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ICERM

Discrete periodic Schrodinger operators describe the behavior of individual electrons in "ideal" crystals in the tight-binding model of solid state physics. Spectra of such operators have the usual band-gap structure, and the corresponding dispersion relations are algebraic varieties. In the 1990's Gieseker, Knorrer, and Trubowitz used toroidal compactifications to solve questions such as irreducibility of Bloch and Fermi varieties and the density of states, for a class of mono-atomic models. Their work showed that while spectral theory is focused on the real part of the Bloch variety, the study of complex singularities and compactifications is crucial for describing formation of bands and gaps. After a gap of 30 years, spectral theory is again interacting with algebraic geometry. Recently, W. Liu gave an algebraic method to obtain more general proofs of irreducibility for Fermi surfaces, Kravaris used free resolutions to study density of states, and Kuchment and coauthors used toric varieties and numerical nonlinear algebra to study spectral edges. These and other developments have led to the realization that many open questions in spectral theory may be studied using modern tools in algebraic geometry. These include the relation of reducibility/irreducibility with physical symmetries of the crystals, the structure of spectral band edges, and Dirac cones. These methods can also be applied to quantum graphs, such as graphene-type structures, and to obtain existence and non-existence theorems for embedded eigenvalues. The goal of this workshop is to bring together experts from spectral theory, mathematical physics, and algebraic geometry to understand, apply, and advance these new methods and interactions. A significant aspect of these reemerging interactions involves computation. A key recent development in algebraic geometry is computation, both symbolic and numerical. Computation and experimentation using tools from algebraic geometry have already been important in two recent papers by Sottile on this subject, and we expect it to become a useful tool for studying periodic operators. Speakers in this workshop are firmly rooted in the uses of computation and experimentation in applications of Algebraic Geometry, and many are familiar with exploiting the atmosphere and facilities of the ICERM to initiate collaboration.

Program Staff;     Tel.: [1-401-863-5030];     Email: programstaff@icerm.brown.edu

Geometrie und Topologie,    Algebra

American Institute of Mathematics (AIM)

This workshop, sponsored by AIM and the NSF, will be devoted to the modeling of malaria to assess the role of heterogeneity in disease dynamics. Malaria is one of the deadliest infectious diseases globally, causing hundreds of thousands of deaths each year. Since the early 1900s, mathematical modeling has been a critical component of malaria research, suggesting optimal interventions

The main topics for the workshop are: Modeling the generation, emergence, and persistence of malaria parasite diversity; Describing the emergence and spread of drug resistance in parasite populations and insecticide resistance in mosquito populations, and the impact on disease spread; Building a framework to understand age-structured immune profiles and their variability with human movement; Quantifying the impact of immunity and parasite diversity on drug resistance evolution.

Society for Industrial and Applied Mathematics (SIAM)

Numerische Analysis,    Algorithmen und Datenstrukturen

Society for Industrial and Applied Mathematics (SIAM)

ICERM

MSML2023 is the third edition of a newly established conference, with emphasis on promoting the study of mathematical theory and algorithms of machine learning, as well as applications of machine learning in scientific computing and engineering disciplines. This conference aims to bring together the communities of machine learning, applied mathematics, and computational science and engineering, to exchange ideas and progress in the fast-growing field of scientific machine learning (SciML).

Program Staff;     Tel.: [1-401-863-5030];     Email: programstaff@icerm.brown.edu

The objective of this annual conference series is to promote the study of: Theory and algorithms of machine learning. Applications in scientific and engineering disciplines such as physics, chemistry, material sciences, fluid and solid mechanics, etc. To provide hands-on tutorials for students and new researchers in the field.

American Institute of Mathematics (AIM)

This workshop, sponsored by AIM and the NSF, will be devoted to solving open problems regarding the stability of nonlinear waves using computer assisted methods of proof. Some results using computer assisted methods of proof include Hilbert's 18th problem and Smale's 14th problem. Researchers have developed efficient methods for obtaining rigorous error bounds for numerical approximations of heteroclinic and homoclinic connections between fixed points in ODE systems. These rigorous computation methods establish the existence and uniqueness of the solution in addition to providing a tight, completely rigorous error bound. Thus, these rigorous computations can be used to prove Theorems. Similarly, researchers have developed efficient and robust numerical methods for computing quantities that relay information about the spectral stability of one-dimensional traveling wave solutions to PDEs, which in turn yields information regarding the nonlinear stability. This workshop will help researchers identify collaborative opportunities to use rigorous computation to prove theorems regarding open problems in nonlinear wave theory.

Computer assisted proofs for stability analysis of nonlinear waves. Stability of multi-dimensional non-planar traveling waves. Rigorous computation of center manifolds

Analysis,    Computer-gestütztes Beweisen

Society for Industrial and Applied Mathematics (SIAM)

ICERM

The field of mathematical and computational biology is rapidly growing. The most applicable computational models have been developed in collaboration between computational and life science researchers. This workshop aims to bring these groups together to facilitate and promote collaborations among them. A mathematical model for one disease might also be useful in modeling another disease. Some researchers are working on theoretical mathematical & statistical problems related to biological and biomedical applications, while others are developing computational methodologies to address fundamental life science knowledge gaps. This workshop fosters and features collaborations among these groups along with experimentalists and physicians. Theoreticians will be exposed to a variety of open biological questions in need of state-of-the-art and efficient mathematical methods. Computational scientists will learn about more robust and efficient methods that could be tailored to answer biological problems.

Program Staff;     Tel.: [1-401-863-5030];     Email: programstaff@icerm.brown.edu

Mathematical Sciences Research Institute (MSRI)

The school will provide the mathematical and theoretical computer science toolbox that forms the foundation of market and mechanism design - two of the burning research areas of the 21st century. Market and mechanism design are beautiful examples of how deep mathematical theory can lead to improved design of real-world marketplaces and auctions. We shall consider the algorithmic, complexity, economic and societal aspects of these topics.

ICERM

In Summer 2023, ICERM hosts the second of two summer programs entitled The Social Justice and Data Science Summer Research Program. This program aims to increase interest, research training, and capacity for data science for social justice, and to develop both quantitative and qualitative approaches to those professional practices that call for community engagement, critical inquiry, and interdisciplinary cooperation. Building off of Summer 2022's program, which included a workshop on network science and analysis as well as foundational conversations with community partners, the Summer 2023 program will advance the mathematics community's understanding of the complexity of computational social justice work through three emphasis areas (1) policy, (2) education, and (3) community-driven research. As a new field emerges at the face of computational and applied mathematics and social justice, this requires new methods for working across community lines. In order to address the novel and interdisciplinary problems arising out of community needs, participants will work together to develop new or refine existing computational methods whose applications may be broader than the original problem. The organizers are committed to working with humility and in solidarity with one another and with the local community. The program will include engagement with the local community and invest in the education of the next generation of researchers by driving the development and direction of new computational methods for quantitative social justice research. Researchers with expertise and interests in using mathematical models and/or data science to examine social justice issues in policy and/or education are particularly encouraged to apply. The organizers also seek applications from researchers with specialties in digital humanities, computational social science, and data science education.

Program Staff;     Tel.: [1-401-863-5030];     Email: programstaff@icerm.brown.edu

Wissenschaftliches Rechnen und Datenwissenschaft,    Numerische Analysis

ICERM

The mathematical and computational toolbox for modern experimental and engineering problems has become more diverse than ever before, with a flurry of new challenges in inverse problems and successful practical solutions that present further theoretical questions. In the spirit of the 2012 “Challenges in Geometry, Analysis, and Computation: High-Dimensional Synthesis” workshop at Yale, the “Modern Applied and Computational Analysis” workshop will be a celebration of different perspectives on inverse problems, models, inference, and harmonic analysis and a debate about the challenges and opportunities in the next decade of applied analysis. The topics include inverse problems, randomized linear algebra, machine learning in applied analysis, and tensor networks.

Program Staff;     Tel.: [1-401-863-5030];     Email: info@icerm.brown.edu

ICERM

Solving systems of nonlinear equations and optimization problems are pervasive issues throughout the mathematical sciences with applications in many areas. Acceleration and extrapolation methods have emerged as a key technology to solve these problems efficiently and robustly. The simple underlying idea of these methods is to recombine previous approximations in a sequence to determine the next term or approximation. This approach has been applied repeatedly and from different angles to numerous problems over the last several decades. Important methods including epsilon algorithms and Anderson acceleration were introduced throughout the early and mid-20th century, and are now common in many applied fields including optimization, machine learning, computational chemistry, materials, and climate sciences. Within the last decade, theoretical advances on convergence, acceleration mechanisms, and the development of unified frameworks to understand these methods have come to light, yet our understanding remains incomplete. Fascinating links exist with methods such as Nesterov acceleration and other momentum-based approaches that have been developed in the fields of optimization and machine learning in the past decades. These links and connections with dynamical systems appear to be promising directions for further insight that remain largely unexplored. The goals of this workshop include assessing the state of the art and exploring connections between closely related methods that may have been independently developed; connecting theory to practice by fostering interaction between theorists and applied practitioners; and, encouraging new and continuing collaborations between participants.

Program Staff;     Tel.: [1-401-863-5030];     Email: programstaff@icerm.brown.edu

Society for Industrial and Applied Mathematics (SIAM)

The SIAM Annual Meeting provides a broad view of the state of the art in applied mathematics, computational science, and their applications through invited presentations, prize lectures, minitutorials, minisymposia, contributed presentations and posters.

Society for Industrial and Applied Mathematics (SIAM)