## Programs & Events

##### 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

##### ONLY OFFERED VIRTUALLY: 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: 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.

##### ONLY OFFERED VIRTUALLY: 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: Featuring Jonathan Mattingly

Oct 28, 2020

Coming soon!

##### ONLY OFFERED VIRTUALLY: Statistical Methods for the Detection, Classification, and Inference of Relativistic Objects

Nov 16 - 20, 2020

This workshop will focus on data analysis strategies for comparing model predictions to data. Special attention will be placed on comparing solutions to the Einstein field equations (as in workshops 2 and 3) with data collected from gravitational-wave or telescopes. The workshop will include (but will not be limited to) coverage of topics involving reduced-order models, surrogate models, machine learning, UQ, and Bayesian techniques.

##### Organizing Committee

- Sara Algeri
- Sarah Caudill
- Katerina Chatziioannou
- Alessandra Corsi
- Scott Field
- Jonathan Gair
- Jae-Hun Jung
- Gaurav Khanna

##### Combinatorial Algebraic Geometry

Feb 1 - May 7, 2021

Combinatorial algebraic geometry comprises the parts of algebraic geometry where basic geometric phenomena can be described with combinatorial data, and where combinatorial methods are essential for further progress.

Research in combinatorial algebraic geometry utilizes combinatorial techniques to answer questions about geometry. Typical examples include predictions about singularities, construction of degenerations, and computation of geometric invariants such as Gromov-Witten invariants, Euler characteristics, the number of points in intersections, multiplicities, genera, and many more. The study of positivity properties of geometric invariants is one of the driving forces behind the interplay between geometry and combinatorics. Flag manifolds and Schubert calculus are particularly rich sources of invariants with positivity properties.

In the opposite direction, geometric methods provide powerful tools for studying combinatorial objects. For example, many deep properties of... (more)

##### Organizing Committee

- Anders Buch
- Melody Chan
- June Huh
- Thomas Lam
- Leonardo Mihalcea
- Sam Payne
- Lauren Williams

##### Introductory Workshop: Combinatorial Algebraic Geometry

Feb 1 - 5, 2021

This introductory workshop in combinatorial algebraic geometry is aimed at early career mathematicians and other mathematicians looking for an entry point into the field. The workshop will feature expository lectures on some of the basic objects of interest, together with "expert'' lectures discussing some current trends in the field. There will also be ample time for problem sessions and discussions.

##### Organizing Committee

- Anders Buch
- Melody Chan
- Thomas Lam
- Leonardo Mihalcea

##### Sage/Oscar Days for Combinatorial Algebraic Geometry

Feb 15 - 19, 2021

This workshop will focus on the development of software to facilitate research in combinatorial algebraic geometry, based on the SAGE Mathematical Software System and the OSCAR Computer Algebra System. Special attention will be given to efficient computations with multi-variate polynomials, which is a critical part of many algorithms in combinatorial algebraic geometry. Aside from development of software, the workshop will feature a series of talks about polynomial computations, as well as introductory lectures about Sage and Oscar.

##### Organizing Committee

- Anders Buch
- Wolfram Decker
- Benjamin Hutz
- Michael Joswig
- Julian Rüth
- Anne Schilling

##### Geometry and Combinatorics from Root Systems

Mar 22 - 26, 2021

The purpose of the workshop is to bring together a diverse group of researchers working on combinatorial and geometric aspects related to spaces with symmetries. The workshop will cover problems arising from various flavors of Schubert Calculus and enumerative geometry on flag manifolds, and problems from geometric representation theory and combinatorial Hodge theory. The topics covered include the study of Littlewood-Richardson coefficients, quantum cohomology and quantum K theory of flag manifolds, Maulik-Okounkov stable envelopes and characteristic classes, conformal blocks, and combinatorics related to moduli spaces, Macdonald theory, and quiver polynomials, Soergel bimodules, Hodge theory of matroids. These are trends in a rapidly developing area, and our aim is to facilitate interactions among researchers who work on different problems but employ similar techniques, at the intersection of algebraic geometry, combinatorics, and representation theory.

##### Organizing Committee

- David Anderson
- Angela Gibney
- June Huh
- Thomas Lam
- Leonardo Mihalcea

##### Safety and Security of Deep Learning

Apr 10 - 11, 2021

Deep learning is profoundly reshaping the research directions of entire scientific communities across mathematics, computer science, and statistics, as well as the physical, biological and medical sciences . Yet, despite their indisputable success, deep neural networks are known to be universally unstable. That is, small changes in the input that are almost undetectable produce significant changes in the output. This happens in applications such as image recognition and classification, speech and audio recognition, automatic diagnosis in medicine, image reconstruction and medical imaging as well as inverse problems in general. This phenomenon is now very well documented and yields non-human-like behaviour of neural networks in the cases where they replace humans, and unexpected and unreliable behaviour where they replace standard algorithms in the sciences.

The many examples produced over the last years demonstrate the intricacy of this complex problem and the questions of safety and... (more)

##### Organizing Committee

- Ben Adcock
- Simone Brugiapaglia
- Anders Hansen
- Clayton Webster

##### Algebraic Geometry and Polyhedra

Apr 12 - 16, 2021

The workshop will revolve around the interplay between algebraic geometry and combinatorial structures such as graphs, polytopes, and polyhedral complexes. In particular, the workshop will foster dialogue among groups of researchers who use similar combinatorial geometric tools for different purposes within algebraic geometry and adjacent fields. The topics covered will include Newton-Okounkov bodies, Ehrhart theory, toric geometry, tropical geometry, matroids, and interactions with mirror symmetry.

##### Organizing Committee

- Federico Ardila
- Man-Wai Cheung
- Yoav Len
- Sam Payne
- Lauren Williams