~~NOCACHE~~ /* DO NOT EDIT THIS FILE */ [[seminaires:doctorants:index|Séminaire des membres non-permanents]]\\ Jeudi 22 mai 2025, 16 heures, Salle 3052\\ **Ricardo Canesin** (IMJ-PRG) //Quiver Representations: Linear Algebra on Steroids// \\ Quivers and their representations offer a natural language for formulating and solving various matrix problems. In this talk, we will start with an elementary approach to the subject and proceed through the lens of the representation theory of associative algebras. We then present Gabriel’s celebrated theorem, which classifies quivers with only finitely many indecomposable representations. Finally, we discuss how the theory developed by Auslander and Reiten provides a method for constructing (many of) the indecomposable representations. The talk will be accessible and requires only a background in linear algebra. [[seminaires:doctorants:index|Séminaire des membres non-permanents]]\\ Jeudi 15 mai 2025, 16 heures, Salle 3052\\ **Lucas Pouillart** //Coxeter systems or the story of combinatorics on words in reflection groups// \\ Reflection groups have been studied for a really long time for their geometry and combinatorics as automorphism groups of regular polyhedrons and have not ceased to appear in many areas of mathematics and computer science such as representation theory, graph theory ever since. In this talk we will try to explain the general structure of a reflection group by looking at their word problem." [[seminaires:doctorants:index|Séminaire des membres non-permanents]]\\ Jeudi 10 avril 2025, 16 heures, Salle 3052\\ **Vincent Moreau** //Introducing the Yoneda lemma through examples// \\ Mathematical structures are usually presented in a set-theoretic way, where the notion of element plays a central role. A tenet at the heart of category theory, however, is that structures of a common kind can alternatively be understood by studying the morphisms between them, without reference to concrete elements. In this presentation, we give a basic introduction to categories and show how to reconcile these two viewpoints. We find it instructive to focus on the categories of sets, graphs and metric spaces. In each case, we explain how to recover elements as morphisms from certain canonical objects, and show that these objects are dense in the categorical sense. These three case studies naturally lead us to the general form of the Yoneda lemma, which states that elements are generalized elements, and to the density of representables. This talk requires no knowledge of category theory. [[seminaires:doctorants:index|Séminaire des membres non-permanents]]\\ Jeudi 27 mars 2025, 16 heures, Salle 3052\\ **Maria Clara Werneck** //From political representation fairness to symbolic dynamical systems// \\ In many countries, the union is divided into states, and the number of deputies in the federal congress depends on the state. Imagine that each year, a congressperson is elected to be the chair of the congress. The challenge is to assign this role in such a way that, at any given time, the accumulated number of chairpersons from each state remains proportional to its assigned weight. This is known as the chairperson assignment problem. In this talk, we will introduce a metric for quantifying fairness in this context and explain its connection to symbolic dynamics. This presentation will also be an introduction to symbolic dynamical systems. [[seminaires:doctorants:index|Séminaire des membres non-permanents]]\\ Jeudi 20 mars 2025, 16 heures, Salle 3052\\ **Roman Edenhofer** //Quantum speedup: A crash course on Grover's algorithm// \\ Building on last week’s talk by Benjamin, we dive into one of the most famous quantum algorithms: Grover’s search. While classical computers need to check items one by one, Grover’s algorithm finds a marked element in an unsorted list of size N in just O(\sqrt(n)) steps - a quadratic speedup that showcases the power of quantum computing. In this talk, we’ll break down the intuition behind Grover’s algorithm, and discuss why its impact extends beyond simple search problems. If you enjoyed Benjamin’s talk or just want a hands-on introduction to quantum search, this is for you! No prior quantum expertise required - just bring your curiosity. [[seminaires:doctorants:index|Séminaire des membres non-permanents]]\\ Jeudi 13 mars 2025, 16 heures, Salle 3052\\ **Benjamin Mathieu-Bloise** //Introduction to Quantum Computing: Key examples as a preparation for the very next talk on Grover's algorithm// \\ Quantum computing represents a paradigm shift in computational theory, its most compelling known application being Peter Shor's factorization algorithm. This talk will introduce the core concepts of quantum computing, with an emphasis on the quantum circuit model. We will observe the most common or well-known methods or algorithms that have a quantum advantage or a special feature, among others the Deutsch-Josza algorithm or quantum teleportation. We will also discuss gate and query complexity. This talk is meant to prepare for Roman's next week's talk, which will focus on one of the most typical quantum algorithms, yet not the most difficult to understand. [[seminaires:doctorants:index|Séminaire des membres non-permanents]]\\ Jeudi 6 mars 2025, 16 heures, Salle 3052\\ **Joshua Wrigley** //Existentially closed models and zero-dimensionality// \\ Algebraically closed fields are those fields that already contain the roots obtained in any field extension. Existentially closed models are the generalisation to an arbitrary first-order theory: any homomorphism from an existentially closed model reflects satisfaction. In general, existentially closed models cannot be axiomatised in finitary logic, but they can be axiomatised in infinitary logic. This axiomatisation resembles a "zero-dimensional-isation" of the theory. This talk will make precise the connection between zero-dimensionality and existentially closed models. We will also discuss how this connection ruptures when considering existentially closed models of infinitary theories. [[seminaires:doctorants:index|Séminaire des membres non-permanents]]\\ Jeudi 20 février 2025, 16 heures, Salle 3052\\ **Miriam Marzaioli** //A Crèche Introduction to Cohen's Forcing// \\ In 1963, Paul Cohen discovered the forcing method and definitively answered the first of Hilbert's 23 problems by using this technique to prove the independence of the Continuum Hypothesis from the ZFC axioms. Since then, forcing has become the primary tool in set theory for establishing independence and consistency results. In this talk, we will present the key ingredients and ideas necessary to understand Cohen's model of ZFC + ¬CH. In particular, we will explore Cohen's forcing via the boolean-valued models approach. [[seminaires:doctorants:index|Séminaire des membres non-permanents]]\\ Jeudi 13 février 2025, 16 heures, Salle 3052\\ **Adrienne Lancelot** //Non Permanent General Assembly// \\ The aim of this assembly is to gather your thoughts, (dis)likes and fears about office space at IRIF. The direction of the lab is currently indicating that we will soon struggle with too many recruitments and not enough desks. This will surely impact non permanents (recruitments are mostly Post Docs and PhD students). I will take part in the discussions about how to deal with this issue, and while I already have some opinions, I would like to hear yours and make them known. As an example of possible discussion, if we were to have more non permanents per office, it would likely be critical to offer specific rooms for video calls. [[seminaires:doctorants:index|Séminaire des membres non-permanents]]\\ Jeudi 6 février 2025, 16 heures, Salle 3052\\ **Emile Larroque** //How to draw quantum processes using categories ? An introduction to ZX-calculus// \\ Linear algebra is the usual mathematical framework in which finite-state quantum processes (such as quantum algorithms) are described. But it fails to make clearly appear the flow of information. That is why an ad-hoc circuit representation is usually used when reasoning on quantum algorithms, in addition of linear algebra. The field of categorical quantum informatics is developing much more powerful graphical languages that enable not only to represent quantum processes with diagrams but also to make algebraic manipulations directly on the diagrams - namely, making proofs with drawings. This diagrammatic reasoning completely hides the matrices, letting us develop a graphical and intuitive understanding of the flow of information. ZX-calculus is one of those graphical languages. This talk is an introduction to ZX-calculus, for people with no background in neither quantum physics nor quantum computing nor category theory. [[seminaires:doctorants:index|Séminaire des membres non-permanents]]\\ Jeudi 30 janvier 2025, 16 heures, Salle 3052\\ **Manu Catz** //Number Systems and Oriented Shapes// \\ Decimal writing is just one way of notating the natural numbers, but we can as well consider the "first" ways of doing so: unary writing (the tally system), binary writing (the language of classical computers) or even ternary writing (examples welcomed!). Unary gives a natural labelling on the family of simplices (the family to which belongs the triangle, the tetrahedron,...) and furthermore a way of orienting any dimensional face of such shapes. Likewise, binary is the natural choice to label and orient the family of cubes (the square, the cube,...). In this talk I will show these constructions, as well as how this particular labelling allows us to easily construct simplices from cubes and cubes from simplices. Lastly, I will address the elephant in the room: what gets labelled and oriented by ternary ?! There are no prerequisites for the content of this talk more than a basic understanding of binary, however these ideas come from higher category theory and type theory, in particular work by Street and Aitchison on the oriented simplices and cubes respectively, as well as work by Ara, Lafont and Métayer to better uncover these constructions, and the notion of parametricity as presented by Herbelin and Ramachandra. [[seminaires:doctorants:index|Séminaire des membres non-permanents]]\\ Jeudi 16 janvier 2025, 16 heures, Salle 3052\\ **Umberto Tarantino** //A gentle introduction to categorical realizability// \\ Realizability was devised by Kleene in 1945 in order to apply the theory of recursive functions to the study of constructive arithmetic: this originated a discipline which sits at the intersection between mathematical logic, computability theory and category theory. In this talk, I will first introduce realizability in its original formulation; then, I will sketch how toposes provide alternative universes in which to do mathematics, and I will present the effective topos, where realizability coincides with the logic of natural numbers. By analysing the effective topos, I will show some examples of how reasoning constructively can lead to sometimes unexpected results, challenging the usual assumptions about our standard universe of sets and functions. No particular background is needed.