International Conference on Probability in Pure Mathematics

This track explores the fundamental principles and axioms of probability theory, emphasizing rigorous mathematical formulations. Topics include measure-theoretic foundations, probability spaces, and the interplay between probability and pure mathematics.

This session focuses on the characterization and properties of random variables, including discrete and continuous distributions. Participants will discuss applications of various probability distributions in pure mathematical contexts.

This track examines the role of stochastic processes in pure mathematics, highlighting their theoretical underpinnings and applications. Key topics include Markov processes, martingales, and their convergence properties.

This session delves into the integration of measure theory with probability, providing a rigorous framework for understanding random phenomena. Discussions will include Lebesgue integration, sigma-algebras, and measurable functions.

This track investigates various limit theorems, including the Central Limit Theorem and Law of Large Numbers, within the context of pure mathematics. Asymptotic analysis techniques will also be explored to understand convergence behaviors.

This session focuses on the mathematical theory of random fields, exploring their properties and applications in various domains. Participants will discuss Gaussian fields, stochastic processes on manifolds, and related topics.

This track covers the theory of martingales, including their convergence properties and applications in probability theory. Emphasis will be placed on the use of martingales in various mathematical proofs and models.

This session examines various probability models that are foundational to pure mathematics, including their theoretical implications. Participants will discuss model construction, validation, and the role of randomness in mathematical proofs.

This track explores the theory of random matrices, focusing on their spectral properties and applications in mathematical statistics. Discussions will include the interplay between random matrices and various fields of pure mathematics.

This session investigates functional limit theorems, which extend classical limit theorems to functionals of stochastic processes. Participants will explore their implications in both theoretical probability and applications.

This track addresses advanced topics in theoretical probability, including ergodic theory, large deviations, and stochastic calculus. Participants are encouraged to present novel research findings and theoretical advancements.