Sacha Ikonicoff
Hi! I'm Sacha.
From January 1st 2023, I am a postdoctoral scholar at the University of Ottawa, in Canada, with Rick Blute, Simon Henry, and Philip Scott.
Before that, I was a postdoctoral scholar at the University of Calgary, in Canada, with Kristine Bauer.
My research interests are in algebraic topology, homotopy theory and category theory. I am especially interested in operads and their divided powers. I also did some work on unstable modules and algebras over the Steenrod algebra. More recently, I have worked with JSPL on a notion of differential and tangent categories. I have a project with Martin Frankland and Ioannis Dokas to study Quillen cohomology of divided power algebras over an operad. I have another project with Tim Van der Linden aiming to study the category of algebras over a reduced operad as a semi-abelian category, and investigating links between semi-abelian categories and differential and tangent categories. I also have a somewhat more ambitious project to define a rigorous framework for divided powers in general categories, with applications in topology, functor calculus, and possible extensions to the ∞-category and ∞-operad viewpoint.
E-mail address: ikonicoff (at) gmail (dot) com
Publications
Published articles :
Cartesian differential comonads and new models of cartesian differential categories, with Jean-Simon Pacaud Lemay. Cahiers de Topologie et Géométrie Différentielle Catégoriques, Volume 64-2, 2023, pp 198–239.
arXiv preprint: https://arxiv.org/abs/2108.04304
Unstable algebras over an operad II. To be published in Homology, Homotopy, and Applications. 2023
arXiv preprint: https://arxiv.org/abs/2011.13002
Divided power algebras and distributive laws. Journal of Pure and Applied Algebra, Volume227, Issue 8, August 2023.
arXiv preprint: https://arxiv.org/abs/2104.11736
Unstable algebras over an operad. Homology, Homotopy, and Applications, Volume 23, 2021, Number 1, pp. 119–141.
https://www.intlpress.com/site/pub/pages/journals/items/hha/content/vols/0023/0001/a008/index.php
Divided power algebras over an operad. Glasgow Mathematical Journal, Volume 62, Issue 3, September 2020, pp. 477 - 517.
arXiv preprint: https://arxiv.org/abs/1712.03694
The Rosický tangent categories of algebras over an operad, with Marcello Lanfranchi and Jean-Simon Pacaud Lemay
Accepted for publication in Higher Structures.
arxiv preprint: https://arxiv.org/abs/2303.05434
Academic career
2023 — Now: Postdoctoral fellow with Rick Blute and Simon Henry, University of Ottawa, Ottawa ON, Canada
2020 — 2022 : Postdoctoral scholar with Kristine Bauer, University of Calgary, Calgary AB, Canada
2019 — 2020 : ATER (temporary teaching and research assistant), Université de Paris, Paris, France
2016 — 2019 : PhD, Université de Paris, Paris, France :
Advisor : Muriel Livernet
Thesis : Level algebras and applications to algebraic topology
2014 — 2016 : Master de mathématiques fondamentales, Université Pierre et Marie Curie, Paris, France :
Advisor : Muriel Livernet
Master thesis : Homotopie des algèbres simpliciales sur une opérade
2010 — 2014 : Licence de Mathématiques, Université Pierre et Marie Curie, Paris, France
List of talks
Conference talks :
December 2023 CMS Winter meeting, homotopy theory session, Montreal, Canada
Octobre 2022 Category Theory OctoberFest, online
Juin 2022 Foundational Methods in Computer Science Workshop, Kananaskis, Canada
Juin 2021 BIRS Workshop: Tangent Categories and their Applications, Foundational Methods in Computer Science Workshop, online and Kananaskis, Canada
December 2020 CMS Winter online meeting, homotopy theory session, online
Octobre 2019 Rencontre annuelle du GDR topologie algébrique, Arras, France
Seminar Talks :
September 2023 University of Ottawa, logic seminar
August 2023 University of Regina, topology seminar
August 2023 University of Calgary, peripatetic seminar
January 2023 University of Ottawa, logic seminar
April 2022 University of Calgary, peripatetic seminar
April 2022 University of Regina, topology seminar
November 2021 University of Ottawa, logic seminar
November 2021 PIMS Emergent Research: PDF Seminar Series
March 2021 University of Nevada at Reno, topology seminar
October 2020 University of Calgary, peripatetic seminar
March 2020 Université d'Angers, séminaire de topologie du LAREMA
January 2020 University of Copenhagen, Centre for Symmetry and Deformation, algebra/topology seminar
January 2020 Université de Paris, séminaire de topologie de l'IMJ–PRG
January 2019 Université de Strasbourg, séminaire de topologie algébrique de l'IRMA
June 2018 Université Paris 13, séminaire de topologie algébrique du LAGA
March 2018 Université d'Angers, séminaire de topologie du LAREMA
February 2018 Université de Lille, séminaire de topologie du laboratoire Paul Painlevé
Tutorial and Surveys :
August 2023 Gradient descent and neural networks: a categorical approach, Math/Computer Science Seminar
University of Regina, Canada
February 2023 Cartesian differential categories and coCartesian differential monads and Algebraic examples of coCartesian differential monads coming from operads,
Peripatetic seminar: mini-conference on tangent categories and algebras over an operad,
University of Calgary, Canada
February 2019 CW-algèbres et filtrations, groupe de travail stabilité homologique d'après l'article Cellular E_k-algebras de Galatius, Kupers, and Randal-Williams
Université de Paris, France
Octobre 2018 Algorithme de Whitehead, Rencontre annuelle du GDR topologie algébrique,
introduction au mini cours Automorphism groups of free groups and Outer space de Karen Vogtmann
Université de Montpellier, France
Juillet 2018 Espaces classifiants: définition géométrique, groupe de travail mapping class groups et stabilité homologique, Université de Lille, France
Mars 2018 What is an operad? séminaire des doctorants de l'IMJ–PRG, Université Pierre et Marie Curie, Paris, France
Mars 2018 What is an operad? séminaire des doctorants LAMFA, de Picardie Jules Vernes, Amiens, France
Octobre 2016 Introduction aux ensembles simpliciaux, Rencontre annuelle du GDR topologie algébrique,
introduction au mini cours Autour du théorème B de Quillen d'Ieke Moerdijk
Université de Picardie Jules Verne, Amiens, France
Teaching experience
Instructor at the University of Ottawa
I am in charge of MAT1748, Mathématiques discrètes pour l'informatique (Discrete Mathematics for Computing), in French, during the Winter term of 2024.
I was in charge of MAT2762, Fondements des Mathématiques (Foundation of Mathematics), in French, during the Fall term of 2023.
I was in charge of MAT3361, Introduction to Mathematical Logic, at the University ofOttawa, during the Winter term of 2023.
Instructor at the University of Calgary
I was in charge of MATH265, University Calculus I, at the University of Calgary, during the Winter and Spring terms of 2021 and 2022.
Examinateur externe
I gave 60 hours of oral interrogation as part of a team of colleurs for the classes préparatoires PTSI and PT* of Lycée de Cachan during the year 2019–2020.
ATER (Temporary assistant of teaching and research) at Université de Paris
2019 – 2020 MA3, Fundamental Analysis and Algebra 1, L2 MIASH (human sciences and mathematics), 72 hours "équivalent TD"
Taylor expansions, parametric curves, numerical series, improper integrals, symmetric groups, matrices and determinants, endomorphisms
MM4, Fundamental Analysis and Algebra, L2 mathematics and double licence mathematics/computer science, 12 hours oral examination
Doctorant Moniteur (Teaching Assistant) at Université de Paris
2017 – 2018 IA3, Introduction to Arithmetic, L2 mathematics, 39 hours "équivalent TD"
groups and rings Z/nZ, Chinese remainder theorem, RSA cryptosystem
RM1, Mathematical Reasoning, L1 double licence mathematics/computer science, 18 hours "équivalent TD"
Basic mathematical logic and proof writing, basic set theory
OB3, Tools for Biologists, L2 biology, 12 hours "équivalent TD"
Differential equations, first and second order, linear differential equation system in dimension 2, introduction to non-linear systems
2016 – 2017 RM1, Mathematical Reasoning, L1 mathematics, 18 hours "équivalent TD"
Basic mathematical logic and proof writing, basic set theory
MP4, Fundamental Algebra and Analysis II, L2 physics, 36 hours "équivalent TD"
Geometry of euclidean spaces, function series, integrals with parameters, Fourier series
Administrative responsibilities
Seminar organiser
I have organised the Peripatetic Seminar, University of Calgary's seminar on category theory, homotopy theory and logic, from May 2021 to August 2022. During this period, I organised 28 talks given by 27 guest researchers located in 8 countries.
I obtained a 2900 CAD PIMS seminar fund for the October 2021 to August 2022 period.
Member of the PhD students' Bureau
During my PhD, I was part of the PhD students' Bureau for the IMJ–PRG laboratory of Université de Paris. As such, I was representing the PhD students in their relations with the direction and administration of the lab.
I was given the rôle of PhD offices manager. As such, I was administrating the PhD students' offices space for the IMJ-PRG and LDRA lab (approx. 80 people) at Université de Paris, managing the offices keys, and welcoming new PhD students.