Programs & Events
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
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
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: 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
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: 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: 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: 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
Summer@ICERM 2020: Fast Learning Algorithms for Numerical Computation and Data Analysis
Jun 8 - Jul 31, 2020
Imagine spending eight-weeks on the beautiful Brown University campus in historic Providence, RI, working in a small team setting to solve mathematical research problems developed by faculty experts in their fields.
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 with support for travel within the U.S., room and board paid, plus a $3,570 stipend*.
The 2020 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 interdisciplinary research... (more)
Organizing Committee
- Yanlai Chen
- Akil Narayan
- Minah Oh
VIRTUAL ONLY: Workshop on Arithmetic Geometry, Number Theory, and Computation
Jun 1 - 5, 2020
This program will host 9 collaborative groups led by invited project leaders, who will propose guiding research questions in consultation with the organizers. Individuals interested in contributing to a project or recommended by its leaders may apply via ICERM's online application system (Cube) to join the group.
In their personal statements, applicants should rank in order their top three choices of projects. Applications are currently under review.
Organizing Committee
- Jennifer Balakrishnan
- Noam Elkies
- Brendan Hassett
- Bjorn Poonen
- Andrew Sutherland
- John Voight
GirlsGetMath@ICERM: Summer Math Camp for High Schoolers
Aug 12 - 16, 2019
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 2019.
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 exciting,... (more)
Organizing Committee
- Amalia Culiuc
- Augustine O'Keefe
- Katharine Ott
- Ulrica Wilson
Applied Mathematical Modeling with Topological Techniques
Aug 5 - 9, 2019
Mathematical modelers face a variety of challenges, including summarizing large data sets to understand and explore a system of interest, inferring the model parameters most accurate for describing a given data set, and assessing the goodness-of-fit between data sets. Computational topology provides a lens through which these challenges may be addressed. At the same time, just as topological techniques provide opportunities for modelers, the challenges that modelers face give rise to opportunities for applied topologists. For instance, topologists may develop techniques that make model predictions based on the topology of experimental or simulation data, that analyze time-varying data, or that turn model outputs into formats suitable for machine learning.
This workshop brings together the applied mathematical modeling and applied topology communities, aiming to give modelers exposure to topological techniques still not commonly used in their community, and to give topologists exposure... (more)
Organizing Committee
- Henry Adams
- Maria D’Orsogna
- Rachel Neville
- Jose Perea
- Chad Topaz