Coarse index theory and quantum physics

Guo Chuan Thiang 程国传  (Peking University)

10:00-11:00, August 22-24 & 14:00-15:00, August 22-23, 2023   Science Building A503

Abstract:

I will present coarse geometry ideas, specifically index theory and cohomology, from the viewpoint of modern mathematical physics.\\ Prerequisites: Basic concepts in functional analysis, differential geometry, algebraic topology, and quantum mechanics.\\ Topics(tentative): Lecture 1: Fredholm index in Quantum mechanics\\ Lecture 2: Operator algebras for coarse geometry\\ Lecture 3: Coarse index of Dirac operators coupled to gauge fields\\ Lecture 4: Partitions, coarse and cyclic cohomology, and trace pairings\\ Lecture 5: Application to large-scale quantization and quantum Hall effect.\\ References: I aim to explain the background to http://faculty.bicmr.pku.edu.cn/~guochuanthiang/conductancequantization.pdf (http://arxiv.org/abs/2308.02819)\\ Other references: 1. Roe, J.: Coarse cohomology and index theory on complete Riemannian manifolds. Mem. Am. Math. Soc. 104(497) 1993\\ 2. B. Blackadar. K-theory for operator algebras, vol.5 of Math. Sci. Res. Inst. Publ. Cambridge Univ. Press, Cambridge, 1998\\ 3. J. Bellissard, A. van Elst, and H. Schulz-Baldes. The noncommutative geometry of the quantum hall effect. J. Math. Phys., 35(10):5373-5451, 1994\\ 4. G.C. Thiang, Topics in Mathematical Physics lecture notes, faculty.bicmr.pku.edu.cn/~guochuanthiang/MP/MPTopicsNotes.pdf

About the speaker:

程国传(Guo Chuan Thiang)在新加坡国立大学获学士学位，剑桥大学获硕士学位，牛津大学获得数学博士学位。2015-2017年在澳大利亚阿德莱德大学做博士后，2017-2020获澳大利亚DECRA基金，2022年入选国家级青年人才项目。程国传的研究领域是数学物理，研究兴趣在物质的拓扑相(topological phases of matter)、量子理论和弦理论等物理中的K-理论，代数拓扑，非交换几何，指标理论和算子代数。在Comm. Math. Phys.等数学物理期刊有近30篇科研论文。

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