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 :


arXiv preprint: https://arxiv.org/abs/2108.04304


arXiv preprint: https://arxiv.org/abs/2011.13002


arXiv preprint:  https://arxiv.org/abs/2104.11736


https://www.intlpress.com/site/pub/pages/journals/items/hha/content/vols/0023/0001/a008/index.php


https://www.cambridge.org/core/journals/glasgow-mathematical-journal/article/abs/divided-power-algebras-over-an-operad/472B6148327ECEBDB434652099FF93A3

arXiv preprint: https://arxiv.org/abs/1712.03694


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.