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SUMMARY:Olaf Müller (Humboldt-Universität zu Berlin)
DTSTART;VALUE=DATE-TIME:20210115T130000Z
DTEND;VALUE=DATE-TIME:20210115T150000Z
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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:
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SUMMARY:Marco Benini (Università di Genova)
DTSTART;VALUE=DATE-TIME:20210205T130000Z
DTEND;VALUE=DATE-TIME:20210205T150000Z
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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
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SUMMARY:Michael Heins (Julius-Maximilians University Würzburg)
DTSTART;VALUE=DATE-TIME:20210212T130000Z
DTEND;VALUE=DATE-TIME:20210212T150000Z
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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
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SUMMARY:Christiaan van de Ven (University of Trento)
DTSTART;VALUE=DATE-TIME:20210226T130000Z
DTEND;VALUE=DATE-TIME:20210226T150000Z
DTSTAMP;VALUE=DATE-TIME:20210228T193002Z
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
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