This panel discussion will explore the different ways in which artists and mathematicians approach mathematical concepts. We expect a dynamic conversation that will spark continued dialogue and future collaborations.

Thurston maps are orientation-preserving branched covering maps of the two-sphere to itself for which the forward orbits of the branch points form a finite set. They arise in the classification of complex dynamical systems.

Recent work has shown close connections between the combinatorial, topological, and algebraic theory of Thurston maps and that of mapping class groups. The algorithmic and computational theories of mapping class groups are highly advanced and have reached the point of effective implementation via computer programs. However, such implementations for Thurston maps are significantly less advanced. The aim of the proposed Hot Topic workshop is to bring together researchers in the computational theory of mapping class groups and those in the combinatorial theory of Thurston maps in order to make headway on fundamental problems.

This workshop is fully funded by a Simons Foundation Targeted Grant to Institutes.

This panel discussion will explore the different ways in which artists and mathematicians approach mathematical concepts. We expect a dynamic conversation that will spark continued dialogue and future collaborations.

The symbiotic relationship between the illustration of mathematics and mathematical research is now flowering in algebra and number theory. This workshop aims to both showcase and develop these connections, including the development of new visualization tools for algebra and number theory. Topics are wide-ranging, and include Apollonian circle packings and the illustration of the arithmetic of hyperbolic manifolds more generally, the visual exploration of the statistics of integer sequences, and the illustrative geometry of such objects as Gaussian periods and Fourier coefficients of modular forms. Other topics may include expander graphs, abelian sandpiles, and Diophantine approximation on varieties. We will also focus on diagrammatic algebras and categories such as Khovanov-Lauda-Rouquier algebras, Soergel bimodule categories, spider categories, and foam categories. The ability to visualize complicated relations diagrammatically has led to important advances in representation theory... (more)

This panel discussion will explore the different ways in which artists and mathematicians approach mathematical concepts. We expect a dynamic conversation that will spark continued dialogue and future collaborations.

Light refreshments will be served following the panel at 5 PM.

The aim of this working group is to bring together theorists and practitioners of computational fiber arts and will have three related themes.

First, we would like to prove theorems about the geometry and topology of knitting. Second, we would like to explore the idea that knitting and textiles can be a physical embodiment of ideas in computational geometry. Third, we will use knitting and other textile arts as a way of visually communicating mathematical ideas to a broader audience.

The working group will take place the week following the Illustrating Geometry and Topology workshop.

Applications closed. Workshop is at capacity.

This workshop will focus on the interaction between visualization, computer experiment, and theoretical advances in all areas of research in geometry and topology. Fruitful interactions of this type have a long history in the field, with physical models and computer images and animations providing both illustration of existing work and inspiration for new developments. Emerging visualization technologies, such as virtual reality, are poised to further increase the tools available for mathematical illustration and experimentation. By bringing together expert practitioners of mathematical visualization techniques and researchers interested in incorporating such tools into their research, the workshop will give participants a clear picture of the state of the art in this fast-moving field while also fostering new collaborations and innovations in illustrating geometry and topology.

This workshop is partially funded by the... (more)

This panel discussion will explore the different ways in which artists and mathematicians approach mathematical concepts. We expect a dynamic conversation that will spark continued dialogue and future collaborations.

This panel discussion will explore the different ways in which artists and mathematicians approach mathematical concepts. We expect a dynamic conversation that will spark continued dialogue and future collaborations.

Participants will be introduced to projects, equipment, and one another. Activities will include:

• participant lightning talk show and tell
• project introductions
• start of the micro courses
• tour of equipment
• short course planning session

There will be ample time for discussions with potential semester collaborators.

The Illustrating Mathematics program brings together mathematicians, makers, and artists who share a common interest in illustrating mathematical ideas via computational tools.

The goals of the program are to:

• introduce mathematicians to new computational illustration tools to guide and inform their research;
• spark collaborations among and between mathematicians, makers and artists;
• find ways to communicate research mathematics to as wide an audience as possible.

The program includes week-long workshops in Geometry and Topology, Algebra and Number Theory, and Dynamics and Probability, as well as master courses, seminars, and an art exhibition.

Mathematical topics include: moduli spaces of geometric structures, hyperbolic geometry, configuration spaces, sphere eversions, apollonian packings, kleinian groups, sandpiles and tropical geometry, analytic number theory, supercharacters, complex dynamics, billiards, random walks, and Schramm–Loewner... (more)