Illustration reveals the hidden structures of mathematics, broadening access to its inherent beauty and pushing the boundaries of research. Here two disciplines are interwoven: on the one hand, the art and craft of presenting ideas and on the other hand, the creativity and scholarship of creating mathematics. This program facilitates research and collaboration on these topics, both between and within these groups, and to promote professional support and recognition both for illustration and for building the infrastructure needed for its creation.

We invite both returning and new members to the Illustrating Mathematics community to this workshop, which will bring together mathematicians, and practitioners from the arts. We seek to expand our community to include a more diverse group of faculty, including those from non-R1 institutions and who identify as members of underrepresented and minoritized groups.

“Algebraic combinatorics” can be thought of as “counting things” and “representation theory” can be thought of as the “study of symmetry”. The notions of “counting” and “symmetry” are all-pervasive in the natural sciences — thus the pure mathematical questions we consider often have ramifications across physics, quantum theory, chemistry, cryptography. . .

The past decade has been one of the most exciting and fruitful times in the history of combinatorics and representation theory. One of the overarching themes in this story is the search for richer structures which secretly underpin the classical problems in the field — these might manifest themselves as algebraic or geometric structures, or even as diagrammatic categories.

The discovery of these richer structures has led to the recent rise and fall of some of the most famous conjectures in the history of combinatorics and representation theory: the Macdonald constant term conjectures, the shuffle... (more)

In many scientific fields, advances in data collection and numerical simulation have resulted in large amounts of data for processing; however, relevant and efficient computational tools appropriate to analyze the data for further prediction and decision-making are still in their infancy. To tackle these challenges, the scientific research community has developed and used probabilistic tools in at least two different ways: first, stochastic methods to model and quantify these uncertainties in applications where there is underlying uncertainty; second, in applications that may be inherently deterministic but randomness is used as an algorithmic tool to drastically reduce computational costs while retaining the high accuracy of classic approaches.

Stochastic and randomized algorithms have already made a tremendous impact in areas such as numerical linear algebra (where matrix sketching and randomized approaches are used for efficient matrix approximations), Bayesian inverse problems... (more)