Denis Nardin

I am a postdoc at the Université Paris 13, in the LAGA research group. My main mathematical interests are on equivariant and motivic homotopy theory and algebraic K-theory.

I completed my Ph.D. at the Massachusetts Institute of Technology under the supervision of Clark Barwick.

Papers

• Dualizing cartesian and cocartesian fibrations
  with Clark Barwick and Saul Glasman. September 2014, submitted for publication.
• Categorifying rationalization
  with Clark Barwick, Marc Hoyois, Saul Glasman and Jay Shah.
• Parametrized higher category theory and higher algebra:
  I am taking part in a project with Clark Barwick, Saul Glasman, Emanuele Dotto and Jay Shah whose aim is to provide common foundations for several different parts of homotopy theory, among which equivariant homotopy theory, parametrized homotopy theory and Goodwillie calculus. For a general introduction see this lecture by Clark Barwick.
• Parametrized higher category theory and higher algebra: A general introduction
  with Clark Barwick, Emanuele Dotto, Saul Glasman and Jay Shah.
• Parametrized higher category theory and higher algebra: Exposé I -- Elements of parametrized higher category theory
  with Clark Barwick, Emanuele Dotto, Saul Glasman and Jay Shah.
• Parametrized higher category theory and higher algebra: Exposé IV -- Stability with respect to an orbital ∞-category
• Stability and distributivity over an orbital ∞-category
  My ph.D. thesis

Expository notes and undegraduate work

• Levine's Chow's moving lemma
  Forthcoming. An exposition of Levine's proof of Chow's moving lemma for higher Chow groups.
• Crossing Browder's bridge
  Forthcoming. An explanation in modern language of Browder's original proof of his theorem relating the Kervaire invariant of framed manifolds and the 2-line of the Adams spectral sequence.
• The purity theorem in motivic homotopy theory
  A short discussion of the proof of the purity theorem in motivic homotopy theory.
• Fundamental quandle of knots and the Alexander module
  A short essay defining the fundamental quandle and proving some of its main properties.
• Superfici di Riemann, teorema di Riemann-Roch e applicazioni
  In italian. My bachelor thesis, about Riemann-Roch theorem for Riemann surfaces. Contains an elementary proof that every plane Riemann surface is algebraic.
• Essential dimension of finite group schemes
  My master thesis about the basic theory of essential dimension for finite group schemes. Contains a small improvement on a result by Ledet.