Programs & Events
VIRTUAL ONLY: 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
VIRTUAL ONLY: 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
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
A Virtual ICERM Public Event: Q&A with Kip Thorne, Nobel Prize-winning Theoretical Physicist
Dec 2, 2020
Please join us for an exciting Q&A with Nobel prize-winning physicist Kip Thorne. Professor Thorne will briefly review the crucial role and history of computation in the detection of gravitational waves, and take your questions on all issues relating to computational physics and science in general.
The event will be introduced and moderated by renowned physicist Professor Richard Price, and Professor Saul Teukolsky (the 2021 Einstein Prize awardee) will give an introductory talk on the computational challenges and solutions for simulating black holes and gravitational waves on computers, and the interesting science that can be done thanks to the LIGO and VIRGO gravitational-wave detectors.
NOTE: those with confirmed registrations who have provided a valid email address will receive Zoom credentials for joining this lecture the day before the event, as well as a reminder email 1 hour prior to the event.
VIRTUAL ONLY: 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
A Virtual ICERM Public Lecture: Quantifying and Understanding Gerrymandering - How a quest to understand his state's political geography led a mathematician to court
Oct 28, 2020
The US political system is built on representatives chosen by geographically localized regions. This presents the government with the problem of designing these districts. Every ten years, the US census counts the population and new political districts must be drawn. The practice of harnessing this administrative process for partisan political gain is often referred to as gerrymandering.
How does one identify and understand gerrymandering? Can we really recognize gerrymandering when we see it? If one party wins over 50% of the vote, is it fair that it wins less than 50% of the seats? What do we mean by fair? How can math help illuminate these questions?
How does the geopolitical geometry of the state (where which groups live and the shape of the state) inform these answers?
For me, these questions began with an undergraduate research program project in 2013 and have led me to testify twice in two cases: Common Cause v. Rucho (that went to the US Supreme Court) and Common Cause v.... (more)
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 Einsteinâs 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