Luís Alexandre Pereira

Office 309, Department of Mathematics, University of Virginia,Charlottesville, VA 22904
e-mail: lp2h@virginia.edu

Research interests

My area of study is Algebraic Topology.
In particular I am interested in Goodwillie calculus, the theory of operads and their Koszul duality, and moreover, the interplay between these subjects.
More recently, I have taken an interest in the theory of equivariant operads. My first major result on this topic was a generalization of Cisinski-Moerdijk-Weiss' dendroidal sets to the equivariant setting, based on a new notion of equivariant trees.
Currently, I am in the process of using those equivariant trees to build a new algebraic structure, which we dub "genuine equivariant operads", and showing that it provides an equivalent model to usual equivariant operads (joint with Peter Bonventre).

Research Statement: link

Papers and preprints

In Preparation

  • Genuine Equivariant Operads (with Peter Bonventre)
  • Graph stable equivalences and operadic constructions in equivariant spectra (with Markus Hausmann) link
  • Filtrations of colored operadic constructions and excisiveness of truncated operadic functors link

Publications

  • Cofibrancy of operadic constructions in positive symmetric spectra link
    (Homology, Homotopy and Applications, vol.13(2), 2016, pp.133-168)
  • Operad bimodules and composition products on André-Quillen filtrations of algebras (with Nick Kuhn) link
    (Algebraic & Geometric Topology, vol.17(2), 2017, pp.1105-1130)

Preprints

  • Equivariant dendroidal sets link (updated 3/20/2017, submitted)
  • A general context for Goodwillie calculus link
  • Goodwillie calculus in algebras over a spectral operad link

Research talks

  • A (equivariant) tree description of (genuine equivariant) operads (Spring 2016 at UVa)
  • Genuine equivariant operads (Fall 2016 at UVa and Notre Dame and Spring 2017 at U. of Louisiana at Lafayette)
  • N-infinity operads and equivariant trees (Spring 2016 at JHU and at UVa)
  • Cofibrancy of operadic constructions in spectra (Fall 2014 at UVa)
  • Goodwillie calculus in algebras over a spectral operad (Fall 2014 at OSU and Fall 2013 at UVa)
a paper polyhedron