非交换几何会议研讨会

时间：2024.01.28-2024.02.03

召集人：陈晓漫、李寒峰、姚一隽

会议日程

说明:

* 腾讯会议: 700-359-94420 会议密码: 891937
https://meeting.tencent.com/dm/WlI18XGN53GF
# 腾讯会议：495-737-707  https://meeting.tencent.com/dw/7qxbWZ8qVVMg

摘要

Jingbo XIA

（嘉兴大学）

题目：Fock space: a bridge between Fredholm index and the quantum Hall effect

摘要：We identify the quantized Hall conductance of Landau levels with a Fredholm index, by using the theories of Helton-Howe-Carey-Pincus, and Toeplitz operators on the classic Fock space and higher Fock spaces. The index computations reduce to the single elementary one for the lowest Landau level. This brings new insights to the extraordinarily accurate quantization of the Hall conductance as measured in quantum Hall experiments.  This is joint work with Guo Chuan Thiang.

熊枭

（哈尔滨工业大学）

题目：Commutators of Calder\’on transforms on quantum Euclidean spaces

摘要：We characterize the (weak) Schatten class membership of commutators of singular integral operators on quantum euclidean spaces in terms of Besov spaces, and calculate the Dixmier trace of the commutators.

刘锐

（南开大学）

题目：球覆盖性质从交换空间到非交换空间

摘要：若赋范空间的球面被可数个不包含原点的球的并集覆盖, 称该空间具有球覆盖性质. 本报告介绍球覆盖性质的部分研究进展, 包括: 通过交换空间给出球覆盖性质的拓扑刻画, 从而引出关于C*代数的相关问题; 判定一部分Banach代数B(X)及其子代数的球覆盖性质, 刻画了有球覆盖性质的von Neumann代数.

黄辉斥

（重庆大学）

题目：Strongly independent matrices and measure rigidity on $d$-torus

摘要：We introduce the concept of strongly independent matrices over a field and prove the existence of such matrices over the rational field. Also we prove the nonexistence of such matrices over algebraically closed field. Finally we use this concept to get a measure rigidity on $d$-torus. This is joint work with Hanfeng Li, Enhui Shi and Hui Xu.

刘智超

（大连理工大学）

题目：Classification of homomorphisms into simple C*-algebras with strict comparison

摘要：In this talk, we will explore the classification of homomorphisms from a large class of C

*-algebras to into simple C*-algebras with strict comparison in terms of the Cuntz semigroup.

安庆楠

 （东北师范大学）

题目：A counterexample to Elliott Conjecture of real rank zero setting and classification of extension algebras

摘要： We will talk about the Elliott conjecture of real rank zero C*-algebras. We exhibit two unital, separable, nuclear C*-algebras of stable rank one and real rank zero with the same ordered scaled total K-theory satisfying UCT, but they are not isomorphic with each other, which forms a counterexample to Elliott Classification Conjecture for real rank zero setting. Such a result will modify the original conjecture into two modified versions. We will introduce an additional normal condition and give a classification result in terms of total K-theory. For the general setting, with a new invariant—total Cuntz semigroup, we classify a large class of C*-algebras obtained from extensions. The total Cuntz semigroup, which distinguish the algebras of our counterexample, could possibly classify all the C*-algebras of stable rank one and real rank zero.

王晓峰

（广州大学）

题目：L^p − L^q Boundedness of Multiparameter Forelli-Rudin Type Operators on the Product of Unit Balls of Cn

摘要：In this paper, two classes of multiparameter Forelli-Rudin type operators defined on the product of unit balls of Cn are introduced, which are natural extensions of the wellknown Forelli-Rudin type operators originated by Forelli and Rudin in 1974, and further studied by Kures-Zhu in 2006, Zhao in 2015, and Zhao-Zhou in 2022. By establishing some new Schur’s tests, in this paper, we completely characterize the boundedness of these two classes operators from one mixed-norm Lebesgue space L⃗p to another space L⃗q, when 1 ≤⃗p ≤ ⃗q < ∞, equipped with possibly different weights. With these characterizations, we are able to obtain the necessary and suffcient conditions for both L⃗p − L⃗q boundedness of the weighted multiparameter Berezin transform and L⃗p − A⃗q boundedness of the weighted multiparameter Bergman projection, where A⃗q denotes the mixed-norm Bergman space.

归斌

（清华大学）

题目：Strong commutativity in conformal quantum field theory

摘要：In algebraic quantum field theories (AQFT), observables are basic ingredients and are described by (unbounded) self-adjoint operators. One of the most important aspects in AQFT is that two observables localized in spacelike separated regions should have mutually commuting spectral projections. In particular, these two self-adjoint operators commute on their common core. However, by Nelson's counterexample in 1960s, (algebraic) commutativity of self-adjoint operators does not in general imply strong commutativity, i.e. commutativity of spectral projections. Thus, proving strong commutativity for spacelike separated observables is a difficult task in AQFT. In this talk, I will present the current understanding of strong commutativity in 2d conformal field theory and its relationship with infinite dimensional Lie groups, Tomita-Takesaki theory, and Jones' subfactor theory.

史维娟

（陕西师范大学）

题目：Ortho-isomorphisms and Lp-isometries on Grassmann spaces in a semifinite factor

摘要：Let M be a semifinite factor with a faithful normal semifinite tracial weight τ , and P the set of all projections in M. Denote by Pc the Grassmann space of all projections in P with trace c, where c is a positive real number. The aim of this report is to describe the general forms of ortho-isomorphisms and Lp-isometries between two Grassmann spaces Pc in a semifinite factor. We show that an ortho-isomorphism ψ : Pc → Pc can be extended to a Jordan ∗-isomorphism ρ of M onto M.

刘泓志

（上海财经大学）

题目：Relative L theory and Relative index

摘要：我们给出了相对手术正合列的新描述，并借助这个新描述证明了相对手术正合列其实是群的正合列。进而我们利用相对指标构造了相对 L 理论到群C*代数K理论的群同态。

乔雨

（陕西师范大学）

题目：The Lie-Rinehart Algebra of a Continuous Family Groupoid

摘要：Continuous family groupoids were introduced by Alan Paterson around 2000, which are a sort of generalization of Lie groupoids. It is well-known that there is the associated Lie algebroid to a Lie groupoid. In this talk, we introduce and discuss the Lie-Rinehart algebra associated to a continuous family groupoid by analogy. It is joint work with Ivan Beschastnyi, Catarina Carvalho, and Victor Nistor.

蒋报捷

（重庆师范大学）

题目：Rigidity for geometric ideals in uniform Roe algebras

摘要：The rigidity problem for Roe algebras was initially studied by \v{S}pakula and Willett in 2013 and has been completely solved in 2022. In this talk, we will investigate the rigidity problems for geometric ideals in uniform Roe algebras associated to discrete metric spaces with bounded geometry.  Our main result is that if two geometric ideals in uniform Roe algebras are stably isomorphic, then the coarse spaces associated to these ideals are coarsely equivalent.  This presentation is based on a joint work with Jiawen Zhang.

王勤

（华东师范大学）

题目：Ideal Structure of Roe Algebras

摘要：We will discuss ideal structure of uniform Roe algebras and Roe algebras of metric spaces and related topics.

齐霄霏  

(山西大学)

题目：Quantum coherence of Fermionic Gaussian states

摘要：In this talk, we investigate quantum coherence of fermionic Gaussian states from the point of quantum resource theory.<br> We give characterizations of incoherent fermionic Gaussian states and incoherent fermionic Gaussian channels, <br>and give two measures of quantum coherence of fermionic Gaussian states based on the relative entropy and the Hellinger distance, respectively.

贺衎

（太原理工大学）

题目: 探测量子网络中的非经典资源

摘要：量子网络通过独立的资源连接用户。一个网络中的量子资源分布决定了这个网络的实用性。我们介绍探测量子网络非经典资源个数的不等式标准的最新成果。

徐胜芝

（复旦大学）

题目：The paring of KK-group and L-group

摘要：In this talk, a paring between KK-groups and L-groups is established.

王显金

（重庆大学）

题目：Uniform Roe algebras of discrete groups and their dense spectral invariant subalgebras

摘要：In this talk, we discuss the spectral invariant dense subalgeras of uniform Roe algebras of countable discrete groups.

章嘉雯

（复旦大学）

题目：Quasi-local algebras for groupoids

摘要：The notion of quasi-locality was originally introduced by Roe to describe operators in (uniform) Roe algebras, and it attracted more and more attention recently. In this talk, I will introduce a generalisation of quasi-locality to the theory of groupoids, based on a joint work with Baojie Jiang and Jianguo Zhang. We show that when the groupoid is etale and amenable, then the quasi-local algebra coincides with the reduced groupoid C*-algbera. This unifies the classic case of groups and metric spaces, and also gives new results for group actions and groupoid uniform Roe algebras.

王智拓

（哈尔滨工业大学）

题目：Phase Transitions in Quantum Many-body system

摘要：In this talk I will present some recent progress on the construction of ground state of the 2-dimensional Hubbard model, which is a prototypical model for studying phase transitions in quantum many-body system. Using fermionic cluster expansions and constructive renormalization theory, we proved that the ground state of the 2-d Hubbard model on the honeycomb lattice with triangular Fermi surfaces is not a Fermi liquid in the mathematical precise sense of Salmhofer. I will also discuss the crossover phenomenon in the 2-d square Hubbard model and universalities.

张建国

（陕西师范大学）

题目：The Banach property RD and its applications

摘要：We will talk about the Banach property RD for groups introduced by B. Liao and G. Yu. In particular, we want to discuss its applications to $K$-theory and the idempotent problem of group Banach algebras. Some results in this talk are based on a joint work with Yifan Liu.

汪镇

（吉林大学）

题目：$p$-nuclearity of $L^p$-operator crossed products

摘要：The aim of this talk is to study a problem raised by N. C. Phillips concerning the $L^p$ operator crossed products.Let $(X,\mathcal{B},\mu)$ be a measure space and $A$ be a closed subalgebra of $\mathcal{B}(L^p(X,\mu))$, where $p\in [1,\infty)\setminus\{2\}$.Let $(G,A,\alpha)$ be an $L^p$-operator algebra dynamical system, where $G$ is a countable discrete amenable group. We prove that the full $L^p$-operator crossed product $F^p(G,A,\alpha)$ is $p$-nuclear if and only if $A$ is $p$-nuclear provided the action $\alpha$ of $G$ on $A$ is $p$-completely isometric. As applications, we prove that $L^p$-Cuntz algebras and rotation $L^p$-operator algebras are both $p$-nuclear. Our results solve the $p$-nuclearity problem for $L^p$-Cuntz algebras raised by N. C. Phillips.

王子竞

（华东师范大学）

题目：Index theorem for homogeneous spaces of Lie groups

摘要：We study index theory on homogeneous spaces associated to an almost connected Lie group in terms of the topological aspect and the analytic aspect. On the topological aspect, we obtain a topological formula as a result of the Riemann-Roch formula for proper cocompact actions of the Lie group, inspired by the work of Paradan and Vergne. On the analytic aspect, we apply heat kernel methods to obtain a local index formula representing the higher indices of equivariant elliptic operators with respect to a proper cocompact actions of the Lie group. This is a joint work with Hang Wang.

任百颖

（华东师范大学）

题目：Equivariant Index Theorem on R^n in the Context of Continuous Fields of C*-algebras

摘要：We prove an equivariant index theorem on the Euclidean space using a continuous field of C*-algebras. This generalizes the work of Elliott, Natsume and Nest, which is a special case of the algebraic index theorem by Nest-Tsygan. The equivariant index of the Bott-Dirac operator on R^{2n} can be explicitly calculated by our formula. This is a joint work with Hang Wang and Zijing Wang.

刘超

（云南大学）

题目：Cesaro Exponents of Mixed Norm Spaces

摘要：In 1934, G. H. Hardy and J. E. Littlewood calculated the optimal Cesaro exponent for Hardy spaces. In this talk, we calculate it for mixed norm spaces, hence including the Bergman spaces in particular. The main technical challenge lies in the analysis of the example needed for the critical case.

参会名单