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Cihan Okay
Приєднався 27 чер 2020
BilTop | Aziz Kharoof | The category of bundle scenarios of simplicial complexes (part 1)
In this talk, we begin by introducing the sheaf-theoretic framework for contextuality. We then define the category of scenarios, based on this framework. The definition of morphisms between scenarios allows us to deal with simulation between empirical models. Next, we extend this framework to define the category of bundle scenarios. A bundle scenario is a map between simplicial complexes that satisfies specific properties, allowing it to behave analogously to a contextuality scenario. The transition from scenarios to bundle scenarios is facilitated by the nerve complex functor, which operates as a monad on simplicial complexes. Finally, we introduce the concept of an empirical model over a bundle scenario.
Переглядів: 34
Відео
BilTop | Aziz Kharoof | Homotopical characterization of strong contextuality (part 2)
Переглядів 28Місяць тому
For a simplicial scenario, the space of measurements and the space of outcomes are represented by simplicial sets, so one can ask what the role of the homotopy theory of simplicial sets is in the theory of simplicial distributions. In this talk, we will give a homotopical characterization of strongly contextual simplicial distributions with binary outcomes, specifically those defined in 1-dimen...
BilTop | Selman Ipek | Topological methods for studying contextuality and Bell inequalities
Переглядів 20Місяць тому
Going back to the seminal work of J.S. Bell [1], and later A. Fine [2] and M. Froissart [3], it is possible to study the separation between noncontextual and contextual measurement statistics using polyhedral geometry. From this geometric point of view a distribution is termed noncontextual if it lies within the convex hull of so-called deterministic distributions, and contextual otherwise. The...
BilTop | Aziz Kharoof | Homotopical characterization of strong contextuality
Переглядів 23Місяць тому
For a simplicial scenario, the space of measurements and the space of outcomes are represented by simplicial sets, so one can ask what the role of the homotopy theory of simplicial sets is in the theory of simplicial distributions. In this talk, we will give a homotopical characterization of strongly contextual simplicial distributions with binary outcomes, specifically those defined in 1-dimen...
BilTop | Selman Ipek | Simplicial distributions and polyhedral geometry
Переглядів 7Місяць тому
Simplicial distributions are collections of probability distributions that satisfy certain compatibility conditions that can be encoded topologically using simplicial sets. For a simplicial scenario where the measurement space X and outcome space Y are finitely generated the space sDist(X,Y) of allowed simplicial distributions is a convex set, in fact, a convex polytope. By the Minskowski-Weyl ...
BilTop | Aziz Kharoof | Gluing and extending simplicial distributions
Переглядів 19Місяць тому
In the theory of simplicial distributions, contextuality is determined by a natural map. As a result, any diagram of measurement spaces induces a diagram that can be used to compare contextuality. In this talk, we will focus on two cases: (1) an Inclusion map between measurement spaces and (2) a pushout square of measurement spaces. These two cases lead to the Extending Lemma and the Gluing Lem...
BilTop | Aziz Kharoof | The monoid of simplicial distributions
Переглядів 6Місяць тому
In this talk, we will discuss the monoid structure of simplicial distributions (when the outcome space is a simplicial group) and its applications. We give some important examples of subgroups and submonoids when the outcome space is the nerve of a finite cyclic group. We then show the importance of the action of deterministic distributions on the simplicial distributions to understand their ge...
BilTop | Aziz Kharoof | Simplicial distributions, convex categories, and contextuality
Переглядів 402 місяці тому
In a quantum mechanical experiment, the data describing outcome probabilities consists of a family of probability distributions indexed by subsets of jointly permissible measurements. The simplicial framework introduced in the first talk models this data as a morphism in the Kleisli category associated with the distribution monad. By studying certain properties of the distribution monad, we gai...
BilTop | Aziz Kharoof | The monoid of simplicial distributions
Переглядів 262 місяці тому
In this talk, we will discuss the monoid structure of simplicial distributions (when the outcome space is a simplicial group) and its applications. We give some important examples of subgroups and submonoids when the outcome space is the nerve of a finite cyclic group. We then show the importance of the action of deterministic distributions on the simplicial distributions to understand their ge...
BilTop | Cihan Okay | Introduction to simplicial distributions
Переглядів 552 місяці тому
Simplicial distributions [1] is a new approach to studying measurement statistics of experiments, mainly quantum, from a topological perspective. The topology that comes in is combinatorial in flavor and is based on the theory of simplicial sets. In this talk, I will introduce the basic notions of the theory and explain the origins connecting to earlier work on preserves of distributions by Abr...
BilTop | Redi Haderi | What is an infinity operad? (part 2)
Переглядів 403 місяці тому
We will discuss some of the details of the nerve construction which we presented in the previous talk. Then, we will explain how the category of simplicial lists has the structure of a presheaf category. We will also present a homotopy coherent nerve construction which, among other things, outputs a quasi-operad for all operads enriched in Kan complexes. This is joint work with Özgün Ünlü.
BilTop | Redi Haderi | What is an infinity operad? (part I)
Переглядів 803 місяці тому
We propose a combinatorial model for non-symmetric infinity operads. Our approach is simplicial, except that the simplicial objects we study take values in a category of sets in which morphisms assign lists of elements in the codomain to an element in the domain. We briefly discuss ordinary operads and their algebras in order to motivate our constructions. This is joint work with Özgün Ünlü.
BilTop | Ulrich Bauer | Connect the dots: from data through complexes to persistent homology
Переглядів 473 місяці тому
In this talk, I will survey some recent results on theoretical and computational aspects of applied topology. I will illustrate various aspects of persistent homology: its structure, which serves as a topological descriptor, its stability with respect to perturbations of the data, its computation on a large scale, and connections to Morse theory. These aspects will be motivated and illustrated ...
BilTop | Victor Torres Castillo | Quantum nonlocal games and the d-torsion commutative space
Переглядів 283 місяці тому
Nonlocal games have played a prominent role in quantum information theory by demonstrating the power of non-locality. In particular, the 'magic' examples due to Mermin and Peres belong to the class of linear system games. The Mermin-Peres games have no classical solutions, but they admit operator solutions. In this talk, we translate the problem of finding operator solutions into a problem of e...
BilTop | Philip Hackney | Partial groups and symmetric simplicial sets
Переглядів 133 місяці тому
Partial groups are a generalization of groups which allow for the possibility that some n-fold products of elements may be undefined. They were introduced by Chermak to serve in the study of the p-local structure of a finite group. These partial groups may be viewed as certain simplicial sets, or better yet, as certain symmetric simplicial sets. I'll explain this viewpoint, as well as some impl...
BilTop | Ozgun Unlu | Zigzag Persistence in Topological Data Analysis
Переглядів 593 місяці тому
BilTop | Ozgun Unlu | Zigzag Persistence in Topological Data Analysis
BilTop | Walker Stern | Limits and colimits in quasi-categories
Переглядів 513 місяці тому
BilTop | Walker Stern | Limits and colimits in quasi-categories
BilTop | Walker Stern | II: The infinity category of infinity categories
Переглядів 513 місяці тому
BilTop | Walker Stern | II: The infinity category of infinity categories
BilQC | Walker Stern | Higher quantum theory and 2-Hilbert spaces
Переглядів 1133 місяці тому
BilQC | Walker Stern | Higher quantum theory and 2-Hilbert spaces
BilQC | Redi Haderi | Bicategories and monoidal bicategories
Переглядів 253 місяці тому
BilQC | Redi Haderi | Bicategories and monoidal bicategories
BilQC | Selman Ipek | Complete positivity
Переглядів 153 місяці тому
BilQC | Selman Ipek | Complete positivity
BilQC | Selman Ipek | Applications of Categorical Quantum Mechanics: ZX calculus
Переглядів 833 місяці тому
BilQC | Selman Ipek | Applications of Categorical Quantum Mechanics: ZX calculus
BilQC | Selman Ipek | Categorical treatment of the Deutsch-Jozsa algorithm
Переглядів 683 місяці тому
BilQC | Selman Ipek | Categorical treatment of the Deutsch-Jozsa algorithm
BilQC | Victor Torres Castillo | Frobenius algebras and complementarity
Переглядів 813 місяці тому
BilQC | Victor Torres Castillo | Frobenius algebras and complementarity
BilQC | Redi Haderi | No-cloning theorem in categorical quantum mechanics
Переглядів 763 місяці тому
BilQC | Redi Haderi | No-cloning theorem in categorical quantum mechanics
BilQC | Selman Ipek | Categorical quantum mechanics
Переглядів 953 місяці тому
BilQC | Selman Ipek | Categorical quantum mechanics
BilTop | Kadri İlker Berktav | Homotopy theory of stacks and higher structures
Переглядів 28610 місяців тому
BilTop | Kadri İlker Berktav | Homotopy theory of stacks and higher structures
BilTop | Walker Stern | First constructions
Переглядів 9110 місяців тому
BilTop | Walker Stern | First constructions
BilQC | Walker Stern | Symmetric Monoidal Categories (III)
Переглядів 21310 місяців тому
BilQC | Walker Stern | Symmetric Monoidal Categories (III)
BilQC | Redi Haderi | Symmetric Monoidal Categories (II)
Переглядів 7110 місяців тому
BilQC | Redi Haderi | Symmetric Monoidal Categories (II)
merhaba ben yıldırım beyazıt üniversitesinde matematik öğrencisiyim ve redi hocamız şuanda benim danışman hocam olarak gözüküyor ve ders kaydımla alakalı bir sıkıntı yaşıyorum ama kendisine bir türlü ulaşamıyorum siz kendisini tanıyorsanız bana yardımcı olma şansınız var mı acaba?