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)

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.

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.

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)

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.

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)