## Programs & Events

##### VIRTUAL ONLY: Mathematical and Computational Approaches for the Einstein Field Equations with Matter Fields

Oct 26 - 30, 2020

This workshop will focus on theoretical and computational approaches to solving the Einstein field equations (the master equation of general relativity: a nonlinear, coupled, hyperbolic-elliptic PDE system) with (fluid) matter field sources, as typical of binary neutron stars and supernovae. Simulations of these systems are targets of interest to both LIGO and telescopes such as Hubble, Fermi, and CHANDRA. In this workshop, special attention will be given to the governing equations of relativistic (magneto- ) hydrodynamics and multi-scale, multi-physics modeling challenges.

##### Organizing Committee

- Stefanos Aretakis
- Manuela Campanelli
- Scott Field
- Jan Hesthaven
- Gaurav Khanna
- Luis Lehner
- Steven Liebling
- Jared Speck

##### A Virtual ICERM Public Lecture: One Person, One Vote

Oct 20, 2020

About a quarter of Americans report believing that double voting is a relatively common occurrence, casting doubt on the integrity of elections. But, despite a dearth of documented instances of double voting, it’s hard to know how often such fraud really occurs (people might just be good at covering it up!). I’ll describe a simple statistical trick to estimate the rate of double voting -- one that builds off the classic birthday paradox -- and show that such behavior is exceedingly rare. I’ll further argue that current efforts to prevent double voting can in fact disenfranchise many legitimate voters.

##### VIRTUAL ONLY: Mathematical and Computational Approaches for Solving the Source- Free Einstein Field Equations

Oct 5 - 9, 2020

This workshop will focus on theoretical and computational approaches to solving the vacuum Einstein field equations (the master equation of general relativity: a nonlinear, coupled, hyperbolic-elliptic PDE system) without matter field sources. A particular important special case is the simulation of two merging black holes, which will be emphasized throughout the workshop. Gravitational wave solutions will be another important aspect of this workshop, and special attention will be given to modeling techniques for the computation of these waves. The topics covered in this workshop will be relevant to both LIGO and LISA scientific efforts.

##### Organizing Committee

- Stefanos Aretakis
- Scott Field
- Jan Hesthaven
- Jae-Hun Jung
- Gaurav Khanna
- Stephen Lau
- Steven Liebling
- Deirdre Shoemaker
- Jared Speck
- Helvi Witek

##### A Virtual ICERM Public Lecture: Uncovering Lottery Shenanigans

Sep 22, 2020

It is very rare to meet anyone who has won a prize worth at least $600 or more in the lottery. (You could expect to buy thousands of scratcher tickets before winning such a prize.) Nonetheless, when looking at publicly-available data, we discovered that some individuals had won hundreds of these big prizes! That much success smelled fishy. We wondered: are they up to something? This talk will describe the data we saw, what mathematics had to say about it, and the legal and illegal schemes that on-the-ground investigations revealed.

This webinar event will be recorded live and made available via ICERM's video archive.

##### VIRTUAL ONLY: Advances and Challenges in Computational Relativity

Sep 14 - 18, 2020

This kick-off workshop will seek to provide an overview of both the state-of-the-art and open challenges drawing from multiple themes (theory, analysis of the equations, computation, and data analysis) within the broad context of Einsteinâ€™s general relativity theory. We welcome participation from physics, mathematics, statistics, and astrophysics, and the speaking schedule will reflect this diversity of scientific disciplines.

The workshop will also feature a series of hands-on, computational tutorials in the afternoon. We plan to hold tutorials on (i) the SXS gravitational waveform catalog which contains important simulation outputs from the numerical relativity code SpEC, (ii) the Einstein Toolkit software platform for numerically solving the Einstein equation, the relativistic (magneto-)hydrodynamics equations,... (more)

##### Organizing Committee

- Douglas Arnold
- Scott Field
- Gaurav Khanna
- Deirdre Shoemaker
- Saul Teukolsky
- Niels Warburton
- Barry Wardell

##### Advances in Computational Relativity

Sep 9 - Dec 11, 2020

The Nobel-Prize-winning detection of gravitational waves from binary black hole systems in 2015 by the Laser Interferometer Gravitational-Wave Observatory (LIGO) and the LIGO Scientific Collaboration has opened a new window on the universe. In addition, the 2017 observation of both gravitational and electromagnetic waves emitted by a binary neutron star system marked a new era of multi-messenger astronomy. While these successes are a remarkable experimental feat, they also constitute a significant computational achievement due to the crucial role played by accurate numerical models of the astrophysical sources in gravitational-wave data analysis. As current detectors are upgraded and new detectors come online within an international network of observatories, accurate, efficient, and advanced computational methods will be indispensable for interpreting the diversity of gravitational wave signals. This semester program at ICERM will emphasize the fundamental mathematical and... (more)

##### Organizing Committee

- Stefanos Aretakis
- Douglas Arnold
- Manuela Campanelli
- Scott Field
- Jonathan Gair
- Jae-Hun Jung
- Gaurav Khanna
- Stephen Lau
- Steven Liebling
- Deirdre Shoemaker
- Jared Speck
- Saul Teukolsky

##### 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 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