Related papers: Topological modular and automorphic forms
This thesis studies modular forms from a classical and adelic viewpoint. We use this interplay to obtain results about the arithmetic of the Fourier coefficients of modular forms and their generalisations. In Chapter 2, we compute lower…
We determine the image of the 2-primary tmf-Hurewicz homomorphism, where tmf is the spectrum of topological modular forms. We do this by lifting elements of tmf_* to the homotopy groups of the generalized Moore spectrum M(8,v_1^8) using a…
Recent work on homotopy type theory exploits an exciting new correspondence between Martin-Lof's dependent type theory and the mathematical disciplines of category theory and homotopy theory. The category theory and homotopy theory suggest…
In this paper, we generalize the fundamental theorems of functional analysis to the framework of bicomplex topological modules.
A brief introduction to universal algebra and the theory of topological algebras, their varieties, and free topological algebras is presented. Free topological Mal'tsev algebras are studied. Their properties, relationship with topological…
The deformation of a topological field theory, namely the pure BF theory, gives the first order formulation of Yang-Mills theory; Feynman rules are given and the standard uv-behaviour is recovered. In this formulation new non local…
We develop a theory of \emph{Katetov functors} which provide a uniform way of constructing Fraisse limits. Among applications, we present short proofs and improvements of several recent results on the structure of the group of automorphisms…
In these lectures we discuss some basic aspects of Hamiltonian formalism, which usually do not appear in standard texbooks on classical mechanics for physicists. We pay special attention to the procedure of Hamiltonian reduction…
By introducing various topologies on the homotopy groups of a topological space, some researchers make these well known notions in algebraic topology more useful and powerful. In this paper, first we recall and review some known topologies…
In this short note we provide a review of some developments in the area of homotopy quantum field theories, loosely based on a talk given by the second author at the Xth Oporto Meeting on Geometry, Topology and Physics.
This paper is a survey on the homotopy theory of $E_n$-operads written for the new handbook of homotopy theory.
A reflective subuniverse in homotopy type theory is an internal version of the notion of a localization in topology or in the theory of $\infty$-categories. Working in homotopy type theory, we give new characterizations of the following…
This work serves as an opening and basis of an ongoing program investigating topological and geometric aspects of the moduli space of smooth fiberings on a manifold. The present paper focuses on the algebraic and differential topology of…
This article investigates the homotopy theory of simplicial commutative algebras with a view to homological applications.
We exhibit an internal coproduct on the Hopf algebra of finite topologies recently defined by the second author, C. Malvenuto and F. Patras, dual to the composition of "quasi-ormoulds", which are the natural version of J. Ecalle's moulds in…
It has been observed that certain localizations of the spectrum of topological modular forms are self-dual (Mahowald-Rezk, Gross-Hopkins). We provide an integral explanation of these results that is internal to the geometry of the…
The first part of this dissertation defines "dependently typed algebraic theories", which are a strict subclass of the generalised algebraic theories (GATs) of Cartmell. We characterise dependently typed algebraic theories as finitary…
The aim of this paper is to introduce the concepts of homotopical smallness and closeness. These are the properties of homotopical classes of maps that are related to recent developments in homotopy theory and to the construction of…
We prove the Sato-Tate conjecture for Hilbert modular forms. More precisely, we prove the natural generalisation of the Sato-Tate conjecture for regular algebraic cuspidal automorphic representations of $\GL_2(\A_F)$, $F$ a totally real…
We obtain restrictions on the rational homotopy types of mapping spaces and of classifying spaces of homotopy automorphisms by means of the theory of positive weight decompositions. The theory applies, in particular, to connected components…