## Programs & Events

##### 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

##### 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

##### 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: 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

##### 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

##### VIRTUAL ONLY: D-modules, Group Actions, and Frobenius: Computing on Singularities

Aug 9 - 13, 2021

The adoption of D-module techniques has transformed the interface between commutative algebra and algebraic geometry over the last two decades. The discovery of interactions and parallels with the Frobenius morphism has been an impetus for many new results, including new invariants attached to singularities but also D- and F-module based algorithms for computing quantities that used to be unattainable.

Our goal for this workshop is to discuss computational aspects and new challenges in singularity theory, focusing on special varieties that arise from group actions, canonical maps, or universal constructions. By bringing together geometers, algebraists, and invariant theorists, we will address problems from multiple perspectives. These will include comparisons of composition chains for D- and F-modules, the impact of group actions on singularity invariants, and the structure of differential operators on singularities in varying characteristics.

##### Organizing Committee

- Christine Berkesch
- Linquan Ma
- Claudia Miller
- Claudiu Raicu
- Uli Walther

##### VIRTUAL ONLY: Research Community in Algebraic Combinatorics

Aug 5 - 6, 2021

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

##### VIRTUAL ONLY: Workshop on Advances in Theory and Algorithms for Deep Reinforcement Learning

Aug 2 - 4, 2021

There has been significant progress over the last few years in the theory and applications of Reinforcement Learning (RL). While RL theory and applications have had a rich history going back several decades, the major recent successes have occurred due to a successful marriage between deep learning approaches for function approximation embedded within a reinforcement learning framework for decision-making (Deep RL). On one hand, there has been a richer understanding of Stochastic Gradient Descent (SGD) for non-convex optimization, its impact in driving training error to zero in deep neural networks, and on the generalization ability of such networks for inference. On the other hand, there has been an explosion of research on iterative learning algorithms with strong statistical guarantees in the settings of reinforcement learning, stochastic approximation and multi-armed bandits.

This workshop aims to bring leading researchers from these two threads, with the goal of understanding... (more)

##### Organizing Committee

- Nan Jiang
- Sanjay Shakkottai
- R. Srikant
- Mengdi Wang

##### A Virtual ICERM Public Lecture: Knotty Knits and Evening of Math and Crafts

Jul 28, 2021

Dr. Sabetta Matsumoto from Georgia Institute of Technology will be discussing creative crafts and math research. What can physics learn from crochet? How does a simple stitch change the stretch of a scarf, and how are modern materials and manufacturing learning from their wooly ancestors? Join Dr. Matsumoto for a talk about curvature using pattern making, symmetries using quilt squares and flags, hyperbolic space using quilting at crochet, and knot theory and coding using knits.

Dr. Sabetta Matsumoto is an Assistant Professor in the School of Physics at the Georgia Institute of Technology. She is passionate about using textiles, 3D printing, and virtual reality to teach geometry and topology to the public.

##### VIRTUAL ONLY: Applications of Rough Paths: Computational Signatures and Data Science

Jul 6 - 9, 2021

Rough path theory emerged as a branch of stochastic analysis to give an improved approach to dealing with the interactions of complex random systems. In that context, it continues to resolve important questions, but its broader theoretical footprint has been substantial. Most notable is its contribution to Hairerâ€™s Fields-Medal-winning work on regularity structures. At the core of rough path theory is the so-called signature transform which, while being simple to define, has rich mathematical properties bringing in aspects of analysis, geometry, and algebra. Hambly and Lyons (Annals of Math, 2010) built upon earlier work of Chen, showing how the signature represents the path uniquely up to generalized reparameterizations. This turns out to have practical implications allowing one to summarise the space of functions on unparameterized paths and data streams in a very economical way.

Over the past five years, a significant strand of applied work has been undertaken to exploit the... (more)

##### Organizing Committee

- Thomas Cass
- Terry Lyons
- Hao Ni
- Harald Oberhauser
- Mihaela van der Schaar