Inverse Problems are problems where causes for a desired or an observed effect are to be determined. They lie at the heart of scientific inquiry and technological development. Applications include a number of medical as well as other imaging techniques, location of oil and mineral deposits in the earth's substructure, creation of astrophysical images from telescope data, finding cracks and interfaces within materials, shape optimization, model identification in growth processes and, more recently, modelling in the life sciences.

The workshop will consist of several minicourses addressing several of the theoretical and practical issues arising in inverse problems including boundary rigidity and travel time tomography, cloaking and invisibility, electrical impedance imaging, statistical methods and biological applications, thermoacoustic and x-ray tomography, and resonances.

The goal of this workshop is two-fold: (1) to describe many of the recent advances that have been made in the application of random matrix theory to problems in mathematics and physics (2) to develop some of the mathematical tools that are needed to enter the field. Applications of random matrix theory are now being made to number theory, combinatorics, statistical physics and statistics amongst other fields. The techniques employed in the field include methods from integrable systems, combinatorics, complex analysis, orthogonal polynomials and of course random matrix theory per se.

Toric varieties are algebraic varieties defined by combinatorial data, and there is a wonderful interplay between algebra, combinatorics and geometry involved in their study. Many of the key concepts of abstract algebraic geometry (for example, constructing a variety by gluing affine pieces) have very concrete interpretations in the toric case, making toric varieties an ideal tool for introducing students to abstruse concepts.

Teaching Undergraduates Mathematics will be the sixth in a series of Critical Issues in Education workshops hosted by the Mathematical Sciences Research Institute (MSRI) in Berkeley, CA. Whereas previous workshops focused on K-12 education and teacher education, this workshop will focus on undergraduate education.

Themes: Carbon cap-and-trade and economic consequences; Game theory and self-enforcing treaties; Economic mechanisms and incentive for greenhouse gas emission reductions.

This conference will bring together experienced math circle directors and professional mathematicians along with secondary school teachers and students, with the three- fold goal of inspiring and equipping individuals to begin math circles in their communities, passing along successful math circle presentations and best practices in math circle administration, and renewing and strengthening ties among members of the existing math circle network.

The goal of the conference is to bring individuals from genetics and the mathematical sciences into closer contact so that they might share objectives and skills needed to advance both areas, and especially their intersection.

This workshop will present the state of the art in combinatorial, enumerative, and toric algebraic geometry. It
will highlight this part of modern algebraic geometry within the context of the broader parent program at MSRI, and convey its scope to young researchers.

This workshop features numerous hands on introductory tutorials about Sage, and the interface between Sage and Macaulay2. There were discussions and talks about doing algebraic geometry with both Sage and Macaulay2, and the unique advantages of both systems. There were also talks about working with lattice polytopes and doing Lie theory in Sage. In addition to the talks and tutorials, we had numerous coding sprints.

This workshop will convene experts specializing on the minimal model program, derived categories and moduli
spaces in an informal environment to facilitate the cross-fertilization of ideas across these different fields of algebraic geometry.
 

The main theme of the workshop will be to explore modern approaches to
problems originating in Classical Algebraic Geometry, and at the same time
offer an introduction to various subfields to the younger participants in
the semester-long program.