## Programs & Events

##### 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 â€œnaive'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

##### 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

##### 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

##### 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

##### 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

##### 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.

##### 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

##### 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

##### 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 manyÂ 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.Â 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

##### VIRTUAL ONLY: Spectra LGBTQ+ in Mathematics Conference

Aug 18 - 20, 2021

Spectra, the Association for LGBTQ+ Mathematicians, was conceived in the last ten years with its first official event in 2015 -- a panel discussion at the JMM in San Antonio. Since then, Spectra has organized events at various conferences to bring together people of the LGBTQ+ community.

Spectra is organizing this conference to provide opportunities for LGBTQ+ mathematicians both to celebrate achievements and to spark conversations of challenges in our community. This will be a space for attendees to share their research across all areas of mathematics (theoretical, applied, and math education) and to interact and create support networks within and across their research communities.

Spectra is proud to organize its first official conference and create an intentional space for LGBTQ+ mathematicians. This will be an event where LGBTQ+ mathematicians at all career stages can interact and network with their peers. Further, it will facilitate discussions for creating better environments... (more)

##### Organizing Committee

- Rustum Choksi
- David Crombecque
- Alexander Hoover
- Brian Katz
- Freda Li
- Claire Plunkett
- Konstantina Trivisa
- Alexander Wiedemann

##### 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.

##### GirlsGetMath@ICERM: Summer Math Camp for High Schoolers

Aug 16 - 20, 2021

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 2021. (Exceptions made for existing 2020 applicant pool.)

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, matrix algebra, prime numbers and factoring, and fractals.

The goals of the program are:

- to show young... (more)

##### Organizing Committee

- Amalia Culiuc
- Katharine Ott
- Ulrica Wilson