Programs & Events
A Virtual ICERM Public Lecture: Hidden Narratives in Mathematics - The Power of Storytelling
Aug 18, 2021
Behind every famous theorem, every new research area, every classroom, and every individual, there is a mathematical story. Many of the stories we learn inspire us to persist, to imagine ourselves as thriving members of a quantitative community, and to contextualize how mathematics shows up in the world around us. In this lecture, we invite you to consider your own mathematical story and the ones that have impacted you. Upon reflection, which mathematical stories have been elevated, and which stories remain hidden?
We invite you to explore how storytelling that centers diversity, inclusion, and community in mathematics can lead us down interesting paths of mathematical discovery and understanding. Join Dr. Edmonds to learn how her research into Hidden Figures in mathematics led to a newfound love of slide rules, an appreciation for aeronautics, a first introduction to fractals, and an interesting group of mathematicians determined to do away with determinants in linear algebra.
VIRTUAL ONLY: Prediction and Variability of Air-Sea Interactions: the South Asian Monsoon
Aug 23 - 27, 2021
A challenge for mathematical modeling, from toy dynamical system models to full weather and climate models, is applying data assimilation and dynamical systems techniques to models that exhibit chaos and stochastic variability in the presence of coupled slow and fast modes of variability. Recent collaborations between universities and government agencies in India and the United States have resulted in detailed observations of oceanic and atmospheric processes in the Bay of Bengal, the Arabian Sea, and the Indian Ocean, collectively observing many coupled modes of variability. One key target identified by these groups was the improvement of forecasts of variability of the summer monsoon, which significantly affects agriculture and water management practices throughout South Asia. The Monsoon Intraseasonal Oscillation is a northward propagating mode of precipitation variability and is one of the most conspicuous examples of coupled atmosphere-ocean processes during the summer... (more)
Organizing Committee
- Baylor Fox-Kemper
- Jennifer MacKinnon
- Hyodae Seo
- Emily Shroyer
- Aneesh Subramanian
- Amit Tandon
Hamiltonian Methods in Dispersive and Wave Evolution Equations
Sep 8 - Dec 10, 2021
Dispersive equations are ubiquitous in nature. They govern the motion of waves in plasmas, ferromagnets, and elastic bodies, the propagation of light in optical fibers and of water in canals. They are relevant from the ocean scale down to atom condensates. There has been much recent progress in different directions, in particular in the exploration of the phase space of solutions of semilinear equations, advances towards a soliton resolution conjecture, the study of asymptotic stability of physical systems, the theoretical and numerical study of weak turbulence and transfer of energy in systems out of equilibrium, the introduction of tools from probability and the recent incorporation of computer assisted proofs. This semester aims to bring together these new developments and to explore their possible interconnection.
Dispersive phenomena appear in physical situations, where some energy is conserved, and are naturally related to Hamiltonian systems. This semester proposes to explore... (more)
Organizing Committee
- Diego Cordoba
- Erwan Faou
- Patrick Gerard
- Pierre Germain
- Alexandru Ionescu
- Alex Kiselev
- Andrea Nahmod
- Kenji Nakanishi
- Benoit Pausader
- Themistoklis Sapsis
- Gigliola Staffilani
Numerics, Modeling, and Experiments in Wave Phenomena
Sep 20 - 24, 2021
The workshop will be devoted to the analysis of wave phenomena from different perspectives: mathematical modeling and analysis, experimental physics, and numerical analysis. One of the goals of this event is to gather scientists coming from a priori distant communities but sharing a common interest in wave propagation phenomena in a broad sense (fluid mechanics, quantum mechanics, plasma physics, rigorous analysis). We plan to focus on various themes representing topical problems in these fields, from experimental reproduction of physical phenomena, numerical issues, to the most recent rigorous mathematical results.
In experimental physics, several topics will be addressed, from rogues waves and wave breaking phenomena, vortex filaments, to wave turbulence in fluids or in acoustics. The analysis of observational and experimental data, combined with PDE physical models also yields the question of data assimilation and machine learning technics in the context of wave propagation. The... (more)
Organizing Committee
- Diego Cordoba
- Emmanuel Dormy
- Erwan Faou
- Themistoklis Sapsis
- Luis Vega
A Virtual ICERM Public Lecture: More data, more problems - Double-dipping in statistics
Sep 22, 2021
In recent years, the availability of huge amounts of data across virtually all fields has ushered in an entirely new way of thinking about and using data. The scientific method --- and classical statistics --- involves formulating a hypothesis, and then testing that (pre-specified) hypothesis on some data. However, as datasets have continued to grow in size, the goal of data generation has increasingly moved away from using data to test a pre-specified hypothesis. Instead, people use data to generate new hypotheses and then test those hypotheses on the same data. Unfortunately, classical statistical methods do not apply when the same data are used for hypothesis generation and hypothesis testing. In this talk, I'll show what can go wrong when people engage in this sort of "double-dipping". I will also present some solutions, using the new statistical framework of selective inference.
Generic Behavior of Dispersive Solutions and Wave Turbulence
Oct 18 - 22, 2021
The large-time behavior of (generic) solutions of nonlinear dispersive equations set on bounded domains is almost completely open as far as rigorous analysis goes, and fairly mysterious, even from a less rigorous viewpoint. Under the assumption of weak nonlinearity, physicists and applied mathematicians have devised a theory to approach this question, known as weak turbulence, a branch of statistical physics. Weak turbulence theory predicts that the equation will enter a chaotic regime, where the exchange of energy in phase space is governed by the so-called kinetic wave equation. Justifying the derivation of the kinetic wave equation is a fascinating mathematical task, for which some results are already known, but whose solution will likely require input from nonlinear PDEs, but also probability theory. Intimately related questions are the question of Sobolev growth (how much can or does, the Sobolev norm of a nonlinear dispersive equation grow over time), as well as the analysis of... (more)
Organizing Committee
- Patrick Gerard
- Pierre Germain
- Alex Kiselev
- Andrea Nahmod
Foam Evaluation
Nov 5 - 7, 2021
The purpose of this workshop is to bring together mathematicians interested in foams and their use in low-dimensional topology, representation theory, categorification, mathematical physics, and combinatorics. The workshop will focus on the foam evaluation formula and its applications. More concretely, we aim to:
(a) Give a more intrinsic definition of the foam evaluation, in order, for instance, to find similar formulas for the other Lie types;
(b) Understand the interplay between foams and matrix factorizations and further use foams for a unified and comprehensive approach to Khovanov-Rozansky link homology theories;
(c) Compare combinatorial foam evaluation with the geometric structures and invariants coming from gauge theory and symplectic geometry;
(d) Study potential applications of the foamy definition of link homology theories.
This workshop is fully funded by a Simons Foundation Targeted Grant to Institutes.
Organizing Committee
- Mikhail Khovanov
- Aaron Lauda
- Louis-Hadrien Robert
Hamiltonian Methods and Asymptotic Dynamics
Dec 6 - 10, 2021
Recent progress in the analysis of dispersive PDE's has revealed various aspects of long-time dynamics or behavior of solutions, from the basic three types (scattering, blow-up, and solitons) to more complicated combinations, transitions, and oscillations among them, and so on. The goal of this workshop is for the participants to draw integrated landscapes of those diverse phenomena, aiming towards more a complete description, classification, and prediction of global dynamics, as well as new phenomena and methods.
Organizing Committee
- Alexandru Ionescu
- Yvan Martel
- Kenji Nakanishi
- Monica Visan
Geometric and Topological Methods in Data Science
Dec 16 - 17, 2021
The goal of this meeting is to bring together researchers using geometric and topological methods to study data. Fields of interest include manifold learning, topological data analysis, neural networks, and machine learning. While this plan is to focus on the mathematics, applications to neuroscience and quantitative biology will also be explored.
Organizing Committee
- Ian Adelstein
- Jeffrey Brock
- Smita Krishnaswamy
- Bjorn Sandstede
Holistic Design of Time-Dependent PDE Discretizations
Jan 10 - 14, 2022
The workshop aims to spur a holistic approach to the design of time-dependent PDE discretizations, particularly in terms of developing time integration techniques that are intertwined with spatial discretization techniques, focusing on: generalized ImEx methods, asymptotic-preserving and structure-preserving methods, methods that exploit low-rank dynamics, analysis of order reduction, parallel in time methods, and performant, maintainable, extensible software implementations.
Recent decades have seen increasing use of first-principles-based simulations via time-dependent partial differential equations (PDE), with applications in astrophysics, climate science, weather prediction, marine science, geosciences, life science research, defense, and more. Growing computational capabilities have augmented the importance of sophisticated high-order and adaptive methods over ânaive'â low-order methods. However, there are fundamental challenges to achieving truly high order and full... (more)
Organizing Committee
- David Ketcheson
- David Keyes
- Michael Minion
- Jingmei Qiu
- Benjamin Seibold
- Carol Woodward
Braids
Feb 1 - May 6, 2022
Braid groups were introduced by Emil Artin almost a century ago. Since then, braid groups, mapping class groups, and their generalizations have come to occupy a significant place in parts of both pure and applied mathematics. In the last 15 years, fields with an interest in braids have independently undergone rapid development; these fields include representation theory, low-dimensional topology, complex and symplectic geometry, and geometric group theory. Braid and mapping class groups are prominent players in current mathematics not only because these groups are rich objects of study in their own right, but also because they provide organizing structures for a variety of different areas. For example, in modern representation theory, important equivalences of categories are organized into 2-representations of braid groups, and these same 2-representations appear prominently in parts of geometry and mathematical physics concerned with mirror dualities; in low-dimensional topology,... (more)
Organizing Committee
- Marc Culler
- Ben Elias
- John Etnyre
- Benson Farb
- Juan González-Meneses
- Matthew Hedden
- Keiko Kawamuro
- Joan Licata
- Anthony Licata
Research Community in Algebraic Combinatorics
Feb 10 - 11, 2022
The Women in Algebraic Combinatorics Research Community will bring together researchers at all stages of their careers in algebraic combinatorics, from both research and teaching-focused institutions, to work in groups of 4-6, each directed by a leading mathematician. The goals of this program are: to advance the frontiers of cutting-edge algebraic combinatorics, including through explicit computations and experimentation, and to strengthen the community of women working in algebraic combinatorics.
Successful applicants will be assigned to a group based on their research interests. The groups will work on open problems in algebraic combinatorics and closely related areas, including representation theory, special functions, and discrete geometry. Several of the proposed projects will extensively involve experimentation and computation, which will increase the likelihood that concrete progress is made over the course of the initial workshop and following 6 months, and provide useful... (more)
Organizing Committee
- Susanna Fishel
- Pamela E. Harris
- Rosa Orellana
- Stephanie van Willigenburg