Programs & Events
VIRTUAL ONLY: Lattice Point Distribution and Homogeneous Dynamics
Jun 22 - 26, 2020
In the last decade, there have been several important breakthroughs in Number Theory, where progress on long-standing open problems has been achieved by utilizing ideas originated in the theory of dynamical systems on homogeneous spaces, and their application to lattice point counting and distribution.
The aim of this workshop is to expose young researchers to these fields and provide them with the necessary background from dynamics, number theory, and geometry to allow them to appreciate some of the recent advancements, and prepare them to make new original contributions.
The workshop will include four mini-courses on the topics
1) Dynamics and lattice point counting 2) Thermodynamic formalism 3) Diophantine approximation 4) Fine-scale statistics in number theory and dynamics
In addition, there will be a number of research and expository talks. The talks will emphasize the role that computation and experiment have thus far played in stating key conjectures and establishing key... (more)
Organizing Committee
- Dubi Kelmer
- Alex Kontorovich
- Min Lee
VIRTUAL ONLY: Circle Packings and Geometric Rigidity
Jul 6 - 10, 2020
This workshop brings together two distinct streams of mathematics - on the one hand, the classical rigidity theory of bar-joint frameworks in combinatorics and discrete geometry, and on the other the theory of generalized circle packings that arose from the study of 3-manifolds in geometric topology.
Combinatorial and Geometric rigidity theory is concerned with the local and global uniqueness of congruence classes of frameworks as solutions to their underlying geometric constraint system.
The focal point of circle packing theory is the Koebe-Andre'ev-Thurston Theorem that gives conditions that guarantee the existence and rigidity of circle packings on closed surfaces in the pattern of a given triangulation of the surface.
A scattering of results in recent years has started to forge connections between these research areas. The main aim of the workshop is to develop a cross-fertilization of such ideas, with particular emphasis on the rigidity of inversive distance packings. As well... (more)
Organizing Committee
- Philip Bowers
- John Bowers
- Robert Connelly
- Steven Gortler
- Miranda Holmes-Cerfon
- Anthony Nixon
VIRTUAL ONLY: Geometry Labs United Conference
Jul 16 - 17, 2020
Experimental geometry labs create an environment ripe for students and faculty to treat mathematics as a laboratory science. Visualization and computational pattern discovery help guide research, formulate conjectures and develop ideas in proofs. In addition to research, experimental geometry labs foster community engagement via grassroots outreach activities in local schools, libraries, and museums. These activities spread the wonder and excitement of mathematics to people both within and outside the academy.
This workshop is partially supported by the Department of Mathematical Sciences and the College of Science at George Mason University.
For this workshop, ICERM welcomes applications from undergraduates, graduates, postdocs, and faculty who wish to participate. Undergraduate students and graduate students who apply should ask their advisor to submit a statement of support by July 3. We will ask students to present their work.
Organizing Committee
- William Goldman
- Sean Lawton
- Jack Love
- Anton Lukyanenko
VIRTUAL ONLY: Women in Algebraic Geometry
Jul 27 - 31, 2020
The Women in Algebraic Geometry Collaborative Research Workshop will bring together researchers in algebraic geometry to work in groups of 4-6, each led by one or two senior mathematicians. The goals of this workshop are: to advance the frontiers of modern algebraic geometry, including through explicit computations and experimentation, and to strengthen the community of women and non-binary mathematicians working in algebraic geometry. This workshop capitalizes on momentum from a series of recent events for women in algebraic geometry, starting in 2015 with the IAS Program for Women in Mathematics on algebraic geometry.
Successful applicants will be assigned to a group based on their research interests. The groups will work on open-ended projects in diverse areas of current interest, including moduli spaces and combinatorics, degenerations, and birational geometry. Several of the proposed projects extensively involve experimentation and computation, which will increase the likelihood... (more)
Organizing Committee
- Melody Chan
- Antonella Grassi
- Rohini Ramadas
- Julie Rana
- Isabel Vogt
VIRTUAL ONLY: Free Resolutions and Representation Theory
Aug 3 - 7, 2020
The structure of free resolutions plays an important role in analyzing singularities of varieties of low codimension. Codimension 2 Cohen-Macaulay varieties (resp. codimension 3 Gorenstein varieties) come from rank conditions on an n x (n+1) matrix (resp. a skew-symmetric (2n+1) x (2n+1) matrix).
This workshop seeks to push such results to Cohen-Macaulay varieties of codimension 3 and Gorenstein varieties of codimension 4.
This problem turns out to be related to the classification of semi-simple Lie algebras. These new methods allow one to create a âmapâ of free resolutions of a given format. The calculations that arise are very demanding and require new computational methods involving both commutative algebra and representation theory.
The organizers have shared two sets of notes for attendees to review before the workshop. These are downloadable here:
Organizing Committee
- Lars Christensen
- Claudia Miller
- Steven Sam
- Jerzy Weyman
ON-LINE MODULES OFFERED: GirlsGetMath: Summer Math Camp for High Schoolers
Aug 10 - 14, 2020
GirlsGetMath@ICERM is a five-day non-residential mathematics program that is open to high schoolers, regardless of gender identity, who live in or near greater Rhode Island and who will be entering the 10th or 11th grade in the fall of 2020.
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... (more)
VIRTUAL ONLY: Symmetry, Randomness, and Computations in Real Algebraic Geometry
Aug 24 - 28, 2020
Real algebraic (and semi-algebraic) geometry studies subsets of R^n defined by a finite number of polynomial equalities and inequalities. Such sets occur ubiquitously in practice both inside and outside of mathematics. While being easy to define, semi-algebraic sets can be complicated topologically, which restricts the application of many algorithms. In recent years, there has been progress in proving much stronger results â both quantitative and algorithmic -- when the problem under consideration involves the invariance under some group action.
In this workshop, we plan to focus on two situations where this phenomenon happens.
The first one is the statistical study of the topology of random real algebraic varieties as well as semi-algebraic sets, where the polynomials defining these objects are picked from a distribution invariant under the action of a certain group (usually the orthogonal group) acting on the space of variables. The behavior of the set of zeros (or more... (more)
Organizing Committee
- Saugata Basu
- Antonio Lerario
- Annie Raymond
- Cordian Riener
VIRTUAL ONLY: Monodromy and Galois groups in enumerative geometry and applications
Aug 31 - Sep 2, 2020
Galois groups encode the internal structure of field extensions. Less well-known is that (families) of systems of polynomial equations or geometric problems also have Galois groups that encode the internal structure of the equations or geometric problems. During the 2018 Fall program at the ICERM on Nonlinear Algebra, different groups of researchers who were studying or using Galois groups in their work became more aware of their related interests. This common thread connects recent work in enumerative geometry, statistics, computer vision, number theory, and numerical nonlinear algebra. Further connections have subsequently been realized to arithmetic enhancements of intersection theory and to random real algebraic geometry. This workshop will bring representatives of these research groups together to deepen these interactions and chart new research goals.
This workshop is fully funded by a Simons Foundation Targeted Grant to Institutes.
Organizing Committee
- Alexander Esterov
- Jose Rodriguez
- Frank Sottile
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, imagine 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: 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
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: 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 Hairerâs 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