Oisín Flynn-Connolly

Welcome to my website. Since November 2024, I am a postdoc in Leiden University in the research group of Henning Basold, where I am currently working on a project to develop homotopical and coalgebraic approachs to the study of optimization algorithms. An important part of this is developing a probabilistic approach to homotopy theory using techniques from categorical probability such as Markov categories and probability monads. I was previously a PhD student in the algebraic topology team at Université Sorbonne Paris Nord where my advisor was Grégory Ginot.

How to contact me My office is BM2.14, Gorlaeus Building. A photo of me can be found here. My email address is oisinflynnconnolly@gmail.com

Keywords: Homotopy, Operads, Massey products, E-infinity algebras

Research

Preprints & Papers

  1. A p-adic de Rham complex (pdf) Abstract
  2. An obstruction theory for strictly commutative algebras in positive characteristic (ArXiv) Submitted Abstract
  3. Higher order Massey products for algebras over algebraic operads (with José M. Moreno-Fernández) (ArXiv) Submitted Abstract
  4. A recognition principle for iterated suspensions as coalgebras over the little cubes operad (with José M. Moreno-Fernández and Felix Wierstra) (ArXiv) Submitted Abstract
  5. Three Schur functors related to pre-Lie algebras (with Vladimir Dotsenko) (journal, ArXiv ) Mathematical Proceedings of Cambridge Philosophical Society Abstract

In preparation

Modulo some small intended additions before submission, these articles currently exist as the final two chapters of my thesis and will be available on the ArXiv shortly.

  1. Homotopically, E-infinity algebras do not generalise commutative dg-algebras Abstract
  2. A higher Hochschild-Konstant-Rosenberg Theorem and the Deligne conjecture Abstract

Ongoing projects

  1. Homotopy operations from the little cubes operad (with José M. Moreno-Fernández and Felix Wierstra)

Theses

  1. PhD thesis: Higher commutativity in algebra and algebraic topology (pdf), defended 4/10/24 (slides), supervised by Grégory Ginot
  2. Master thesis: The homotopy theory of the little n-discs operad (pdf), defended 17/07/20 (slides), supervised by Felix Wierstra

Talks and notes

Research talks
  1. Corecognition for iterated suspensions, October 2024, Rencontre 2024 de Topologie algébrique, Toulouse
  2. Strictly commutative algebra in positive characteristic, September 2024, seminar of Université de Lille. Slides
  3. Strictly commutative algebra in positive characteristic, September 2024, seminar of Université de Toulouse. Slides
  4. Higher invariants in homotopy theory, August 2024, 37th Annual Meeting of the Irish Mathematical Society, Belfast. Slides
  5. Strictly commutative algebra in positive characteristic, February 2024, seminar of Seville University Slides
  6. Strictly commutative algebra in positive characteristic, January 2024, seminar of Stockholm University
  7. The geometry of iterated suspensions, November 2023, seminar of Université de Lille
  8. p-adic homotopy theory, November 2023, seminar of Universidad de Malaga
  9. The geometry of iterated suspensions, October 2023, seminar of Université Sorbonne Paris Nord
Poster presentations
  1. Corecognition for iterated suspensions , July 2023, Young Topologist's Meeting, Lausanne. Poster
  2. Corecognition for iterated suspensions, September 2023, 36th Meeting of the Irish Mathematical Society
Popularization talks
  1. Introduction to ∞-categories, November 2022, PhD topology seminar of USPN
  2. Groebner bases and automated theorem proving, April 2024, PhD student seminar of USPN
A complete list of attended conferences and research visits may be found on my Activities page.

Teaching

2020-2021
  1. Analyse 2, first year, USPN
  2. Algèbre 6, third year, USPN
2018-2019
  1. Trinity Access Program - Maths for STEM component, first year, Trinity College Dublin