## Programs & Events

##### VIRTUAL ONLY: 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

##### VIRTUAL ONLY: 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

##### VIRTUAL ONLY: 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

##### VIRTUAL ONLY: Mathematical and Computational Approaches to Social Justice

Mar 8 - 10, 2021

Social justice refers to fair relations between individuals and society, including issues such as equity, diversity, and inclusion. While the study of social justice historically has been rooted in the social sciences and humanities, mathematics and computation provide complementary and powerful approaches. Tools from dynamical systems, network science, applied topology, stochastic processes, data mining, and more have been applied to issues ranging from voting to hate speech.

This Hot Topics workshop seeks to promote new areas of research on quantitative approaches to social justice. We will bring together mathematical and computational scientists who are equipped with tools and methodologies that could be applied to social justice, as well as those who already have expertise with social justice work. We aim to showcase research at the intersection of mathematics, computing, and social justice, as well as build community among scientists interested in quantitative social justice... (more)

##### Organizing Committee

- Veronica Ciocanel
- Nancy Rodriguez
- Chad Topaz

##### Schubert Seminar Series

Feb 24 - May 5, 2021

The seminar is aimed at graduate students and early career researchers, and it will showcase both surveys of particular topics, and the latest developments, in Schubert Calculus and related areas. All speakers are encouraged to make at least the first half of their talks introductory and strictly accessible to graduate students.

Talks will be Wednesdays from 3:30 PM- 4:30 PM ET. See the schedule below for details.

##### Organizing Committee

- Anders Buch
- Leonardo Mihalcea

##### 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 RĂ¼th
- 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.

##### Tutorial Materials:

Tutorial: Learn basics of gravitational-wave data analysis with the community-developed PyCBC toolkit

##### 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