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:20260404T094701Z UID:DQSeminar/1 DESCRIPTION:Title: New geometrical methods in mathematical relativity\nby Olaf M üller (Humboldt-Universität zu Berlin) as part of Deformation Quantizati on Seminar\n\n\nAbstract\nThis talk presents some new geometric approaches to global behavior of solutions to classical field\nequations. The result s comprise:\n\n• the existence of global solutions for Dirac-Higgs-Yang- Mills Theories (like the standard model)\nin spacetimes close to Minkowski spacetime 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 -Einstein theories (e.g.\nthe minimal coupling of the standard model to gr avity and its sectors like Einstein-DiracMaxwell theory) with the main too l being the Universal Spinor Bundle (joint work with Nikolai\nNowaczyk)\,\ n\n• some old and new results about how concentration of energy implies the development of black\nholes\, and the “flatzoomer” method (develop ped in a joint work with Marc Nardmann) applied\nin the construction of sp acetimes metrics satisfying energy conditions in a given conformal class.\ n LOCATION:https://stable.researchseminars.org/talk/DQSeminar/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Marco Benini (Università di Genova) DTSTART:20210205T130000Z DTEND:20210205T150000Z DTSTAMP:20260404T094701Z UID:DQSeminar/2 DESCRIPTION:Title: Homotopical quantization of linear gauge theories\nby Marco B enini (Università di Genova) as part of Deformation Quantization Seminar\ n\n\nAbstract\nIn a gauge theory\, gauge transformations encode a useful h igher structure that enables one to\nperform powerful constructions\, e.g. BRST/BV quantization. The efficacy of the BRST/BV approach\nrelies on the flexibility of introducing auxiliary fields\, an operation which is forma lized by quasiisomorphisms. This flexibility comes at the price that all c onstructions must be derived\, i.e. invariant\nunder quasi-isomorphisms (a s opposed to isomorphisms). Focusing on the prototypical example of\nlinea r Yang-Mills theory\, I will present a standard model for its derived crit ical locus and equip the\nassociated complex of linear observables with it s canonical shifted Poisson structure (antibracket). I\nwill show how glob al hyperbolicity of the background Lorentzian manifold entails that this s hifted\nPoisson structure is (homologically) trivial and observe the exist ence of two distinguished ways to\ntrivialize it. Combining these triviali zations leads to a non-trivial unshifted Poisson structure\, which\nI will quantize via canonical commutation relations. This leads to an explicit e xample of a homotopy\nalgebraic quantum field theory\, where the time-slic e axiom is encoded weakly by quasi-isomorphisms\n(as opposed to isomorphis ms).\n LOCATION:https://stable.researchseminars.org/talk/DQSeminar/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Michael Heins (Julius-Maximilians University Würzburg) DTSTART:20210212T130000Z DTEND:20210212T150000Z DTSTAMP:20260404T094701Z UID:DQSeminar/3 DESCRIPTION:Title: The Universal Complexification of a Lie Group\nby Michael Hei ns (Julius-Maximilians University Würzburg) as part of Deformation Quanti zation Seminar\n\n\nAbstract\nIn classical Lie theory\, a\n complexificat ion of a Lie group with Lie algebra $\\mathfrak{g}$ is a\n complex Lie gr oup\, whose Lie algebra is given by the\n complexification $\\mathfrak{g} _{\\mathbb{C}}$ of $\\mathfrak{g}$ in the sense\n of vector spaces. Both from an analytical and a categorical point of\n view\, this definition tu rned out to be too naive to be truly\n useful. Historically\, this lead t o the refined concept of\n universal complexification\, which is based on an analytically\n desirable universal property. In this talk\, we motiva te this\n definition by briefly reviewing the vector space\n situation. Afterwards\, we give a rather geometric construction of\n the universal c omplexification of a given Lie group\, which was\n formalized by Hochschi ld around 1955 and refined by the Bourbaki\n group in the following decad e. Along the way\, we review Lie's\n seminal Theorems and meet the univer sal covering group. While many\n properties of the resulting universal co mplexification align with\n what we geometrically expect\, some notable a spects turn out to\n differ\, which we discuss in detail. Finally\, we pr ovide some\n examples to illustrate the power and limitations of the mach inery we\n have developed.\n LOCATION:https://stable.researchseminars.org/talk/DQSeminar/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Christiaan van de Ven (University of Trento) DTSTART:20210226T130000Z DTEND:20210226T150000Z DTSTAMP:20260404T094701Z UID:DQSeminar/4 DESCRIPTION:Title: Asymptotic equivalence of two strict deformation quantizations an d applications to the classical limit\nby Christiaan van de Ven (Unive rsity of Trento) as part of Deformation Quantization Seminar\n\n\nAbstract \nThe concept of strict deformation\n quantization provides a mathematica l formalism that describes the\n transition from a classical theory to a quantum theory in terms of\n deformations of (commutative) Poisson algebr as (representing the\n classical theory) into non-commutative $C^*$-algeb ras\n (characterizing the quantum theory). In this seminar we introduce\n the definitions\, give several examples and show how quantization of\n the closed unit 3-ball $B^3 \\subset \\mathbb{R}^3$ is related to\n quant ization of its smooth boundary (i.e. the two-sphere\n $S^2 \\subset \\mat hbb{R}^3$.) We will moreover give an application\n regarding the classica l limit of a quantum (spin) system and discuss\n the concept of spontaneo us symmetry breaking (SSB).\n LOCATION:https://stable.researchseminars.org/talk/DQSeminar/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Madeleine Jotz Lean (Univ. Göttingen) DTSTART:20210326T130000Z DTEND:20210326T150000Z DTSTAMP:20260404T094701Z UID:DQSeminar/6 DESCRIPTION:Title: Transitive double Lie algebroids via core diagrams\nby Madele ine Jotz Lean (Univ. Göttingen) as part of Deformation Quantization Semin ar\n\n\nAbstract\nThis talk begins by explaining Brown and Mackenzie’s e quivalence of locally trivial double groupoids with locally trivial core d iagrams (of groupoids). Then it establishes an equivalence between\nthe ca tegory of transitive double Lie algebroids and the category of transitive core diagrams (of Lie\nalgebroids). The construction of this equivalence u ses the comma double Lie algebroid of a morphism\nof Lie algebroids\, whic h is introduced as well. The proofs of the results in this talk rely heavi ly on\nGracia-Saz and Mehta’s equivalence of decomposed VB-algebroids wi th super-representations\, and\nthey showcase the power of this recent too l in the study of VB-algebroids. Since core diagrams of\n(integrable) Lie algebroids integrate to core diagrams of Lie groupoids\, the equivalences above yields\na simple method for integrating transitive double Lie algebr oids to transitive double Lie groupoids.\nThis is joint work with Kirill M ackenzie\, who sadly passed in 2020.\n LOCATION:https://stable.researchseminars.org/talk/DQSeminar/6/ END:VEVENT BEGIN:VEVENT SUMMARY:João Nuno Mestre (University of Coimbra) DTSTART:20210312T130000Z DTEND:20210312T150000Z DTSTAMP:20260404T094701Z 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 Qu antization Seminar\n\n\nAbstract\nSeveral objects that appear naturally in differential geometry - the zero set \nof a smooth function\, or the quot ient 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 ex tent possible\, 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 ins piration from algebraic geometry and study the object via an \nappropriate ly defined algebra\, or sheaf\, of smooth functions\; or maybe to decompos e the object into smaller \npieces that are themselves smooth manifolds an d fit together nicely\; or to describe the object in kind of a \n"generato rs and relations" presentation\, where the generators and the relations ar e smooth\, and work with the \npresentation instead. These lead us to the study of differentiable spaces\, stratified spaces\, and Lie \ngroupoids ( which give presentations for differentiable stacks).\n\nIn this introducto ry talk we will see the definitions of these concepts\, some examples in w hich they can be \nof use\, and some classes of singular spaces which are quite well behaved and have good descriptions in all \nthree pictures. I w ill also try to mention a panoramic view of other approaches to singular s paces\, such as \ndiffeological spaces\, or noncommutative geometric techn iques\, and how they relate to the examples presented.\n LOCATION:https://stable.researchseminars.org/talk/DQSeminar/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Vasily Dolgushev (Temple University\, Philadelphia) DTSTART:20210423T120000Z DTEND:20210423T133000Z DTSTAMP:20260404T094701Z UID:DQSeminar/10 DESCRIPTION:Title: GT-shadows and their action on Grothendieck’s child’s drawin gs\nby Vasily Dolgushev (Temple University\, Philadelphia) as part of Deformation Quantization Seminar\n\n\nAbstract\nThe absolute Galois group of the field of rational numbers and the Grothendieck-Teichmueller\ngroup introduced by V. Drinfeld in 1990 are among the most mysterious objects in mathematics. My\ntalk will be devoted to GT-shadows. These tantalizing ob jects may be thought of as “approximations”\nto elements of the myster ious Grothendieck-Teichmueller group. They form a groupoid and act on\nGro thendieck’s child’s drawings. Currently\, the most amazing discovery r elated to GT-shadows is\nthat the orbits of child’s drawings with respec t to the 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-shad ows\ncoincide! If time permits\, I will say a few words about GT-shadows i n the Abelian setting. My talk\nis partially based on the joint paper http s://arxiv.org/abs/2008.00066 with Khanh Q. Le and\nAidan A. Lorenz.\n LOCATION:https://stable.researchseminars.org/talk/DQSeminar/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Jan Vysoký (Czech Technical University in Prague) DTSTART:20210507T120000Z DTEND:20210507T133000Z DTSTAMP:20260404T094701Z UID:DQSeminar/11 DESCRIPTION:Title: Introduction to Graded Manifolds\nby Jan Vysoký (Czech Tech nical University in Prague) as part of Deformation Quantization Seminar\n\ n\nAbstract\nA need for a geometrical theory with integer graded coordinat es arose both in geometry (Courant algebroids\, Poisson geometry) and phys ics (AKSZ and BV formalism). Based on the approach of Berezin-Leites and K ostant to supermanifolds\, $\\mathbb{Z}$-graded manifolds are usually defi ned as (graded) locally ringed spaces\, that is certain sheaves of graded commutative algebras over (second countable Hausdorff) topological spaces\ , locally isomorphic to a suitable "local model".\n\nThis approach works w ith no major issues for non-negatively (or non-positively) graded manifold s\, which is sufficient for most of the applications. However\; if one tri es to include coordinates of both positive and negative degrees\, issues a ppear on several levels. This was addressed recently by M. Fairon by exten ding the local model sheaf. Interestingly\, this modification creates a ne w subtle issue on the level of $\\mathbb{Z}$-graded linear algebra.\n\nThi s talk intends to point out the aforementioned issues and to offer the mod ifications required to obtain a consistent theory of $\\mathbb{Z}$-graded manifolds with coordinates of an arbitrary degree.\n LOCATION:https://stable.researchseminars.org/talk/DQSeminar/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Severin Barmeier (Universität zu Köln) DTSTART:20211022T120000Z DTEND:20211022T133000Z DTSTAMP:20260404T094701Z UID:DQSeminar/12 DESCRIPTION:Title: Strict deformation quantizations of polynomial Poisson structure s\nby Severin Barmeier (Universität zu Köln) as part of Deformation Quantization Seminar\n\n\nAbstract\nAfter Kontsevich's general existence r esult for formal star products of Poisson manifolds\, the convergence of f ormal star products is an essential but nontrivial next step in the deform ation quantization programme. In this talk I will present a combinatorial approach to the quantization of polynomial Poisson structures on $\\mathbb {R}^d$ which can be used to obtain star products converging on polynomials . The construction uses the natural L$_\\infty$ algebra structure on multi -vector fields obtained by homotopy transfer from the DG Lie algebra struc ture on the Hochschild complex and Maurer-Cartan elements can be viewed as a systematic way of deforming the commutativity relations of the polynomi al algebra. The associated "combinatorial" star product is closely related to the Gutt star product and it admits a graphical description resembling the graphical description of Kontsevich's universal formula. Finally\, I will give some examples to illustrate how this star product can be used to obtain strict deformation quantizations of nonlinear Poisson structures b y applying 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 progress joint with Philipp Schmitt.\n LOCATION:https://stable.researchseminars.org/talk/DQSeminar/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Alejandro Cabrera (Universidade Federal do Rio de Janeiro) DTSTART:20211029T120000Z DTEND:20211029T133000Z DTSTAMP:20260404T094701Z UID:DQSeminar/13 DESCRIPTION:Title: About quantization and symplectic groupoids\nby Alejandro Ca brera (Universidade Federal do Rio de Janeiro) as part of Deformation Quan tization Seminar\n\n\nAbstract\nIn this talk\, we will review some recent topics relating\nquantization of Poisson manifolds and (local) symplectic groupoids. In\nparticular\, focusing on the case of a Poisson structure on a coordinate\ndomain\, we will explain how analytic Lie-theoretic formula s are related to\na ("tree level") part of Kontsevich's star product formu la after a suitable\nTaylor expansion. We will also comment on the relatio n to the Poisson Sigma\nModel through a system of PDEs that captures its s emiclassical\ncontributions. If time permits\, we will also briefly commen t on how the\nintegrability into a global symplectic groupoid is reflected on\nquantizations.\n LOCATION:https://stable.researchseminars.org/talk/DQSeminar/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Matias del Hoyo (Universidade Federal Fluminense) DTSTART:20211105T130000Z DTEND:20211105T143000Z DTSTAMP:20260404T094701Z UID:DQSeminar/14 DESCRIPTION:Title: Lie groupoids\, Morita equivalences and quantum tori\nby Mat ias del Hoyo (Universidade Federal Fluminense) as part of Deformation Quan tization Seminar\n\n\nAbstract\nLie groupoids are categorified manifolds\, they provide a unified framework for classic geometries\,\nand they can b e used to model stacks in differential geometry. Stacks have manifolds\, o rbifolds\,\norbit spaces and leaf spaces as examples\, and two groupoids p resent the same stack if they are\nMorita equivalent. In this talk I will survey the foundations of Lie groupoids\, Morita equivalences\nand differe ntiable stacks\, and present as an application a geometric version of Rief fel’s Theorem on\nquantum tori.\n LOCATION:https://stable.researchseminars.org/talk/DQSeminar/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Jean Gutt (Institut de Mathématiques de Toulouse) DTSTART:20211112T130000Z DTEND:20211112T143000Z DTSTAMP:20260404T094701Z UID:DQSeminar/17 DESCRIPTION:Title: On the equivalence of symplectic capacities\nby Jean Gutt (I nstitut de Mathématiques de Toulouse) as part of Deformation Quantization Seminar\n\n\nAbstract\nAn important problem in symplectic topology is to determine when symplectic embeddings exist\,\nand more generally to classi fy the symplectic embeddings between two given domains. Modern work\non th is topic began with the Gromov nonsqueezing theorem\, which asserts that t he 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 sy mplectic embeddings remain open\, even for simple examples such as ellipso ids and\npolydisks. To obtain nontrivial obstructions to the existence of symplectic embeddings\, one often\nuses various symplectic capacities. We shall discuss some questions about capacities\, in particular the\nequalit y of two type of symplectic capacities. This is joint work with V.Ramos.\n LOCATION:https://stable.researchseminars.org/talk/DQSeminar/17/ END:VEVENT END:VCALENDAR