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Illustrating Number Theory and Algebra

21st October 2019   -   25th October 2019
ICERM, Providence, United States


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 and knot theory in recent years.