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 http://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.
This conference aims to train working mathematicians and graduate students alike in recent developments and new techniques that have allowed progress in the field of Operator Algebras and their classification. Operator algebras, including C*-algebras and von Neumann algebras, originally arose from quantum physics. Enduring interest in them is largely due to the realization that they can be constructed from, and in some cases encode, many other structures, such as symmetries, time-evolving systems, graphs, and number fields. Alain Connes’ work on the structure and classification of amenable von Neumann algebras in the 1970s remains fundamental to modern von Neumann algebra theory. In the topological setting of C*-algebras, the classification program for amenable C*-algebras was initiated in the 1990s, seeking analogous results. This large-scale worldwide endeavor recently culminated in the proof of the main conjecture in the area, giving a complete classification of a broad class of simple amenable C*-algebras. The principal lectures will provide an accessible introduction to the classification result and the follow-up talks will focus on applications. In addition to the principal lectures there will be five complementary follow-up talks by additional speakers. The conference also will feature a panel discussion about future research directions and include other activities designed to broaden participation and to provide young researchers in the field opportunities to build professional networks and share their research.
This conference will examine the interface between the representation theory of the p-adic groups, the Langlands program, and noncommutative geometry. In more detail, the Langlands program is a series of conjectures that connects representations of algebraic groups over the adeles with number theory. The conference will focus on the local Langlands program, where one works with a p-adic field instead of a number field. The lectures will explore the representation theory of p-adic groups from a new perspective, that of noncommutative geometry and operator algebras. The lectures will introduce the notion of stratified equivalence, formulate the strong form of the ABPS Conjecture (Aubert, Baum, Plymen, Solleveld), and explain the role that asymptotic Hecke algebras are expected to play in the proof of the conjecture. Finally a strategy to construct the explicit local Langlands correspondence applicable for the p-adic group G2 and for all pure inner twists of classical p-adic groups will be described. The 10 principal lectures will be self-contained and accessible to students and non-experts.
This conference will expose early career researchers to cutting-edge research at the interface of applied mathematics and machine learning and also help identify new research directions and will foster the building of new collaborations between research groups in the Texas-Louisiana area and other regions. The 10 principal lectures will be divided into three modules. Module 1 consists of three introductory lectures on machine learning, e.g. deep neural networks and learning problems. The second module of three lectures will introduce important components of applied mathematics in machine learning, such as optimization and regularization. The last 4-lecture module will focus on the use of machine learning in critical problems in computational and applied mathematics, for example inverse problems and high dimensional partial differential equations. The principal lectures will be supplemented by a dozen contributed talks from participants, a poster session, a mentoring academic panel, and a panel that featuring researchers from industry.