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 e31c
X-WR-CALNAME:QM Research Seminar: Dirac operators in representation theory
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TZID:Europe/Copenhagen
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DTSTAMP:20260624T153642Z
DTSTART:20261028T030000
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DTSTART:20260325T020000
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DESCRIPTION:[b]Speaker: Steffen Schmidt[/b] (University of Southern Denmar
 k).\n\n[b]Abstract: [/b]\nSymmetry serves as a guiding principle in mathe
 matics and physics. The language of symmetry groups and their actionsorga
 nizes a wide range of phenomena. In this setting\, Dirac operators form a
  natural bridge between quantum mechanics\, geometry\, and representation
  theory. \n\nIn representation theory\, Dirac operators provide conceptua
 l and computational tools for addressing basic problems concerning a (sem
 isimple) Lie group: they furnish explicit constructions\, give effective 
 criteria for unitarity\, contribute to classification results\, and relat
 e the topology of locally symmetric spaces to representation-theoretic da
 ta. A foundational instance is Parthasarathy's use of a representation-th
 eoretic Dirac operator in the study of discrete series representations. \
 n\nInterest in this circle of ideas intensified in the late 1990s\, follo
 wing Kostant's introduction of the cubic Dirac operator and the subsequen
 t development of \emph{Dirac cohomology}\, including Huang–Pandžić’s proo
 fof Vogan's conjecture. \n\nIn this talk\, I present a modern constructio
 n of (algebraic) Dirac operators and discuss applications of Dirac operat
 ors and Dirac cohomology to representations of Lie superalgebras\, includ
 ing localization principles\, relations with Duflo–Serganova cohomology\,
  and character formulas.
DTEND:20260512T140000Z
DTSTAMP:20260624T153642Z
DTSTART:20260512T130000Z
LOCATION:Syddansk Universitet\, Campusvej 55\, 5230\, Odense M
SEQUENCE:0
SUMMARY:QM Research Seminar: Dirac operators in representation theory
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