样式: 排序: IF: - GO 导出 标记为已读
-
On the Connes–Kasparov isomorphism, II Jpn. J. Math. (IF 1.5) Pub Date : 2024-04-01
Abstract This is the second of two papers dedicated to the computation of the reduced C*-algebra of a connected, linear, real reductive group up to C*-algebraic Morita equivalence, and the verification of the Connes–Kasparov conjecture in operator K-theory for these groups. In Part I we presented the Morita equivalence and the Connes–Kasparov morphism. In this part we shall compute the morphism using
-
On the Connes–Kasparov isomorphism, I Jpn. J. Math. (IF 1.5) Pub Date : 2024-02-09 Pierre Clare, Nigel Higson, Yanli Song, Xiang Tang
This is the first of two papers dedicated to the detailed determination of the reduced C*-algebra of a connected, linear, real reductive group up to Morita equivalence, and a new and very explicit proof of the Connes–Kasparov conjecture for these groups using representation theory. In this part we shall give details of the C*-algebraic Morita equivalence and then explain how the Connes–Kasparov morphism
-
The Whittaker Plancherel theorem Jpn. J. Math. (IF 1.5) Pub Date : 2024-02-09
Abstract The purpose of this article is to give an exposition of a proof of the distributional form of the Whittaker Plancherel Theorem. The proof is an application of Harish-Chandra’s Plancherel Theorem for real reductive groups and its exposition can be used as an introduction to Harish-Chandra’s Plancherel Theorem. The paper follows the basic method in the author’s original approach in his second
-
Old and new challenges in Hadamard spaces Jpn. J. Math. (IF 1.5) Pub Date : 2023-09-06 Miroslav Bačák
Hadamard spaces have traditionally played important roles in geometry and geometric group theory. More recently, they have additionally turned out to be a suitable framework for convex analysis, optimization and non-linear probability theory. The attractiveness of these emerging subject fields stems, inter alia, from the fact that some of the new results have already found their applications both in
-
Orbifolds of lattice vertex algebras Jpn. J. Math. (IF 1.5) Pub Date : 2023-06-14 Bojko Bakalov, Jason Elsinger, Victor G. Kac, Ivan Todorov
To a positive-definite even lattice Q, one can associate the lattice vertex algebra VQ, and any automorphism σ of Q lifts to an automorphism of VQ. In this paper, we investigate the orbifold vertex algebra V σQ , which consists of the elements of VQ fixed under σ, in the case when σ has prime order. We describe explicitly the irreducible V σQ -modules, compute their characters, and determine the modular
-
Three examples of residual pathologies Jpn. J. Math. (IF 1.5) Pub Date : 2023-04-03 Marina Ghisi, Massimo Gobbino
Several counterexamples in analysis show the existence of some special object with some sort of pathological behavior. We present three different examples where the pathological behavior is not an isolated exception, but it is the “typical” behavior of the “generic” object in a suitable class, where here generic means residual in the sense of Baire category. The first example is the revisitation of
-
The structure of metahamiltonian groups Jpn. J. Math. (IF 1.5) Pub Date : 2023-01-26 Mattia Brescia, Maria Ferrara, Marco Trombetti
A group is called metahamiltonian if all its non-abelian subgroups are normal. The aim of this paper is to provide an exhaustive but self-contained reference to the structure of metahamiltonian groups fixing several relevant mistakes appearing in the literature.
-
The lattice of varieties of monoids Jpn. J. Math. (IF 1.5) Pub Date : 2022-10-21 Sergey V. Gusev, Edmond W. H. Lee, Boris M. Vernikov
We survey results devoted to the lattice of varieties of monoids. Along with known results, some unpublished results are given with proofs. A number of open questions and problems are also formulated.
-
K-theory and G-theory of derived algebraic stacks Jpn. J. Math. (IF 1.5) Pub Date : 2022-01-17 Adeel A. Khan
These are some notes on the basic properties of algebraic K-theory and G-theory of derived algebraic spaces and stacks, and the theory of fundamental classes in this setting.
-
On Lax operators Jpn. J. Math. (IF 1.5) Pub Date : 2021-12-10 Alberto De Sole, Victor G. Kac, Daniele Valeri
We define a Lax operator as a monic pseudodifferential operator L(∂) of order N ≥ 1, such that the Lax equations \(\frac{\partial L(\partial)}{\partial t_k}=[(L^\frac{k}{N}(\partial))_+,L(\partial)]\) are consistent and non-zero for infinitely many positive integers k. Consistency of an equation means that its flow is defined by an evolutionary vector field. In the present paper we demonstrate that
-
Grothendieck spaces: the landscape and perspectives Jpn. J. Math. (IF 1.5) Pub Date : 2021-09-22 Manuel González, Tomasz Kania
In 1973, Diestel published his seminal paper Grothendieck spaces and vector measures that drew a connection between Grothendieck spaces (Banach spaces for which weak- and weak*-sequential convergences in the dual space coincide) and vector measures. This connection was developed further in his book with J. Uhl Jr. Vector measures. Additionally, Diestel’s paper included a section with several open problems
-
Classical and variational Poisson cohomology Jpn. J. Math. (IF 1.5) Pub Date : 2021-08-09 Bojko Bakalov, Alberto De Sole, Reimundo Heluani, Victor G. Kac, Veronica Vignoli
We prove that, for a Poisson vertex algebra \({\cal V}\), the canonical injective homomorphism of the variational cohomology of \({\cal V}\) to its classical cohomology is an isomorphism, provided that \({\cal V}\), viewed as a differential algebra, is an algebra of differential polynomials in finitely many differential variables. This theorem is one of the key ingredients in the computation of vertex
-
Borsuk’s partition conjecture Jpn. J. Math. (IF 1.5) Pub Date : 2021-07-21 Chuanming Zong
In 1933, Borsuk proposed the following problem: Can every bounded set in \({{\mathbb{E}}^n}\) be divided into n + 1 subsets of smaller diameter? This problem has been studied by many authors, and a lot of partial results have been discovered. In particular, Kahn and Kalai’s counterexamples surprised the mathematical community in 1993. Nevertheless, the problem is still far away from being completely
-
Topological-antitopological fusion and the quantum cohomology of Grassmannians Jpn. J. Math. (IF 1.5) Pub Date : 2021-01-08 Martin A. Guest
We suggest an explanation for the part of the Satake Correspondence which relates the quantum cohomology of complex Grassmannians and the quantum cohomology of complex projective space, as well as their respective Stokes data, based on the original physics approach using the tt* equations. We also use the Stokes data of the tt* equations to provide a Lie-theoretic link between particles in affine Toda
-
Infinite-dimensional (dg) Lie algebras and factorization algebras in algebraic geometry Jpn. J. Math. (IF 1.5) Pub Date : 2021-01-08 Mikhail Kapranov
Infinite-dimensional Lie algebras (such as Kac-Moody, Virasoro etc.) govern, in many ways, various moduli spaces associated to algebraic curves. To pass from curves to higher-dimensional varieties, it is necessary to work in the setup of derived geometry. This is because many feature of the classical theory seem to disappear in higher dimensions but can be recovered in the derived (cohomological) framework
-
Information geometry Jpn. J. Math. (IF 1.5) Pub Date : 2021-01-02 Shun-ichi Amari
Information geometry has emerged from the study of the invariant structure in families of probability distributions. This invariance uniquely determines a second-order symmetric tensor g and third-order symmetric tensor T in a manifold of probability distributions. A pair of these tensors (g, T) defines a Riemannian metric and a pair of affine connections which together preserve the metric. Information
-
Computation of cohomology of vertex algebras Jpn. J. Math. (IF 1.5) Pub Date : 2020-11-16 Bojko Bakalov, Alberto De Sole, Victor G. Kac
We review cohomology theories corresponding to the chiral and classical operads. The first one is the cohomology theory of vertex algebras, while the second one is the classical cohomology of Poisson vertex algebras (PVA), and we construct a spectral sequence relating them. Since in “good” cases the classical PVA cohomology coincides with the variational PVA cohomology and there are well-developed
-
Rank and duality in representation theory Jpn. J. Math. (IF 1.5) Pub Date : 2020-05-19 Shamgar Gurevich, Roger Howe
There is both theoretical and numerical evidence that the set of irreducible representations of a reductive group over local or finite fields is naturally partitioned into families according to analytic properties of representations. Examples of such properties are the rate of decay at infinity of “matrix coefficients” in the local field setting, and the order of magnitude of “character ratios” in
-
Transgressions of the Euler class and Eisenstein cohomology of GL N (Z) Jpn. J. Math. (IF 1.5) Pub Date : 2020-03-04 Nicolas Bergeron, Pierre Charollois, Luis E. Garcia
These notes were written to be distributed to the audience of the first author’s Takagi Lectures delivered June 23, 2018. These are based on a work-in-progress that is part of a collaborative project that also involves Akshay Venkatesh.In this work-in-progress we give a new construction of some Eisenstein classes for GLN (Z) that were first considered by Nori [41] and Sczech [44]. The starting point
-
Recent results on the Kobayashi and Green-Griffiths-Lang conjectures Jpn. J. Math. (IF 1.5) Pub Date : 2020-01-29 Jean-Pierre Demailly
The study of entire holomorphic curves contained in projective algebraic varieties is intimately related to fascinating questions of geometry and number theory—especially through the concepts of curvature and positivity which are central themes in Kodaira’s contributions to mathematics. The aim of these lectures is to present recent results concerning the geometric side of the problem. The Green-Griffiths-Lang
-
Hankel transform, Langlands functoriality and functional equation of automorphic L -functions Jpn. J. Math. (IF 1.5) Pub Date : 2020-01-18 Bảo Châu Ngô
This is a survey on recent works of Langlands’s work on functoriality conjectures and related works including the works of Braverman and Kazhdan on the functional equation of automorphic L-functions. Efforts have been made to carry out in complete generality the construction of the L-monoid, and certain a kernel which is, we believe, related to the elusive Hankel kernel.
-
Double Yangian and the universal R -matrix Jpn. J. Math. (IF 1.5) Pub Date : 2019-12-28 Maxim Nazarov
We describe the double Yangian of the general linear Lie algebra glN by following a general scheme of Drinfeld. We also describe the centre of the Yangian by using its Hopf algebra structure, and provide a proof of the analogue of the Poincaré—Birkhoff—Witt theorem for the Yangian based on its representation theory. This proof extends to the double Yangian.
-
Abundance of minimal surfaces Jpn. J. Math. (IF 1.5) Pub Date : 2019-06-21 Fernando Codá Marques
This article is concerned with the existence theory of closed minimal hypersurfaces in closed Riemannian manifolds of dimension at least three. These hypersurfaces are critical points for the area functional, and hence their study can be seen as a high-dimensional generalization of the classical theory of closed geodesics (Birkhoff, Morse, Lusternik, Schnirel’mann,…). The best result until very recently
-
The twin prime conjecture Jpn. J. Math. (IF 1.5) Pub Date : 2019-06-21 James Maynard
The Twin Prime Conjecture asserts that there should be infinitely many pairs of primes which differ by 2. Unfortunately this long-standing conjecture remains open, but recently there has been several dramatic developments making partial progress. We survey the key ideas behind proofs of bounded gaps between primes (due to Zhang, Tao and the author) and developments on Chowla's conjecture (due to Matomäki
-
An operadic approach to vertex algebra and Poisson vertex algebra cohomology Jpn. J. Math. (IF 1.5) Pub Date : 2019-06-21 Bojko Bakalov, Alberto De Sole, Reimundo Heluani, Victor G. Kac
We translate the construction of the chiral operad by Beilinson and Drinfeld to the purely algebraic language of vertex algebras. Consequently, the general construction of a cohomology complex associated to a linear operad produces the vertex algebra cohomology complex. Likewise, the associated graded of the chiral operad leads to the classical operad, which produces a Poisson vertex algebra cohomology
-
Singularities in mixed characteristic. The perfectoid approach Jpn. J. Math. (IF 1.5) Pub Date : 2019-05-30 Yves André
The homological conjectures, which date back to Peskine, Szpiro and Hochster in the late 60’s, make fundamental predictions about syzygies and intersection problems in commutative algebra. They were settled long ago in the presence of a base field and led to tight closure theory, a powerful tool to investigate singularities in characteristic p.Recently, perfectoid techniques coming from p-adic Hodge
-
Brownian geometry Jpn. J. Math. (IF 1.5) Pub Date : 2019-05-27 Jean-François Le Gall
We present different continuous models of random geometry that have been introduced and studied in recent years. In particular, we consider the Brownian sphere (also called the Brownian map), which is the universal scaling limit of large planar maps in the Gromov-Hausdorff sense, and the Brownian disk, which appears as the scaling limit of planar maps with a boundary. We discuss the construction of
-
Information complexity and applications Jpn. J. Math. (IF 1.5) Pub Date : 2019-03-05 Mark Braverman
This paper is a lecture note accompanying the 19th Takagi Lectures lectures in July 2017 at Kyoto University.We give a high-level overview of information complexity theory and its connections to communication complexity.We then discuss some fundamental properties of information complexity, and applications to direct sum theorems and to exact communication bounds. We conclude with some open questions
-
Takagi Lectures on Donaldson–Thomas theory Jpn. J. Math. (IF 1.5) Pub Date : 2019-02-18 Andrei Okounkov
These are introductory notes on Donaldson–Thomas counts of curves in threefolds and their connections with other branches of mathematics and mathematical physics. They are based on my 2018 Takagi Lectures at The University of Tokyo.
-
Sharp threshold phenomena in statistical physics Jpn. J. Math. (IF 1.5) Pub Date : 2019-01-28 Hugo Duminil-Copin
This text describes the content of the Takagi Lectures given by the author in Kyoto in 2017. The lectures present some aspects of the theory of sharp thresholds for Boolean functions and its application to the study of phase transitions in statistical physics.
-
Renormalisation of parabolic stochastic PDEs Jpn. J. Math. (IF 1.5) Pub Date : 2018-08-02 Martin Hairer
We give a survey of recent result regarding scaling limits of systems from statistical mechanics, as well as the universality of the behaviour of such systems in so-called cross-over regimes. It transpires that some of these universal objects are described by singular stochastic PDEs. We then give a survey of the recently developed theory of regularity structures which allows to build these objects
-
Equivalence of formulations of the MKP hierarchy and its polynomial tau-functions Jpn. J. Math. (IF 1.5) Pub Date : 2018-07-15 Victor G. Kac, Johan W. van de Leur
We show that a system of Hirota bilinear equations introduced by Jimbo and Miwa defines tau-functions of the modified KP (MKP) hierarchy of evolution equations introduced by Dickey. Some other equivalent definitions of the MKP hierarchy are established. All polynomial tau-functions of the KP and the MKP hierarchies are found. Similar results are obtained for the reduced KP and MKP hierarchies.
-
Spectral asymptotics for Kac–Murdock–Szegő matrices Jpn. J. Math. (IF 1.5) Pub Date : 2018-03-02 Alain Bourget, Allen Alvarez Loya, Tyler McMillen
Szegő’s First Limit Theorem provides the limiting statistical distribution of the eigenvalues of large Toeplitz matrices. Szegő’s Second (or Strong) Limit Theorem for Toeplitz matrices gives a second order correction to the First Limit Theorem, and allows one to calculate asymptotics for the determinants of large Toeplitz matrices. In this paper we survey results extending the First and Second Limit
-
Hilbert schemes of lines and conics and automorphism groups of Fano threefolds Jpn. J. Math. (IF 1.5) Pub Date : 2018-02-14 Alexander G. Kuznetsov, Yuri G. Prokhorov, Constantin A. Shramov
We discuss various results on Hilbert schemes of lines and conics and automorphism groups of smooth Fano threefolds of Picard rank 1. Besides a general review of facts well known to experts, the paper contains some new results, for instance, we give a description of the Hilbert scheme of conics on any smooth Fano threefold of index 1 and genus 10. We also show that the action of the automorphism group
-
Categorification of invariants in gauge theory and symplectic geometry Jpn. J. Math. (IF 1.5) Pub Date : 2017-11-30 Kenji Fukaya
This is a mixture of survey article and research announcement. We discuss instanton Floer homology for 3 manifolds with boundary. We also discuss a categorification of the Lagrangian Floer theory using the unobstructed immersed Lagrangian correspondence as a morphism in the category of symplectic manifolds.During the year 1998–2012, those problems have been studied emphasizing the ideas from analysis
-
The size of infinite-dimensional representations Jpn. J. Math. (IF 1.5) Pub Date : 2017-08-21 David A. Vogan
An infinite-dimensional representation π of a real reductive Lie group G can often be thought of as a function space on some manifold X. Although X is not uniquely defined by π, there are “geometric invariants” of π, first introduced by Roger Howe in the 1970s, related to the geometry of X. These invariants are easy to define but difficult to compute. I will describe some of the invariants, and recent
-
Algebraic representations and constructible sheaves Jpn. J. Math. (IF 1.5) Pub Date : 2017-08-21 Geordie Williamson
I survey what is known about simple modules for reductive algebraic groups. The emphasis is on characteristic p > 0 and Lusztig’s character formula. I explain ideas connecting representations and constructible sheaves (Finkelberg–Mirković conjecture) in the spirit of the Kazhdan–Lusztig conjecture. I also discuss a conjecture with S. Riche (a theorem for GL n ) which should eventually make computations
-
Conformal embeddings of affine vertex algebras in minimal W -algebras II: decompositions Jpn. J. Math. (IF 1.5) Pub Date : 2017-07-31 Dražen Adamović, Victor G. Kac, Pierluigi Möseneder Frajria, Paolo Papi, Ozren Perše
We present methods for computing the explicit decomposition of the minimal simple affine W-algebra \({W_k(\mathfrak{g}, \theta)}\) as a module for its maximal affine subalgebra \({\mathscr{V}_k(\mathfrak{g}^{\natural})}\) at a conformal level k, that is, whenever the Virasoro vectors of \({W_k(\mathfrak{g}, \theta)}\) and \({\mathscr{V}_k(\mathfrak{g}^\natural)}\) coincide. A particular emphasis is
-
Kodaira fibrations and beyond: methods for moduli theory Jpn. J. Math. (IF 1.5) Pub Date : 2017-07-31 Fabrizio Catanese
Kodaira fibred surfaces are remarkable examples of projective classifying spaces, and there are still many intriguing open questions concerning them, especially the slope question. The topological characterization of Kodaira fibrations is emblematic of the use of topological methods in the study of moduli spaces of surfaces and higher dimensional complex algebraic varieties, and their compactifications
-
A sufficient condition for a rational differential operator to generate an integrable system Jpn. J. Math. (IF 1.5) Pub Date : 2017-01-15 Sylvain Carpentier
For a rational differential operator \({L=AB^{-1}}\), the Lenard–Magri scheme of integrability is a sequence of functions \({F_n, n \geq 0}\), such that (1) \({B(F_{n+1})=A(F_n)}\) for all \({n \geq 0}\) and (2) the functions \({B(F_n)}\) pairwise commute. We show that, assuming that property (1) holds and that the set of differential orders of \({B(F_n)}\) is unbounded, property (2) holds if and only
-
Cohomology of arithmetic groups and periods of automorphic forms Jpn. J. Math. (IF 1.5) Pub Date : 2016-12-21 Akshay Venkatesh
We recall some unusual features of the cohomology of arithmetic groups, and propose that they are explained by a hidden action of certain motivic cohomology groups.
-
Synthetic theory of Ricci curvature bounds Jpn. J. Math. (IF 1.5) Pub Date : 2016-08-29 Cédric Villani
Synthetic theory of Ricci curvature bounds is reviewed, from the conditions which led to its birth, up to some of its latest developments.
-
From Riemann and Kodaira to Modern Developments on Complex Manifolds Jpn. J. Math. (IF 1.5) Pub Date : 2016-08-09 Shing-Tung Yau
We survey the theory of complex manifolds that are related to Riemann surface, Hodge theory, Chern class, Kodaira embedding and Hirzebruch–Riemann–Roch, and some modern development of uniformization theorems, Kähler–Einstein metric and the theory of Donaldson–Uhlenbeck–Yau on Hermitian Yang–Mills connections. We emphasize mathematical ideas related to physics. At the end, we identify possible future
-
Asymptotic theory of path spaces of graded graphs and its applications Jpn. J. Math. (IF 1.5) Pub Date : 2016-06-29 Anatoly M. Vershik
The survey covers several topics related to the asymptotic structure of various combinatorial and analytic objects such as the path spaces in graded graphs (Bratteli diagrams), invariant measures with respect to countable groups, etc. The main subject is the asymptotic structure of filtrations and a new notion of standardness. All graded graphs and all filtrations of Borel or measure spaces can be
-
Hurwitz theory and the double ramification cycle Jpn. J. Math. (IF 1.5) Pub Date : 2016-06-29 Renzo Cavalieri
This survey grew out of notes accompanying a cycle of lectures at the workshop Modern Trends in Gromov–Witten Theory, in Hannover. The lectures are devoted to interactions between Hurwitz theory and Gromov–Witten theory, with a particular eye to the contributions made to the understanding of the Double Ramification Cycle, a cycle in the moduli space of curves that compactifies the double Hurwitz locus
-
Free analysis and random matrices Jpn. J. Math. (IF 1.5) Pub Date : 2016-05-16 Alice Guionnet
We describe the Schwinger–Dyson equation related with the free difference quotient. Such an equation appears in different fields such as combinatorics (via the problem of the enumeration of planar maps), operator algebra (via the definition of a natural integration by parts in free probability), in classical probability (via random matrices or particles in repulsive interaction). In these lecture notes
-
Knots, groups, subfactors and physics Jpn. J. Math. (IF 1.5) Pub Date : 2016-04-20 Vaughan F. R. Jones
Groups have played a big role in knot theory. We show how subfactors (subalgebras of certain von Neumann algebras) lead to unitary representations of the braid groups and Thompson’s groups \({F}\) and \({T}\). All knots and links may be obtained from geometric constructions from these groups. And invariants of knots may be obtained as coefficients of these representations. We include an extended introduction
-
Riemann–Hilbert correspondence for irregular holonomic $${\mathscr{D}}$$ D -modules Jpn. J. Math. (IF 1.5) Pub Date : 2016-04-07 Masaki Kashiwara
This is a survey paper on the Riemann–Hilbert correspondence on (irregular) holonomic \({\mathscr{D}}\)-modules, based on the 16th Takagi Lectures (2015/11/28). In this paper, we use subanalytic sheaves, an analogous notion to the one of indsheaves.
-
The Kervaire invariant problem Jpn. J. Math. (IF 1.5) Pub Date : 2016-03-25 Michael J. Hopkins
The history and solution of the Kervaire invariant problem is discussed, along with some of the future prospects raised by its solution.