**Analysis:**

Research in analysis at APRG ranges over diverse areas of the subject. It includes Harmonic analysis, Matrix analysis, Spectral graph theory, Operator theory, Partial differential equations, Complex analysis in several variables, Metric geometry, and Non-linear dynamics.

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**Probability:**

Research in probability at APRG covers both the theoretical and applied aspects of the subject. On the theoretical side there is interest in Interacting particles and statistical physics, Exclusion processes, Geometric random graphs and percolation, Random matrices and random polynomials, Large deviations, and Anti-concentration phenomena among others.

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On the applied side, the research areas include, but are not limited to, Information theory, Network science, Statistical learning and inference, Machine learning, Stochastic approximation, Stochastic control, Convex optimization, and Simulation based optimization.

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