Explore advanced mathematical concepts in this comprehensive workshop focusing on random matrix theory and point processes. Delve into cutting-edge research topics including determinantal point processes, Dyson-Schwinger equations, and their applications in dynamical systems and control theory. Study the mathematical properties of point processes arising from random matrices, including their adherence to the Kolmogorov 0-1 Law, Soshnikov's Central Limit Theorem, and rigidity properties as defined by Ghosh and Peres. Examine Palm-Khintchine theory applications and connections to integrable systems theory. Investigate eigenvalue statistics, spectral curves, and asymptotic behaviors in various matrix ensembles including Wigner, Ginibre, and Toeplitz matrices. Learn about quantum spin chains, the KPZ equation, and soliton quantization methods. Discover applications in coding theory for Kleinian groups and analyze geometric aspects of SL(2,Z)-dynamics. Engage with numerous open research problems, particularly those related to Pfaffian point processes and their rigidity properties.

Syllabus

Random matrices and the uses of Dyson-Schwinger equations - I
Determinantal point processes - I
Random walk at weak and strong disorder
Color-position symmetry in interacting particle systems
Spin current for the quantum 1D XX spin chain and the Bessel kernel
On spectra of quasiperiodic matrices
Variational problems and spectral curves for the hermitian matrix model with external source
Determinantal point processes - II
Random matrices and the uses of Dyson-Schwinger equations - II
Local eigenvalue statistics for band matrices with a transfer operator approach
Edge universality for non-Hermitian random matrices
Asymptotics of orthogonal polynomial ensembles via integrable methods
Christoffel deformations of discrete ensembles
Random matrices and the uses of Dyson-Schwinger equations - III
Determinantal point processes - III
Eigenvalue distribution for non linear models of random matrices
Asymptoticcs for the lower tail of the KPZ equation
Noise Sensitivity of the Top Eigenvector of a Wigner Matrix
Soliton quantization and random partitions
Free Field Approach to the Macdonald Process
Determinantal point processes - IV
Random matrices and the uses of Dyson-Schwinger equations - IV
Analysis and Geometry in SL(2,Z)-dynamics
Absolute continuity of limiting spectral distributions of Toeplitz and Hankel random matrices
The point processes at turning points of large lozenge tilings
Rigidity for Pfaffian point processes
Wroten type coding for Kleinian groups
Random matrices and the uses of Dyson-Schwinger equations - V
Determinantal point processes - V
Asymptotics of the averaged characteristic polynomial for Ginibre Ensemble
Large deviations for traces of Wigner matrices