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Geometry, Analysis and Probability

Part of the Progress in Mathematics Book Series (volume 310)

Editors: Bost, Jean-Benoît; Hofer, Helmut; Labourie, François; Le Jan, Yves; Ma, Xiaonan; Zhang, Weiping

DOI: 10.1007/978-3-319-49638-2

ISBN: 978-3-319-49636-8

Publisher: Springer International Publishing - Springer Journals

Apr 27, 2017

1 - 10 of 13 Chapters

LitStream

Chapter 1Geometric Higher Groupoids and Categories

Behrend, Kai; Getzler, Ezra

Pages: 1 –45

[In an enriched setting, we show that higher groupoids and higher categories form categories of fibrant objects, and that the nerve of a differential graded algebra is a higher category in the category of algebraic varieties.]
LitStream

Chapter 2Hodge Type Theorems for Arithmetic Hyperbolic Manifolds

Bergeron, Nicolas; Millson, John; Moeglin, Colette

Pages: 47 –56

[This note is a variation on the lecture given by the first named author at the conference celebrating the work (and sixty-fifth anniversary) of Jean-Michel Bismut. In this lecture a proof of some new cases of the Hodge conjecture for Shimura varieties uniformized by complex balls was sketched...
LitStream

Chapter 3The Ding Functional, Berndtsson Convexity and Moment Maps

Donaldson, S. K.

Pages: 57 –67

[The paper discusses the formal structure of the Kähler–Einstein equations over Fano manifolds, introducing a “moment map” interpretation. The key is a result of Berndtsson, which leads to a metric on the space of almost-complex structures. An application to the Kähler–Ricci flow is given.]
LitStream

Chapter 4Dimers and Curvature Formulae

Dubédat, Julien

Pages: 69 –87

[In this expository note, we discuss different formalisms for determinants of families of elliptic operators (in the continuum) and finite-difference operators (in a discrete setting), how they relate, and consequences for the asymptotic analysis of some combinatorial models in 2d statistical...
LitStream

Chapter 5The Norm of the Weierstrass Section

Faltings, Gerd

Pages: 89 –98

[In diophantine geometry over function fields, Weierstrass divisors are an important tool. Trying to make this tool available over numberfields we prove estimates for the archimedean and p-adic norms of the sections which define them.]
LitStream

Chapter 6Higher Analytic Torsion, Polylogarithms and Norm Compatible Elements on Abelian Schemes

Kings, Guido; Rössler, Damian

Pages: 99 –126

[We give a simple axiomatic description of the degree 0 part of the polylogarithm on abelian schemes and show that its realisation in analytic Deligne cohomology can be described in terms of the Bismut–Köhler higher analytic torsion form of the Poincaré bundle.]
LitStream

Chapter 7Teichmüller Theory for Conic Surfaces

Mazzeo, Rafe; Weiss, Hartmut

Pages: 127 –164

[This paper develops the local deformation theory, and some aspects of the global Teichmüller theory, of constant curvature metrics on a surface Σ with a finite number of conic singularities, with all cone angles less than 2π. We approach this using techniques of geometric analysis and the theory...
LitStream

Chapter 8On the Analytic Torsion of Hyperbolic Manifolds of Finite Volume

Müller, Werner

Pages: 165 –189

[In this paper we study the analytic torsion for a complete oriented hyperbolic manifold of finite volume. This requires the definition of a regularized trace of heat operators. We use the Selberg trace formula to study the asymptotic behavior of the regularized trace for small time. The main...
LitStream

Chapter 9Log-correlated Gaussian Fields: An Overview

Duplantier, Bertrand; Rhodes, Rémi; Sheffield, Scott; Vargas, Vincent

Pages: 191 –216

[We survey the properties of the log-correlated Gaussian field (LGF), which is a centered Gaussian random distribution (generalized function) h on ℝd, defined up to a global additive constant.]
LitStream

Chapter 10A Variation Formula for the Determinant Line Bundle. Compact Subspaces of Moduli Spaces of Stable Bundles over Class VII Surfaces

Teleman, Andrei

Pages: 217 –243

[This article deals with two topics: the first, which has a general character, is a variation formula for the determinant line bundle in non-Kählerian geometry. This formula, which is a consequence of the non-Kählerian version of the Grothendieck–Riemann–Roch theorem proved recently by Bismut...

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