## Programs & Events

##### 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 â€˜mapâ€™ 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

- John Bowers
- Philip 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

##### VIRTUAL ONLY: Competitive Equilibrium with Gross Substitutes, with Applications to Problems in Matching, Pricing, and Market Design

May 11 - 12, 2020

**A short history of equilibrium computation**. The computation of economic equilibrium is making a
spectacular comeback in economics, mathematics and computer science. The availability of massive
real-time datasets and the affordability of computing power, including parallel computation, has made it
possible to implement and build on an effort that had been stalled since the end of the 1970s. But even
more than the new technical possibilities, it is the novel applications to online platforms and market
design tools that led to the surge of interest in computation. Pricing engines like Uberâ€™s, matchmakers
like OkCupid, allocation mechanisms like those that are used by public school districts â€“ all need to
compute an equilibrium problem.

While the problem of equilibrium computation is hard in general, a particular instance of the problem, namely the gross substitutes property, makes it analytically tractable and computable in practice, while able to cover a large number of... (more)

##### Organizing Committee

- Gabrielle Demange
- Alfred Galichon
- Robert Mccann
- Larry Samuelson

##### VIRTUAL ONLY: Variable Precision in Mathematical and Scientific Computing

May 7 - 8, 2020

From its introduction in the 1980s, the IEEE-754 standard for floating-point arithmetic has ably served a wide range of scientists and engineers. Even today, the vast majority of numerical computations employ either IEEE single or IEEE double, typically one or the other exclusively in a single application. However, recent developments have exhibited the need for a broader range of precision levels, and a varying level of precision within a single application. There are clear performance advantages to a variable precision framework: faster processing, better cache utilization, lower memory usage, and lower long-term data storage. But effective usage of variable precision requires a more sophisticated mathematical framework, together with corresponding software tools and diagnostic facilities.

At the low end, the explosive rise of graphics, artificial intelligence, and machine learning has underscored the utility of reduced precision levels. Accordingly, an IEEE 16-bit "half"... (more)

##### Organizing Committee

- David Bailey
- Neil Burgess
- Jack Dongarra
- Alyson Fox
- Jeffrey Hittinger
- Cindy Rubio-González

##### VIRTUAL ONLY: Computational Statistics and Data-Driven Models

Apr 20 - 24, 2020

The advancement in computing and storage capabilities of modern computational clusters fosters use of novel statistical techniques in machine learning and deep networks. Such data-driven techniques allow one to learn model features and characteristics that are difficult for mathematical methods alone to reveal. Many computational methods achieve model and complexity discovery using methods that lie at the nexus of mathematical, statistical, and computational disciplines. Statistical methods often employ “big data” approaches that glean predictive capability from diverse and enormous databases of information. Emerging methods in machine learning and deep networks can provide impressive results. This workshop gathers researchers at the frontier of large-scale statistical computation, data science, tensor decompositions and approximations, and data-driven model learning, to focus on modern challenges that use data to reduce complexity of models.

##### Organizing Committee

- Lexin Li
- Youssef Marzouk
- Shari Moskow
- Benjamin Peherstorfer
- Abel Rodriguez
- Daniele Venturi
- Rachel Ward

##### VIRTUAL ONLY: Algorithms for Dimension and Complexity Reduction

Mar 23 - 27, 2020

Mathematical advances that reduce the complexity of models are complemented by algorithms that achieve the desired reduction in computational effort. This workshop focuses on the synthesis and development of algorithmic approaches to model order reduction. These methods tackle fundamental problems in structure- and topology-preserving reductions, low-rank models and dimension reduction, multi-level approaches, and empirical interpolation and approximations, etc. Complementary approaches that target computational efficiency include strategies with offline and online phases and divide-and-conquer algorithms.

##### Organizing Committee

- Kevin Carlberg
- Yanlai Chen
- Francisco Chinesta
- Misha Kilmer
- Yvon Maday
- Gianluigi Rozza

##### Soergel Bimodules and Categorification of the Braid Group

Feb 28 - Mar 1, 2020

The purpose of this workshop is to bring together experts in representation theory, categorification, low-dimensional topology, mathematical physics, and combinatorics, in order to understand how categorifications of the braid groups and Hecke algebras allow one to compute and understand link invariants. Our concrete goals are to:

(a) develop and compare various algebro-geometric models for link homology, and use them to explicitly compute Khovanov-Rozansky homology of various links

(b) categorify various structures in the Hecke algebra (center, cocenter, Kazhdan-Lusztig cells, Jones-Wenzl projectors) using Soergel bimodules

(c) compare the geometric and algebraic constructions above, and understand the connection between the (co)center of the Soergel category and the Hilbert scheme of points on the plane

This workshop is fully funded by a Simons Foundation Targeted Grant to Institutes.

##### Organizing Committee

- Ben Elias
- Eugene Gorsky
- Andrei Negut