Ramanujan’s Partition Congruences, Mock Theta Functions, and Beyond
The conference lecture series will explore these major themes: extending Ramanujan’s classical partition congruences, furthering the combinatorics of partition congruences, extending partition statistics and cranks, and ranks and mock modular forms. They will include these topics in the context of number theory, combinatorics, physics, and other areas. Much of the recent work has been motivated by data obtained from innovative use of both the mathematical theory and the use of computer algebra systems.
Analysis, Geometry, and Partial Differential Equations in a Lower-Dimensional World
This conference will deal with recent groundbreaking advances pertaining to connections between analysis, partial differential equations, and geometric properties of multi-dimensional sets. This work has surprising and intricate applications across several areas of physics, materials science, and engineering. Participants will be exposed to the ways in which seemingly abstract concepts and results at the cutting edge of pure mathematics can immediately influence state-of-the-art engineering of photonic devices and the physics behind them.
Interface of Mathematical Biology and Linear Algebra
This conference focuses on the cutting-edge studies at the interface of these two long-time interacting mathematical branches, which has witnessed significant new advances at a higher level. Specifically, recent advances of new algebraic theories and novel applications of classic matrix results have helped to resolve many challenges in mathematical biology, while biologically-driven research problems have also attracted an increasing number of researchers in the field of linear algebra.
Parallel Time Integration
The primary focus of this workshop is to educate and inspire researchers and students in new and innovative numerical techniques for the parallel-in-time solution of large-scale evolution problems on modern supercomputing architectures, and to stimulate further studies in their analysis and applications. The lecture series will expose participants to the numerical analysis of parallel-in-time methodologies and their implementations using appropriate mathematical methodologies from the theory of partial differential equations in a functional analytic setting, numerical discretizations, integration techniques, and convergence analyses of these iterative methods.
Topological Data Analysis and Persistence Theory
The main goal of this conference is to provide an introduction to topological data analysis (TDA) and persistence theory (PT) to a broader audience. TDA and PT are relatively recent methods useful for finding important features in large data sets using ideas from traditionally theoretical branches of mathematics such as algebra and topology. The lectures will include a review of the basic mathematical concepts related to TDA and PT, interactions with statistical methods and machine learning, and current applications and software implementation.
Nonstandard Finite Difference Methods: Advances in Theory and Applications
The conference will introduce participants to the basic foundations and formulations of Nonstandard Finite Difference Methods (NSFD), discuss the state-of-the-art and latest advances in NSFD theory and applications, and summarize open problems as well as possible future directions in the field. Advances in theory will include explorations of potentially transformative concepts for generalized NSFD construction methods for systems of ordinary, partial, delay, and fractional differential equations. Advances in applications will be highlighted with various studies of engineering, science, and mathematical phenomena of classic or emerging interest modeled by the various classes of differential equations.
Bayesian Forecasting and Dynamic Models
Adequate modeling and forecasting of temporal data, particularly in large-dimensional settings, is key in a wide range of applications. Recent important research advances in this area have led to a massive body of literature that comprise new sophisticated models and methods for analysis and forecasting of time series data, as well as powerful computational tools and related software for inference and forecasting in an efficient manner. This conference will facilitate introduction to the area by providing a comprehensive review of Bayesian modeling and forecasting tools.
K-Theory of Operator Algebras
In the last decade, there have been exciting developments in this field of research with applications to several areas of mathematics. The conference lectures will highlight the recent advances, identify promising new research directions, and help a diverse group of students and early career mathematicians navigate to the frontier of this exciting yet challenging research field.
These conferences are intended to stimulate interest and activity in mathematical research. Each five day conference features a distinguished lecturer or team of lecturers delivering ten lectures on a topic of important current research in one sharply focused area of the mathematical sciences.
The lecturer or lecturers prepare extensive online materials that are made available at https://www.cbmsweb.org/regional-conferences/past-conferences/. They are also expected to prepare an expository monograph based upon these lectures, which is normally published as a part of a regional conference series.
Depending upon the conference topic, the monograph is published by the American Mathematical Society, the Society for Industrial and Applied Mathematics, or jointly by the American Statistical Association and the Institute of Mathematical Statistics.
Support for about 30 participants is provided and the conference organizer invites both established researchers and interested newcomers, including postdoctoral fellows and graduate students, to attend. Information about an individual conference may be obtained by contacting the conference organizer.