Título: Kähler geometry of moduli of parabolic bundles in mathematical physics
Palestrante: Claudio Meneses (Christian-Albrechts-Universität Kiel)
Data: 14/09/2021
Horário: 14:00h
Local: Transmissão online
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Resumo: Since their introduction in the 1980s, moduli spaces of parabolic bundles have arisen in a surprisingly large and ever-increasing number of occasions at the interface of geometry, topology, and mathematical physics. The natural Kähler structure carried by these moduli spaces constitutes a primary piece in the broad puzzle of relations between these subjects. In this talk I will present a condensed overview of the beautiful history of these interactions, focusing on the peculiarities of the genus 0 case.
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Palestra: "Métricas Higgs-Hermite-Einstein fracas sobre variedades assintoticamente cilíndricas"
Palestrante: Pedro Manfrim Magalhães de Paula (Unicamp)
Data: 15/08/2019
Local e horário: A confirmar
Resumo: Nesta apresentação vou introduzir o teorema clássico de Simpson-Uhlenbeck-Yau e mostrar como é possível estende-lo para o caso de variedades assintoticamente cilíndricas. Para isso vou relembrar alguns fatos sobre fibrados de Higgs e apresentarei algumas das propriedades analíticas das variedades assintoticamente cilíndricas. Utilizando-se destes resultados, explicarei como podemos adaptar o método da continuidade de Uhlenbeck e Yau para este contexto e provar a existência de métricas Higgs-Hermite-Einstein fracas.
Palestra: Real and complex algebraic geometry of Hamiltonian reductions
Palestrante: Hans-Christian Herbig (UFRJ)
Data: 30/05/2019
Hora: 12:00h
Local: C119
Resumo: I will explain how invariant theory can be used to study the symplectic quotient arising from reduction at zero level of the moment map of a unitary representation of a compact Lie group. I will elaborate on the symplectomorphism problem for these spaces. In particular, I will explain what general feature they have and what “invariants” can be used to distinguish them. I will elaborate on how to complexify the spaces and the discuss the role of largeness in all of this.
Palestrante: Alessia Mandini (PUC-Rio)
Palestra: Hyperpolygons and parabolic Higgs bundles
Data: 06/06/2019
Horário: 12h
Local: C116
Resumo: Hyperpolygons spaces are a family of (finite dimensional, non-compact) hyperkaehler spaces, that can be obtained from coadjoint orbits by hyperkaehler reduction. Jointly with L. Godinho, we show that these space are diffeomorphic (in fact, symplectomorphic) to certain families of parabolic Higgs bundles. In this talk I will describe this relation and use it to analyse the fixed points locus of a natural involution on the moduli space of parabolic Higgs bundles. I will show that each connected components of the fixed point locus of this involution is identified with a moduli spaces of polygons in Minkowski 3-space.
Palestra: Modular Tensor Categories and Riemann Surfaces
Palestrante: Jethro van Ekeren (UFF)
Data: 24/04/2019 (quarta-feira)
Hora: 13:30
Local: C116
Resumo: Two of the key notions to arise from the synthesis of Lie theory, quantum field theory and low dimensional topology of the 1980-1990s were the notions of vertex algebra (VA) and modular tensor category (MTC). Morphisms in an MTC are naturally describable by a sort of braid notation, and this makes MTCs a source of knot invariants like the Jones polynomial. Following ideas from physics, a vertex algebra V can be used to produce a certain coherent assignment of vector spaces (called conformal blocks) to Riemann surfaces. This data in turn can be used to endow the category of V-modules with the structure of an MTC. In this talk I would like to give an introductory overview of these constructions, with examples, and finally to announce some recent work with T. Arakawa in which we construct an apparently new class of MTCs as categories of representations of subregular affine W-algebras.
