## Programs & Events

##### 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

##### VIRTUAL ONLY: MAA - SIAM & TRIPODS Advanced Workshop in Data Science for Mathematical Sciences Faculty

Jun 28 - Jul 2, 2021

The MAA â€“ SIAM & TRIPODS Advanced Workshop in Data Science for Mathematical Sciences Faculty is a 5-day hands-on workshop for mathematical sciences faculty who have had some exposure to and experience with data science but who are not themselves data science experts. Participants of the 2017 or 2019 PIC Math Data Science Workshops that were held at BYU qualify and those who have experience coding in Python and applying basic statistical techniques to a large data set. The goal of the workshop is to bring together faculty from a range of institutions and expand the knowledge of the participants so that they are better armed to prepare students for the data science workforce.

Participants will learn more advanced techniques in the fields of data science, statistical learning, and machine learning. They will collaborate on data science projects that will involve accessing and cleaning large data sets... (more)

##### Organizing Committee

- Michael Dorff
- Deirdre L. Smeltzer
- Randy Paffenroth
- Suzanne Weekes

##### VIRTUAL ONLY: Computational Aspects of Discrete Subgroups of Lie Groups

Jun 14 - 18, 2021

This workshop is at the interface of algebra, geometry, and computer science. The major theme deals with a novel domain of computational algebra: the design, implementation, and application of algorithms based on matrix representations of groups and their geometric properties. The setting of linear Lie groups is amenable to calculation and modeling transformations, thus providing a bridge between algebra and its applications.

The main goal of the proposed workshop is to synergize and synthesize the independent strands in the area of computational aspects of discrete subgroups of Lie groups. We aim to facilitate solutions of theoretical problems by means of recent advances in computational algebra and additionally stimulate development of computational algebra oriented to other mathematical disciplines and applications.

##### Organizing Committee

- Alla Detinko
- Michael Kapovich
- Alex Kontorovich
- Peter Sarnak
- Richard Schwartz

##### Summer@ICERM 2021: Computational Polygonal Billiards

Jun 14 - Aug 6, 2021

Imagine creating career-building connections between peers, near peers (graduate students and postdocs), and academic professionals.

Imagine spending your summer in a fun, memorable, and intellectually stimulating environment.

Now, imagineÂ having this experience while being paid a $3,570 stipend. (Providence, RI room, board, and travel funding provided for in-person programming, pandemic permitting.)

The 2021 Summer@ICERM program at Brown University is an eight-week residential program designed for a select group of 18-22 undergraduate scholars.

The faculty advisers will present a variety of research projects on the theme of computational polygonal billiards and flat surfaces. This overarching theme will allow participants to use the theory of flat surfaces, along with the computational tools of pre-existing free... (more)

##### Organizing Committee

- Paul Apisa
- Diana Davis
- Samuel Lelièvre
- Jane Wang

##### VIRTUAL ONLY: Advances and Challenges in Hyperbolic Conservation Laws

May 17 - 21, 2021

In the field of hyperbolic conservation laws, theory, computation, and applications are deeply connected, with each one providing to the other two technical support as well as insights. Major progress has been achieved, over the past 40 years, on the theory and computation of solutions in one space dimension. By contrast, the multi-space dimensional case is still covered by mist, which is now gradually lifting, revealing new vistas. For instance, in two space dimensions, significant progress has been achieved in the study of transonic gas flow, of central importance to aerodynamics. Parallel progress has been reported on the numerical side, with the design of high-order accurate discontinuous Galerkin and finite volume computational schemes, even for multidimensional systems. Finally, we are witnessing an explosion in the applications, not only on the traditional turf of fluid dynamics but also in new directions, in materials science, biology, traffic theory, etc.

Nevertheless, the... (more)

##### Organizing Committee

- Alberto Bressan
- Gui-Qiang Chen
- Constantine Dafermos
- Fengyan Li
- Chi-Wang Shu
- Eitan Tadmor
- Konstantina Trivisa
- Dehua Wang

##### VIRTUAL ONLY: From Runge--Kutta methods to B-series

May 12, 2021

A short lecture and Q&A with John Butcher

In the early days of Runge-Kutta methods, 1895-1901, the numerical order of particular methods was found by working out the Taylor series for the solution of a generic scalar differential equation. By comparing this with the Taylor series for the Runge-Kutta result, the order of the approximation can be found. This approach was highly successful in finding methods up to order 4 but it became more and more complicated until eventually, in the 1950s, methods up to order 6 were found.

It was discovered, about that time, that the theory based on a scalar problem was not adequate, and a vector differential equation system had to be used as the test problem.

The theory, arising from this high-dimensional approach, has now become B-series analysis.

##### VIRTUAL ONLY: USTARS

Apr 29 - 30, 2021

The primary mission of the Underrepresented Students in Topology and Algebra Research Symposium (USTARS) is to showcase the excellent research conducted by underrepresented students studying topology and algebra. Dedicated to furthering the success of underrepresented students, USTARS seeks to broaden participation in the mathematical sciences by cultivating research and mentoring networks. USTARS is open to all people interested in the topological and algebraic fields.

A note from the organizing committee:

Applicants, for those wanting to give a talk at the conference there is an application deadline of February 26 at 11:59 pm for speakers in order to make a timely decision. We have funding from the NSA for some per diem for both days of the conference, which will also be decided from applicants who apply by the deadline. If you do receive funding, you are required to attend the entire conference.

##### Organizing Committee

- Robyn Brooks
- Ty Frazier
- Paige Helms
- Ryan Moruzzi Jr
- Anisah Nu’Man
- Christopher O'Neill
- Javier Ronquillo Rivera
- Sherilyn Tamagawa