Online Seminar: Random Matrix Theory and Applications

This seminar aims to cover topics on both the theoretical and applied aspects of random matrix theory and related fields.

The meetings will be held on Zoom and typically scheduled monthly on Thursdays in Beijing Time (UTC/GMT +8 hours).

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Zhigang Bao (University of Hong Kong)
Zhenyu Liao (Huazhong University of Science & Technology)
Yuanyuan Xu (AMSS, Chinese Academy of Sciences)
Lun Zhang (Fudan University)

• Date: April 17: 9-10am (Beijing Time)
  Speaker: Lucas Benigni (Université de Montréal)
  

  Title: Spectrum of the Neural Tangent Kernel in a quadratic scaling
  Abstract:Despite their surplus of parameters, modern deep learning models often generalize well, a phenomenon exemplified by the "double descent curve." While this behavior is theoretically grasped for problems such as ridge regression under linear scaling of dimensions, intriguing phenomenon emerge under quadratic scaling, where sample size equals parameter count. In this presentation, we study the eigenvalues of the Neural Tangent Kernel, a matrix model pertinent to wide neural networks trained via gradient descent, within this quadratic regime.





• Date: April 24: 9-10am (Beijing Time)
  Speaker: Jiaoyang Huang (University of Pennsylvania)
  

  Title: Ramanujan Property and Edge Universality of Random Regular Graphs
  Abstract: Extremal eigenvalues of graphs are of particular interest in theoretical computer science and combinatorics. Specifically, the spectral gap—the difference between the largest and second-largest eigenvalues—measures the expansion properties of a graph. In this talk, I will focus on random d-regular graphs.
  I will begin by providing background on the eigenvalues of random d-regular graphs and their connections to random matrix theory. In the second part of the talk, I will discuss our recent results on eigenvalue rigidity and edge universality for these graphs. Eigenvalue rigidity asserts that, with high probability, each eigenvalue concentrates around its classical location as predicted by the Kesten-McKay distribution. Edge universality states that the second-largest eigenvalue and the smallest eigenvalue of random d-regular graphs converge to the Tracy-Widom distribution from the Gaussian Orthogonal Ensemble. Consequently, approximately 69% of d-regular graphs are Ramanujan graphs. This work is based on joint work with Theo McKenzie and Horng-Tzer Yau.
  





• Date: May 22: 9-10 am (Beijing Time)
  Speaker: Zhou Fan (Yale University)
  

  Title: TBA
  Abstract: TBA





• Date: June 12: 9:30-10:30 am (Beijing Time)
  Speaker: Elliot Paquette (McGill University)
  

  Title: TBA
  Abstract: TBA

• TBA.