A fundamental challenge that spans nearly all areas of evolutionary biology is the development of effective techniques for analyzing the unprecedented amount of genomic data that has become readily available within the last decade. Such data present specific challenges for the area of phylogenetic inference, which is concerned with estimating the evolutionary relationships among collections of species, populations, or sequences. These challenges include development of evolutionary models that are sufficiently complex to be biologically realistic while remaining computationally tractable; deriving and implementing algorithms to efficiently estimate phylogenetic relationships that use models whose theoretical properties are well-understood and therefore interpretable; and devising ways to scale novel methodology developed to handle datasets that are increasingly large and complex.

This semester program brings together mathematicians, statisticians, computer scientists, and experimental... (more)

Computational phylogenetic methods have become essential tools for understanding the evolutionary relationships that underlie much life science research. Motivated by biological questions and insights, built on a broad spectrum of mathematical and statistical ideas and approaches, and implemented through novel and sophisticated algorithmic design, their development draws from multiple fields. Bringing together researchers spanning disciplinary perspectives and techniques, this workshop will present a diverse sample of work addressing current challenges in phylogenetics, with an eye toward future progress.

The unprecedented amount of genomic data that has become readily available presents specific challenges for the field of phylogenetic inference, which is concerned with estimating the evolutionary relationships among collections of species, populations, or sequences. These challenges include the development of evolutionary models that are sufficiently complex to be biologically realistic while remaining computationally tractable; deriving and implementing algorithms to efficiently estimate phylogenetic relationships that use models whose theoretical properties are well-understood and therefore interpretable; and devising ways to scale novel methodology developed to handle datasets that are increasingly large and complex.

This workshop focuses on statistical modeling and the scaling of phylogenetic methods. Topics will include modeling (e.g. multispecies coalescent model with extension to networks; diversification models) and inference with speed to scale to genomic datasets,... (more)

The NSF Mathematical Sciences Institutes Diversity Committee hosts the 2024 Blackwell-Tapia Conference and Award Ceremony. The conference and prize honor Dr. David Blackwell, the first African-American member of the National Academy of Science, and Dr. Richard Tapia, winner of the National Medal of Science in 2010, two seminal figures who have inspired generations of Black, Latinx, and Indigenous students and researchers in the mathematical sciences.

The Blackwell-Tapia Prize recognizes a mathematical scientist who has made outstanding contributions to research in their field of expertise and served as a role model for mathematical scientists and students from underrepresented groups, or has contributed in significant ways to addressing the underrepresentation of minorities in math.

The 2024 recipient of the Blackwell-Tapia Prize is (more)

Inferring phylogenetic relationships requires complex mathematical models. As advances are made in modeling complex evolutionary processes, we need practical algorithms that translate the mathematical advances into software tools. This translation of theory to usable tools is more challenging than it may appear. Phylogenetic problems are often NP-hard, necessitating heuristic solutions that can compromise accuracy. The accuracy and scalability of such heuristics are often established only empirically, creating a need for careful simulation and testing. Moreover, software tools are used within complicated pipelines, so the input to tools may be impacted by errors from prior data processing steps. In addition, the output has many aspects, from the discrete-spaced topology to continuous-spaced branch lengths and other numeric parameters, and measures of uncertainty and visualizations. Furthermore, software tools need to be evolvable, allowing the incorporation of new features and new... (more)

In recent years, there has been a significant increase in the interaction between harmonic analysis and convex geometry, leading to solutions for several longstanding open problems, the discovery of new phenomena, and many new intriguing open questions. These connections were studied during the Fall 2022 Harmonic Analysis and Convexity Semester Program at ICERM. The objective of this workshop is to revisit and review the results produced during the semester and the subsequent year.

The primary areas of focus for the workshop will encompass the Fourier approach to geometric tomography; volume and duality; the Bellman technique for extremal problems in harmonic analysis; convexity of solutions to Hamilton–Jacobi–Bellman equations; as well as numerical computations and computer-assisted proofs. The workshop will explore the use of computational methods for theoretical aspects, including optimal algorithms, as well as practical... (more)

Reduced order modeling (ROM) has become an important tool in computational science for accelerating model-based simulations, including those governed by parametrized differential equations. Through the approximation of high-dimensional features with low-dimensional representations, ROM consists of proven strategies that build accurate emulators for the field or response of computationally expensive high-fidelity models using only a fraction of the simulation cost. In forward prediction or outer loop design and optimization, ROM has the potential to substantially improve the efficiency of current simulation-based techniques.

While ROM has seen considerable success in numerous applications, it continues to attract active research and development. This workshop showcases emerging frontiers in ROM by bringing together researchers whose core interests lie in model reduction and approximation theory, but who have also explored and developed novel methods that utilize various aspects of... (more)

Biological systems are typically highly interconnected and complex. With technological advances, it is possible to collect massive amounts of data from these systems, but it is not always clear how to organize the information to draw conclusions and make predictions. In such cases, mathematical formulations are powerful tools allowing researchers to frame questions, explore patterns, and synthesize information. Augmenting and expanding computational algorithms, machine learning algorithms, and data science techniques is necessary to keep pace with the complexity of the models needed for predictive modeling. The interdisciplinary nature of mathematical biology requires a variety of skills and facilitating interaction among research groups and institutions is important to moving the discipline forward.

The workshop aims to build research collaboration among researchers in mathematical biology. Participants will spend a week making significant progress on a research project and foster... (more)

The study of pattern formation in biological, ecological, physical, and social systems involves a rich interplay between theory, modeling, and computation. Analytical approaches using the theory of dynamical systems and partial differential equations have made powerful contributions to our understanding of nonlinear waves and patterns, yet many open questions remain in the study of higher-dimensional patterns and complex spatiotemporal behaviors. These analytical tools go hand-in-hand with computational methods, including numerical continuation and agent-based simulations. Together these approaches also complement empirical techniques, particularly in studies of biological pattern formation, leading to experimentally testable predictions and quantitative summaries of data.

In recent years, new opportunities have emerged for pattern detection and identification in applications using data-scientific approaches. These applications include spiral waves in cardiac dynamics, vegetation... (more)

Given an incidence structure, one may model a variety of geometric problems. This Semester Program will revolve around two fundamental examples and their applications to modern challenges in the study, analysis, and design of materials. (1) Packings and patterns of circles where the underlying combinatorics are mixed with advanced geometric concepts and strong links are made to discrete differential geometry. (2) The rigidity and flexibility of bar-joint structures where real algebraic geometry is intertwined with sparse graph theory and matroidal techniques. A prime objective of the program is to advance the applicability of these topics to fundamental applications, most notably in statistical physics and materials science.

The program will integrate diverse fields of discrete mathematics, geometry, theoretical computer science, mathematical biology, and statistical and soft matter physics. Various workshops will be designed to attract both theoretical and applied practitioners and... (more)

This workshop brings together researchers from three distinct streams of mathematics: the classical rigidity theory of bar-joint and tensegrity frameworks in combinatorics and discrete geometry; the theory of generalized circle packing that arose from the study of 3-manifolds in geometric topology, extending to sphere packing and jamming; and discrete differential geometry. A scattering of results in recent years has started to forge connections among these fields.

Since the discovery that circle packings from triangulations could be used as a scheme for approximating the Riemann mapping of a simply connected proper domain in the plane to the unit disk, the theory of circle packing has enjoyed enormous development and has found widespread theoretical and practical applications. In the theoretical realm, circle packing provides a discrete analytic function theory that is faithful to its continuous cousin and it is closely associated with studies of hyperbolic and projective polyhedra.... (more)