Analysis   Seminar    


Unless specified, all seminars are Wednesday 4-5pm at Room 250. 

January 22                      Guo Chuan Thiang,  Peking University
                                       Exact fractional quantization and topological insulators

                                       Abstract: The spectral problem for the magnetic Laplacian on the plane with uniform magnetic field was solved almost 100 years ago, with the lowest
                                       eigenspace being the Fock space. As this Fock space is also realized as the kernel of an associated Dirac operator, it possesses a certain
                                       index-theoretic stability. I will explain the geometric-analytic meaning of this index, and its significance in the concepts of exact quantization and
                                       topological insulators in modern physics. A tract formula for this index is available, and corresponds to the famous integer-quantized Hall
                                       conductance discovered in experiments in the 1980s. Furthermore, guided by the fractional quantum Hall effect, we find that Fock space has a
                                       hidden rational trace structure.
                                      




 
Past Analysis Seminar