Cracking the neural code is one of the longstanding questions in neuroscience. How does the activity of populations of neurons represent stimuli and perform neural computations? Decades of theoretical and experimental work have provided valuable clues about the principles of neural coding, as well as descriptive understandings of various neural codes. This raises a number of mathematical questions touching on algebra, combinatorics, probability, and geometry. This workshop will explore questions that arise from sensory perception and processing in olfactory, auditory, and visual coding, as well as properties of place field codes and grid cell codes, mechanisms for decoding population activity, and the role of noise and correlations. These questions may be tackled with techniques from information theory, mathematical coding theory, combinatorial commutative algebra, hyperplane arrangements, oriented matroids, convex geometry, statistical mechanics, and more.

In the last decade or so, applied topology and algebraic geometry have come into their own as vibrant areas of applied mathematics. At the same time, ideas and tools from topology and geometry have infiltrated theoretical and computational neuroscience. This kind of mathematics has shown itself to be a natural and useful language not only for analyzing neural data sets but also as a means of understanding principles of neural coding and computation. This workshop will bring together leading researchers at the interfaces of topology, geometry, and neuroscience to take stock of recent work and outline future directions. This includes a focus on topological data analysis (persistent homology and related methods), topological analysis of neural networks and their dynamics, topological decoding of neural activity, evolving topology of dynamic networks (e.g., networks that are changing as a result of learning), and analysis of connectome data. Related topics may include the geometry and... (more)

Limits of discrete random structures appear in different areas of probability, combinatorics, and machine learning. In statistical mechanics, probabilistic and combinatorial techniques are applied to rigorously describe the scaling limits of such random graphical models, which are closely related to phase transitions. In the vicinity of a phase transition, even a tiny change in some local parameter can result in dramatic changes in the macroscopic properties of the entire system. Random discrete structures are also useful mathematical models of large networks, which play a central role in our social and economic lives as the fabric over which we interact, form social connections, conduct economic transactions, transmit information, propagate disease, and much more.

The goal of this workshop is to integrate the algebraic combinatorics, probability, and machine learning paradigms of statistical mechanical models and to bring together researchers in related fields to discuss recent... (more)

One of the fundamental questions in neuroscience is to understand how network connectivity shapes neural activity. Over the last 10 years, tremendous progress has been made in collecting neural activity and connectivity data, but theoretical advances have lagged behind. This workshop will focus on identifying mathematical challenges that arise in studying the dynamics of learning, memory, plasticity, decision-making, sequence generation, and central pattern generator circuits. Mathematical ideas and approaches from dynamical systems, statistical mechanics, linear algebra, graph theory, topology, and traditional areas of applied mathematics are all expected to play an important role.

The goal of this Semester Program is to bring together a variety of mathematicians with researchers working in theoretical and computational neuroscience as well as some theory-friendly experimentalists. However, unlike programs in neuroscience that emphasize connections between theory and experiment, this program will focus on building bridges between theory and mathematics. This is motivated in part by the observation that theoretical developments in neuroscience are often limited not only by lack of data but also by the need to better develop the relevant mathematics. For example, theorists often rely on linear or near-linear modeling frameworks for neural networks simply because the mathematics of nonlinear network dynamics is still poorly understood. Conversely, just as in the history of physics, neuroscience problems give rise to new questions in mathematics. In recent years, these questions have touched on a rich variety of fields including geometry, topology, combinatorics,... (more)

GirlsGetMath@ICERM is a five-day non-residential mathematics program that is open to high schoolers, regardless of gender, who live in or near greater Rhode Island and who will be entering the 10th or 11th grade in the fall of 2023.

GirlsGetMath occurs in an encouraging environment that builds young students' confidence in math and science.

GirlsGetMath expands participants' understanding and knowledge of mathematics through computations and experimentations.

GirlsGetMath provides expert mathematical training and mentoring.

GirlsGetMath@ICERM encourages 20-25 high schoolers to explore topics such as cryptography, the mathematics of voting, image processing, prime numbers and factoring, and fractals.

The goals of the program are:

• to show young adults that the study of mathematics can be exciting,... (more)

This workshop, a formal collaboration between ICERM and the American Institute of Mathematics (AIM), is one in a series of annual REUF workshops. These workshops bring together leading research mathematicians and faculty based at primarily undergraduate institutions to investigate open questions in the mathematical sciences and to equip participants with tools to engage in research with undergraduate students. REUF also serves to jump-start faculty who want to re-engage in research or who are considering a change in their research area.

The workshop will be hosted at ICERM.

The goals of this workshop are to promote undergraduate research and to forge research collaborations among the participating faculty. The majority of the workshop will be spent working on problems in small research groups, reporting on progress, and formulating plans for future work. Note that there are opportunities for participants to continue research activities beyond the workshop week, which will be... (more)

The aim of this reunion meeting is to bring together the participants from the spring 2021 program “Combinatorial Algebraic Geometry” bringing together experts in both pure and applied parts of mathematics as well mathematical programmers, all working at the confluence of discrete mathematics and algebraic geometry, with the aim of creating an environment conducive to interdisciplinary collaboration.

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... (more)

This workshop is designed to highlight the intersections between data science and social justice in K-16 education. The goals of this workshop are to 1) explore, and identify avenues to expand, current research on and methods for using data science in education; 2) raise awareness about research on issues of social justice in education and teaching pedagogy; and 3) work with community partners to create, evaluate and disseminate new K-16 curricular materials.

The week will focus on integrating computational social justice research methods, open problems, and best practices across different levels of training. Participants will collaborate on curating professional artifacts, such as: articulating collections of open problems in data science research in social justice; compiling a collection of computational social justice research projects; and developing course modules suitable for use in K-16 education. The results of these collaborations will be shared publicly by the organizers and... (more)

This will be a one-week conference broadly focused on the topics of the LMFDB, mathematical databases, computation, number theory, and arithmetic geometry. The conference will include invited talks, presentations by authors of papers submitted to the conference and selected by the scientific committee following peer-review, as well as time for research and collaboration. We plan to publish a proceedings volume that will include all of the accepted papers.

The organizers of the first conference on LMFDB, Computation, and Number Theory (LuCaNT) are excited to issue a call for papers for an associated proceedings volume to be published in an open access volume of Contemporary Mathematics. We strongly encourage anyone with research related to mathematical databases or computation to submit a paper here. The suggested length for papers... (more)

Mathematicians have studied elliptic curves for decades, owing to their beautiful abstract structure, powerful applications in number theory and algebraic geometry, and practical relevance in cryptography. It is surprising, therefore, that the so-called murmuration phenomenon was first observed in 2022.

Murmurations can be observed through studying databases of arithmetic and automorphic objects, rather than through studying individual objects. The availability of such databases facilitates the application of machine learning (ML) and other data scientific tools. Indeed, murmuration was first discovered by simply taking averages of certain elliptic curve datasets, and it has been shown that various invariants of arithmetic objects can be learned successfully through standard ML techniques such as logistic regression, random forest and neural networks with high (often greater than 95%) accuracy in classification. This approach opens up... (more)