210115T150000Z DTSTAMP:20260422T225848Z UID:DQSeminar/1 DESCRIPTION:Title: New geometrical methods in mathematical relativity\nby Olaf Müller (Humboldt-Universität zu Berlin) as part of Deformation Quantization Semi nar\n\n\nAbstract\nThis talk presents some new geometric approaches to glo bal behavior of solutions to classical field\nequations. The results compr ise:\n\n• the existence of global solutions for Dirac-Higgs-Yang-Mills T heories (like the standard model)\nin spacetimes close to Minkowski spacet ime in the case of small initial values\, via the useful\nnotion of future conformal compactification (joint work with Nicolas Ginoux)\,\n\n• the existence of maximal Cauchy developments of Dirac-Higgs-Yang-Mills-Einstei n theories (e.g.\nthe minimal coupling of the standard model to gravity an d its sectors like Einstein-DiracMaxwell theory) with the main tool being the Universal Spinor Bundle (joint work with Nikolai\nNowaczyk)\,\n\n• s ome old and new results about how concentration of energy implies the deve lopment of black\nholes\, and the “flatzoomer” method (developped in a joint work with Marc Nardmann) applied\nin the construction of spacetimes metrics satisfying energy conditions in a given conformal class.\n LOCATION:https://researchseminars.org/talk/DQSeminar/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Marco Benini (Università di Genova) DTSTART:20210205T130000Z DTEND:20210205T150000Z DTSTAMP:20260422T225848Z UID:DQSeminar/2 DESCRIPTION:Title: Homotopical quantization of linear gauge theories\nby Marco Benini ( Università di Genova) as part of Deformation Quantization Seminar\n\n\nAb stract\nIn a gauge theory\, gauge transformations encode a useful higher s tructure that enables one to\nperform powerful constructions\, e.g. BRST/B V quantization. The efficacy of the BRST/BV approach\nrelies on the flexib ility of introducing auxiliary fields\, an operation which is formalized b y quasiisomorphisms. This flexibility comes at the price that all construc tions must be derived\, i.e. invariant\nunder quasi-isomorphisms (as oppos ed to isomorphisms). Focusing on the prototypical example of\nlinear Yang- Mills theory\, I will present a standard model for its derived critical lo cus and equip the\nassociated complex of linear observables with its canon ical shifted Poisson structure (antibracket). I\nwill show how global hype rbolicity of the background Lorentzian manifold entails that this shifted\ nPoisson structure is (homologically) trivial and observe the existence of two distinguished ways to\ntrivialize it. Combining these trivializations leads to a non-trivial unshifted Poisson structure\, which\nI will quanti ze via canonical commutation relations. This leads to an explicit example of a homotopy\nalgebraic quantum field theory\, where the time-slice axiom is encoded weakly by quasi-isomorphisms\n(as opposed to isomorphisms).\n LOCATION:https://researchseminars.org/talk/DQSeminar/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Michael Heins (Julius-Maximilians University Würzburg) DTSTART:20210212T130000Z DTEND:20210212T150000Z DTSTAMP:20260422T225848Z UID:DQSeminar/3 DESCRIPTION:Title: The Universal Complexification of a Lie Group\nby Michael Heins (Jul ius-Maximilians University Würzburg) as part of Deformation Quantization Seminar\n\n\nAbstract\nIn classical Lie theory\, a\n complexification of a Lie group with Lie algebra $\\mathfrak{g}$ is a\n complex Lie group\, w hose Lie algebra is given by the\n complexification $\\mathfrak{g}_{\\mat hbb{C}}$ of $\\mathfrak{g}$ in the sense\n of vector spaces. Both from an analytical and a categorical point of\n view\, this definition turned ou t to be too naive to be truly\n useful. Historically\, this lead to the r efined concept of\n universal complexification\, which is based on an ana lytically\n desirable universal property. In this talk\, we motivate this \n definition by briefly reviewing the vector space\n situation. Afterwa rds\, we give a rather geometric construction of\n the universal complexi fication of a given Lie group\, which was\n formalized by Hochschild arou nd 1955 and refined by the Bourbaki\n group in the following decade. Alon g the way\, we review Lie's\n seminal Theorems and meet the universal cov ering group. While many\n properties of the resulting universal complexif ication align with\n what we geometrically expect\, some notable aspects turn out to\n differ\, which we discuss in detail. Finally\, we provide s ome\n examples to illustrate the power and limitations of the machinery w e\n have developed.\n LOCATION:https://researchseminars.org/talk/DQSeminar/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Christiaan van de Ven (University of Trento) DTSTART:20210226T130000Z DTEND:20210226T150000Z DTSTAMP:20260422T225848Z UID:DQSeminar/4 DESCRIPTION:Title: Asymptotic equivalence of two strict deformation quantizations and appli cations to the classical limit\nby Christiaan van de Ven (University o f Trento) as part of Deformation Quantization Seminar\n\n\nAbstract\nThe c oncept of strict deformation\n quantization provides a mathematical forma lism that describes the\n transition from a classical theory to a quantum theory in terms of\n deformations of (commutative) Poisson algebras (rep resenting the\n classical theory) into non-commutative $C^*$-algebras\n (characterizing the quantum theory). In this seminar we introduce\n the d efinitions\, give several examples and show how quantization of\n the clo sed unit 3-ball $B^3 \\subset \\mathbb{R}^3$ is related to\n quantization of its smooth boundary (i.e. the two-sphere\n $S^2 \\subset \\mathbb{R}^ 3$.) We will moreover give an application\n regarding the classical limit of a quantum (spin) system and discuss\n the concept of spontaneous symm etry breaking (SSB).\n LOCATION:https://researchseminars.org/talk/DQSeminar/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Madeleine Jotz Lean (Univ. Göttingen) DTSTART:20210326T130000Z DTEND:20210326T150000Z DTSTAMP:20260422T225848Z UID:DQSeminar/6 DESCRIPTION:Title: Transitive double Lie algebroids via core diagrams\nby Madeleine Jot z Lean (Univ. Göttingen) as part of Deformation Quantization Seminar\n\n\ nAbstract\nThis talk begins by explaining Brown and Mackenzie’s equivale nce of locally trivial double groupoids with locally trivial core diagrams (of groupoids). Then it establishes an equivalence between\nthe category of transitive double Lie algebroids and the category of transitive core di agrams (of Lie\nalgebroids). The construction of this equivalence uses the comma double Lie algebroid of a morphism\nof Lie algebroids\, which is in troduced as well. The proofs of the results in this talk rely heavily on\n Gracia-Saz and Mehta’s equivalence of decomposed VB-algebroids with supe r-representations\, and\nthey showcase the power of this recent tool in th e study of VB-algebroids. Since core diagrams of\n(integrable) Lie algebro ids integrate to core diagrams of Lie groupoids\, the equivalences above y ields\na simple method for integrating transitive double Lie algebroids to transitive double Lie groupoids.\nThis is joint work with Kirill Mackenzi e\, who sadly passed in 2020.\n LOCATION:https://researchseminars.org/talk/DQSeminar/6/ END:VEVENT BEGIN:VEVENT SUMMARY:João Nuno Mestre (University of Coimbra) DTSTART:20210312T130000Z DTEND:20210312T150000Z DTSTAMP:20260422T225848Z UID:DQSeminar/7 DESCRIPTION:Title: Some approaches to the differential geometry of singular spaces\nby João Nuno Mestre (University of Coimbra) as part of Deformation Quantizat ion Seminar\n\n\nAbstract\nSeveral objects that appear naturally in differ ential geometry - the zero set \nof a smooth function\, or the quotient of a manifold by a Lie group action\, for example - may not be smooth. \nBut we may still want to study their differential geometry\, to the extent po ssible\, in a way that generalizes \nusual concepts - the zero set of some functions\, and the quotient of some group actions are smooth\, we want \ nto generalize those.\n \nA few possible approaches are to take inspiratio n from algebraic geometry and study the object via an \nappropriately defi ned algebra\, or sheaf\, of smooth functions\; or maybe to decompose the o bject into smaller \npieces that are themselves smooth manifolds and fit t ogether nicely\; or to describe the object in kind of a \n"generators and relations" presentation\, where the generators and the relations are smoot h\, and work with the \npresentation instead. These lead us to the study o f differentiable spaces\, stratified spaces\, and Lie \ngroupoids (which g ive presentations for differentiable stacks).\n\nIn this introductory talk we will see the definitions of these concepts\, some examples in which th ey can be \nof use\, and some classes of singular spaces which are quite w ell behaved and have good descriptions in all \nthree pictures. I will als o try to mention a panoramic view of other approaches to singular spaces\, such as \ndiffeological spaces\, or noncommutative geometric techniques\, and how they relate to the examples presented.\n LOCATION:https://researchseminars.org/talk/DQSeminar/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Vasily Dolgushev (Temple University\, Philadelphia) DTSTART:20210423T120000Z DTEND:20210423T133000Z DTSTAMP:20260422T225848Z UID:DQSeminar/10 DESCRIPTION:Title: GT-shadows and their action on Grothendieck’s child’s drawings\ nby Vasily Dolgushev (Temple University\, Philadelphia) as part of Deforma tion Quantization Seminar\n\n\nAbstract\nThe absolute Galois group of the field of rational numbers and the Grothendieck-Teichmueller\ngroup introdu ced by V. Drinfeld in 1990 are among the most mysterious objects in mathem atics. My\ntalk will be devoted to GT-shadows. These tantalizing objects m ay be thought of as “approximations”\nto elements of the mysterious Gr othendieck-Teichmueller group. They form a groupoid and act on\nGrothendie ck’s child’s drawings. Currently\, the most amazing discovery related to GT-shadows is\nthat the orbits of child’s drawings with respect to th e action of the absolute Galois group (when\nthey can be computed) and the orbits of child’s drawings with respect to the action of GT-shadows\nco incide! If time permits\, I will say a few words about GT-shadows in the A belian setting. My talk\nis partially based on the joint paper https://arx iv.org/abs/2008.00066 with Khanh Q. Le and\nAidan A. Lorenz.\n LOCATION:https://researchseminars.org/talk/DQSeminar/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Jan Vysoký (Czech Technical University in Prague) DTSTART:20210507T120000Z DTEND:20210507T133000Z DTSTAMP:20260422T225848Z UID:DQSeminar/11 DESCRIPTION:Title: Introduction to Graded Manifolds\nby Jan Vysoký (Czech Technical U niversity in Prague) as part of Deformation Quantization Seminar\n\n\nAbst ract\nA need for a geometrical theory with integer graded coordinates aros e both in geometry (Courant algebroids\, Poisson geometry) and physics (AK SZ and BV formalism). Based on the approach of Berezin-Leites and Kostant to supermanifolds\, $\\mathbb{Z}$-graded manifolds are usually defined as (graded) locally ringed spaces\, that is certain sheaves of graded commuta tive algebras over (second countable Hausdorff) topological spaces\, local ly isomorphic to a suitable "local model".\n\nThis approach works with no major issues for non-negatively (or non-positively) graded manifolds\, whi ch is sufficient for most of the applications. However\; if one tries to i nclude coordinates of both positive and negative degrees\, issues appear o n several levels. This was addressed recently by M. Fairon by extending th e local model sheaf. Interestingly\, this modification creates a new subtl e issue on the level of $\\mathbb{Z}$-graded linear algebra.\n\nThis talk intends to point out the aforementioned issues and to offer the modificati ons required to obtain a consistent theory of $\\mathbb{Z}$-graded manifol ds with coordinates of an arbitrary degree.\n LOCATION:https://researchseminars.org/talk/DQSeminar/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Severin Barmeier (Universität zu Köln) DTSTART:20211022T120000Z DTEND:20211022T133000Z DTSTAMP:20260422T225848Z UID:DQSeminar/12 DESCRIPTION:Title: Strict deformation quantizations of polynomial Poisson structures\n by Severin Barmeier (Universität zu Köln) as part of Deformation Quantiz ation Seminar\n\n\nAbstract\nAfter Kontsevich's general existence result f or formal star products of Poisson manifolds\, the convergence of formal s tar products is an essential but nontrivial next step in the deformation q uantization programme. In this talk I will present a combinatorial approac h to the quantization of polynomial Poisson structures on $\\mathbb{R}^d$ which can be used to obtain star products converging on polynomials. The c onstruction uses the natural L$_\\infty$ algebra structure on multi-vector fields obtained by homotopy transfer from the DG Lie algebra structure on the Hochschild complex and Maurer-Cartan elements can be viewed as a syst ematic way of deforming the commutativity relations of the polynomial alge bra. The associated "combinatorial" star product is closely related to the Gutt star product and it admits a graphical description resembling the gr aphical description of Kontsevich's universal formula. Finally\, I will gi ve some examples to illustrate how this star product can be used to obtain strict deformation quantizations of nonlinear Poisson structures by apply ing a general framework developed by Stefan Waldmann.\n\nThis talk will be based on arXiv:2002.10001 joint with Zhengfang Wang and on work in progre ss joint with Philipp Schmitt.\n LOCATION:https://researchseminars.org/talk/DQSeminar/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Alejandro Cabrera (Universidade Federal do Rio de Janeiro) DTSTART:20211029T120000Z DTEND:20211029T133000Z DTSTAMP:20260422T225848Z UID:DQSeminar/13 DESCRIPTION:Title: About quantization and symplectic groupoids\nby Alejandro Cabrera ( Universidade Federal do Rio de Janeiro) as part of Deformation Quantizatio n Seminar\n\n\nAbstract\nIn this talk\, we will review some recent topics relating\nquantization of Poisson manifolds and (local) symplectic groupoi ds. In\nparticular\, focusing on the case of a Poisson structure on a coor dinate\ndomain\, we will explain how analytic Lie-theoretic formulas are r elated to\na ("tree level") part of Kontsevich's star product formula afte r a suitable\nTaylor expansion. We will also comment on the relation to th e Poisson Sigma\nModel through a system of PDEs that captures its semiclas sical\ncontributions. If time permits\, we will also briefly comment on ho w the\nintegrability into a global symplectic groupoid is reflected on\nqu antizations.\n LOCATION:https://researchseminars.org/talk/DQSeminar/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Matias del Hoyo (Universidade Federal Fluminense) DTSTART:20211105T130000Z DTEND:20211105T143000Z DTSTAMP:20260422T225848Z UID:DQSeminar/14 DESCRIPTION:Title: Lie groupoids\, Morita equivalences and quantum tori\nby Matias del Hoyo (Universidade Federal Fluminense) as part of Deformation Quantizatio n Seminar\n\n\nAbstract\nLie groupoids are categorified manifolds\, they p rovide a unified framework for classic geometries\,\nand they can be used to model stacks in differential geometry. Stacks have manifolds\, orbifold s\,\norbit spaces and leaf spaces as examples\, and two groupoids present the same stack if they are\nMorita equivalent. In this talk I will survey the foundations of Lie groupoids\, Morita equivalences\nand differentiable stacks\, and present as an application a geometric version of Rieffel’s Theorem on\nquantum tori.\n LOCATION:https://researchseminars.org/talk/DQSeminar/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Jean Gutt (Institut de Mathématiques de Toulouse) DTSTART:20211112T130000Z DTEND:20211112T143000Z DTSTAMP:20260422T225848Z UID:DQSeminar/17 DESCRIPTION:Title: On the equivalence of symplectic capacities\nby Jean Gutt (Institut de Mathématiques de Toulouse) as part of Deformation Quantization Semina r\n\n\nAbstract\nAn important problem in symplectic topology is to determi ne when symplectic embeddings exist\,\nand more generally to classify the symplectic embeddings between two given domains. Modern work\non this topi c began with the Gromov nonsqueezing theorem\, which asserts that the ball symplectically\nembeds into the cylinder if and only if the radius of the ball is larger than that of the cylinder. Many\nquestions about symplecti c embeddings remain open\, even for simple examples such as ellipsoids and \npolydisks. To obtain nontrivial obstructions to the existence of symplec tic embeddings\, one often\nuses various symplectic capacities. We shall d iscuss some questions about capacities\, in particular the\nequality of tw o type of symplectic capacities. This is joint work with V.Ramos.\n LOCATION:https://researchseminars.org/talk/DQSeminar/17/ END:VEVENT END:VCALENDAR