Related papers: An introduction to the categorical p-adic Langland…
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…
We discuss further around the generalized Langlands Program, by using $\infty$-categoricalization and $\infty$-analytic stackification.
The objective of this article is to give an introduction to p-adic analysis along the lines of Tate's thesis, as well as incorporating material of a more recent vintage, for example Weil groups.
These notes give a statement of the "fundamental lemma," which is a conjectural identity between p-adic integrals that arises as part of the Langlands program.
The article provides an introduction to infinite-dimensional differential calculus over topological fields and surveys some of its applications, notably in the areas of infinite-dimensional Lie groups and dynamical systems.
A survey of real differential geometry and loop theory is given in order to introduce the construction of an analytic loop associated to p-adic differential manifold.
We propose a p-adic Langlands correspondence in families.
This work is intended as an introduction to the statement and the construction of the local Langlands correspondence for GL(n) over p-adic fields. The emphasis lies on the statement and the explanation of the correspondence.
In this short survey we look at a few basic features of p-adic numbers, somewhat with the point of view of a classical analyst. In particular, with p-adic numbers one has arithmetic operations and a norm, just as for real or complex…
We present a denotational semantics for higher-order probabilistic programs in terms of linear operators between Banach spaces. Our semantics is rooted in the classical theory of Banach spaces and their tensor products, but bears…
These are the notes for an eponymous course given by the authors at the summer school on p-adic arithmetic geometry in Hangzhou.
An explicit understanding of the (category of all smooth, complex) representations of p-adic groups provides an important tool not just within representation theory. It also has applications to number theory and other areas, and, in…
The category of Banach Lie-Poisson spaces is introduced and studied. It is shown that the category of W*-algebras can be considered as one of its subcategories. Examples and applications of Banach Lie-Poisson spaces to quantization and…
In these lecture notes, we give a brief introduction to some elements of category theory. The choice of topics is guided by applications to functional programming. Firstly, we study initial algebras, which provide a mathematical…
We formalise a notion of $p$-adic Langlands functoriality for the definite unitary group. This extends the classical notion of Langlands functoriality to the setting of eigenvarieties. We apply some results of Chenevier to obtain some cases…
We explain how the geometric Langlands program inspires some recent new prospectives of classical arithmetic Langlands program and leads to the solutions of some problems in arithmetic geometry.
We show how categorial deduction can be implemented in higher-order (linear) logic programming, thereby realising parsing as deduction for the associative and non-associative Lambek calculi. This provides a method of solution to the parsing…
This book is a graduate-level introduction to probabilistic programming. It not only provides a thorough background for anyone wishing to use a probabilistic programming system, but also introduces the techniques needed to design and build…
In this paper, we introduce a new class of subsets of bounded linear operators between Banach spaces which is p-version of the uniformly completely continuous sets. Then, we study the relationship between these sets with the equicompact…
We present a new construction of the p-adic local Langlands correspondence for GL(2, Q_p) via the patching method of Taylor--Wiles and Kisin. This construction sheds light on the relationship between the various other approaches to both the…