Related papers: $\infty$-Categorical Generalized Langlands Corresp…
A new definition for the notion of a (general) $\infty$-category is given.
We discuss generalizations of the Langlands program, from reductive groups to the local and automorphic spectra of spherical varieties, and to more general representations arising as "quantizations" of suitable Hamiltonian spaces. To a…
Recent work has generalized the Furstenberg correspondence between sets of integers and dynamical systems to versions which involve sequences of finite graphs or sequences of $L^\infty$ functions. We give a unified version of the theorem…
In this Note, we propose a line bundle approach to odd-dimensional analogues of generalized complex structures. This new approach has three main advantages: (1) it encompasses all existing ones; (2) it elucidates the geometric meaning of…
A growing body of research on probabilistic programs and causal models has highlighted the need to reason compositionally about model classes that extend directed graphical models. Both probabilistic programs and causal models define a…
We consider a fractional generalization of gradient systems. We use differential forms and exterior derivatives of fractional orders. Examples of fractional gradient systems are considered. We describe the stationary states of these…
We propose an extension of the classical dichotomous categorization of research programmes into progress and degeneration according to Lakatos in the form of a neutral third category: the stagnant research programme. First, a critical…
In this work, we establish a categorification of the classical Dold-Kan correspondence in the form of an equivalence between suitably defined $\infty$-categories of simplicial stable $\infty$-categories and connective chain complexes of…
This Dissertation collects my results on the interpretation, characterization, quantification and application of bipartite and multipartite entanglement in Gaussian states of continuous variable systems.
We provide a motivated introduction to the theory of categorical actions of groups and the local geometric Langlands program. Along the way we emphasize applications, old and new, to the usual representation theory of reductive and affine…
This is a draft version of an invited article for a forthcoming book `The genesis of Langlands Program', eds. Julia Mueller and Freydoon Shahidi, which will be published by Cambridge University Press. This is a survey of Langlands spectral…
The ramification method in Implicit Computational Complexity has been associated with functional programming, but adapting it to generic imperative programming is highly desirable, given the wider algorithmic applicability of imperative…
Given a thick subcategory of a triangulated category, we define a colocalisation and a natural long exact sequence that involves the original category and its localisation and colocalisation at the subcategory. Similarly, we construct a…
Based on previous work we consturct an equation (Lagrange equation) and relate it with a system of generalized integrals and differential equations in such a way to provide useful evaluations and connections between them.
Categorical random variables are a common staple in machine learning methods and other applications across disciplines. Many times, correlation within categorical predictors exists, and has been noted to have an effect on various algorithm…
We establish the Geometric Langlands correspondence for rank one groups over the projective line with three points of tame ramification.
We introduce a new concept of s-recollements of extriangulated categories, which generalizes recollements of abelian categories, recollements of triangulated categories, as well as recollements of extriangulated categories. Moreover, some…
Stacked generalization is a general method of using a high-level model to combine lower-level models to achieve greater predictive accuracy. In this paper we address two crucial issues which have been considered to be a `black art' in…
An algebraic formalism for the study of interacting particle systems is developed. Particle processes are described in terms of the category theory. The problem for the unique description of these processes is discussed. Categories relevant…
pystacked implements stacked generalization (Wolpert, 1992) for regression and binary classification via Python's scikit-learn. Stacking combines multiple supervised machine learners -- the "base" or "level-0" learners -- into a single…