# Current Projects

## AlgoFormI (P.I.) - 2023-2024

AlgoFormI stands for "Algorithms: a formalisation and its impact". Is was funded by the Mission for Transversal and Interdisciplinary Initiatives (MITI) of CNRS, as part of the "Aide à la décision" call. It involves both LIPN and IHPST. Conjointly with the FormA project (below), AlgoFormI aims at studying the proposed formal definition of algorithms, but AlgoFormI focusses on how this definition can impact and be impacted by how the notion of algorithm is understood in social sciences. Most of the funding will be used to organise monthly seminars around the use and impact of the notion of algorithm in different fields.

## FormA (P.I.) - 2023

FormA is a one-year collaborative "emergence" project funded by INS2I. Both LIPN and IHPST are involved in the project. The full title is "Formalising the concept of algorithms", and the project aims at studying a proposed formal definition of algorithms, from both an epistemological and a computer science perspective. Funding covers a six month internship, as well as some events to be organised conjointly with the MITI project "AlgoFormI".

## DySCo (P.I.) - 2022-2027

I am leading the ANR JCJC project DySCo (Dynamical Systems and Computation: a logical approach), which was allocated 258k€ for five years -- starting on December 1st 2022.

DySCo will build on the theory of Interaction Graphs I introduced to revisit the foundations for computer science using the mathematics of dynamical systems. Indeed, earlier work shows how graphings – a generalisation of dynamical systems – provide an expressive and powerful mathematical model of computer programs. DySCo will draw out satisfying definitions for the notions of computation, programs and algorithms in a way that will be both general enough to encompass various models of computation and precise enough to provide algorithmically complete models. These theoretical foundations will allow the expansion of the relationship between logic and computation, enabling the Curry-Howard toolbox beyond its current limits. They will also allow the transfer of tools and methods from the mathematical theory of dynamical systems to be used in computer science, notably for proving lower bounds results in computational complexity.

## LambdaComb (Participant) - 2022-2026

I am part of the ANR project LambdaComb (Une expédition cartographique entre le lambda-calcul, la logique, et la combinatoire), lead by Noam Zeilberger (LIX, École Polytechnique).

A link to a dedicated webpage will be provided in due time.

## GoA (Participant) - 2021-2025

I am part of the ANR project GoA (Geometry of Algorithms), lead by Alberto Naibo (IHPST, University Paris 1).

Here is a short description: GoA page @ IHPST. A link to a dedicated webpage will be provided in due time.

## CoHOp (P.I.) - 2020-2021

CoHOp stands for "Complexity, Homology, and Operads". The project is funded by the Île-de-France region, through the DIM RFSI.
Other participants: Maxime Lucas, Damiano Mazza, Samuel Mimram.

A recent work of Pellissier and Seiller exposed a proof method for lower bounds in complexity relying on bounds on both the topological entropy of dynamical systems and the Betti numbers of algebraic varieties. Not only this result improves one of the strongest known lower bound result, it establishes that several strong lower bound results rely on (co)homological invariants.

The CoHoP project aims at developing further this invariant method, through the use of more involved methods from algebraic topology.

A recent work of Pellissier and Seiller exposed a proof method for lower bounds in complexity relying on bounds on both the topological entropy of dynamical systems and the Betti numbers of algebraic varieties. Not only this result improves one of the strongest known lower bound result, it establishes that several strong lower bound results rely on (co)homological invariants.

The CoHoP project aims at developing further this invariant method, through the use of more involved methods from algebraic topology.

## StATyC (co-P.I.) - 2020-2022

StATyC stands for "Static Analyses of Program Flows: Types and Certificate for Complexity". This is a two-year international collaborative project funded by the Thomas Jefferson Fund, from the FACE Foundation, and involving the School of Computer Science of the University of Augusta.

The project aims at providing new static analysis tools based on theoretical results from Implicit computational complexity, building on previous work of Moyen, Rubiano and Seiller (doi:10.1007/978-3-319-68167-2_7).

Co-P.I.: Clément Aubert.

The project aims at providing new static analysis tools based on theoretical results from Implicit computational complexity, building on previous work of Moyen, Rubiano and Seiller (doi:10.1007/978-3-319-68167-2_7).

Co-P.I.: Clément Aubert.

## TrAVAIL (co-P.I.) - 2020-2021

TrAVAIL stands for "Transversal Approaches of Verification, Abstract Interpretation, and Logic". This is a one-year international collaborative project funded by CNRS and involving DIKU, the Computer Science Department of the University of Copenhagen, and the Department of Computer Science of Aarhus University.

## CoGITARe (Participant) - 2019-2023

I am part of the ANR JCJC project CoGITARe (Combining Graded and Intersection Types for the Analyses of Resources), lead by Flavien Breuvart. If you want to know more about this project, there is a dedicated Website.

# Past Projects

2019, LoBE (P.I.) -- "Lower Bounds and Entropy". One-year "emerging" PEPS project (exploratory projects) funded by CNRS's computer science institute INS2I

2018, BIGRe (P.I.) -- "Bornes Inférieures Géométriques par Réalisabilité", aka "Geometric Lower Bounds through Realisability". One-year young investigator project funded by CNRS's computer science institute INS2I

2015-2017, ReACT (P.I.) -- a Realisability Approach to Complexity Theory, H2020-MSCA-IF-2014, 2015--2018,

webpage

webpage

2010-2011, "Vérité et Preuves" (P.I.), national network of PhD students.

webpage (in french)

webpage (in french)