## Welcome to Research Center for Operator Algebras

Title: ** Index theory of spectral truncations and localisation algebras**

Speaker: ** Yuezhao Li ** (Leiden University)

Location: Science Building A503

Time: **14:00-15:00, September 9, 2024**

Abstract: A spectral truncation is the compression of a spectral triple (A,H,D) onto a subspace by a spectral projection of D. Such a subspace can be finite-dimensional, thus we cannot expect a spectral truncation to remember the K-homology data of the spectral triple to begin with. Nevertheless, Terry Loring and Hermann Schulz-Baldes have constructed computational tools called spectral localisers, which are matrices constructed from a finite-dimensional spectral truncation of a spectral triple (A,H,D) and an invertible or a projection in A, that compute the index pairings between this spectral triple and the K-theory class represented by this invertible or projection. In this talk, I will review this construction, and provide a new perspective from Guoliang Yu's localisation algebras. This is an ongoing work with Bram Mesland.

**International Conference on C*-algebras and Non-commutative Geometry
In honor of Guihua Gong's 60th birthday**, Dalian University of Technology, December 19-23, 2022.

**Young Mathematicians in C*-Algebras**, Oslo University, August 8-12, 2022.

**ICM satellite conference: K-Theory, C*-Algebras and Topology of Manifolds**, July 18-23, 2022.

**ICM 2022**, July 6-14, 2022.

** Operator algebras, dynamics and groups**, University of Copenhagen, July 1-4, 2022.

** Conference celebrating the career of Ryszard Nest**, University of Copenhagen, Copenhagen, June 13-16, 2022.

**Canadian Operator Algebras Symposium, 50th anniversary**, University of Ottawa, May 30-June 3, 2022.

**Groups acting on Fractals, Hyperbolicity and Self-similarity**, Institut Henri Poincar , April 11-July 8, 2022.

**Global Noncommutative Geometry Seminar**, Online, 2020- .

**Videos of Autumn Operator Algebras Program 2021**

** Professor Wilhelm Winter's talk on the occasion of the 70th anniversary of ECNU**

**Videos of Special Week on Operator Algebras 2021**

**Videos of the 17th Special Week on Operator Algebras**

**Huaxin Lin's lecture series for operator algebras 2022**

**A revisit to Hilbert C*-module by Huaxin Lin**

**Mikael Rordam»ª¶«Ê¦´óÈÙÓþ½ÌÊÚÆ¸ÈÎÒÇÊ½ôßÑ§Êõ±¨¸æ»á¾ÙÐÐ**

**George A. ElliottÈÙÓþ½ÌÊÚÆ¸ÈÎÒÇÊ½ôßÑ§Êõ±¨¸æ»á¾ÙÐÐ**

**Honorary Doctorate Degree Awarded to Prof. Uffe Haagerup of Copenhagen**

**Uffe Haagerup教授荣誉博士学位授予仪式暨庆祝酒会在我校举行**

**KadisonÈÙÓþ½ÌÊÚÆ¸ÈÎÒÇÊ½ôßÑ§Êõ±¨¸æ»á¾ÙÐÐ**

**Special Week on Operator Algebras 2024**

**Spring Operator Algebras Program, 2024**

**Special Week on Operator Algebras 2023**

**2023 Spring Operator Algebras Program**

**2022 FDU-ECNU Summer School of Operator Algebras and Noncommutative Geometry, August 22-30, 2022 **

**The 17th Special Week on Operator Algebras, August 1-5, 2022**

**Autumn Operator Algebras Program 2021, November 15-24**

**University Outstanding Lecture Series (70ÖÜÄêÐ£Çì×¿Ô½Ñ§Êõ±¨¸æ) - Professor Wilhelm Winter**

**Summer School of Functional Analysis and Noncommutative Geometry 2021, Fudan University, August 2-13, 2021. (Organizer: Fudan University, Co-organizers: East China Normal University & Shanghai University of Finance and Economics.)**

** Special Week on Operator Algebras 2021, June 7-11**

**Special Week on Operator Algebras 2020**

**International Workshop on Operator Theory and Applications 2018**

**Autumn Operator Algebras Program 2019**

**Special Week on Operator Algebras 2019**

**Spring Operator Algebras Program 2019**

**Special Week on Operator Algebras 2018**

**Spring Operator Algebras Program 2018**

**Autumn Operator Algebras Program 2017**

**Special Week on Operator Algebras June 2017**

**Spring Operator Algebras Program 2017 **

**Winter Operator Algebras Program 2016**

**Special Week on Operator Algebras June 2016**

**2016 NSFC Tianyuan Foundation for Functional Analysis **

-- Summer School on Operator Algebras and Noncommutative Geometry

-- Summer School on Operator Algebras and Noncommutative Geometry

**Spring Operator Algebras Program, 2016**

**2016数学天元基金《泛函分析》专题讨论班第二期 **

-- 算子代数与非交换几何 研究生暑期学校 *(July)*

-- 算子代数与非交换几何 研究生暑期学校

*(July)*