Organizing Committee
Abstract

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.

This workshop is partially funded by the Alfred P. Sloan Foundation award G-2019-11406 and supported by a Simons Foundation Targeted Grant to Institutes.

Image for "Illustrating Number Theory and Algebra"
Algebraic numbers in the complex plane.
Image credit: Stephen J. Brooks, (rendering by David Moore)

Confirmed Speakers & Participants

  • Speaker
  • Poster Presenter
  • Attendee
  • Virtual Attendee

Workshop Schedule

Monday, October 21, 2019
TimeEventLocationMaterials
8:30 - 8:55am EDTRegistration - ICERM 121 South Main Street, Providence RI 0290311th Floor Collaborative Space 
8:55 - 9:00am EDTWelcome - ICERM Director11th Floor Lecture Hall 
9:00 - 9:45am EDTNumber Theory by design - Martin Weissman, UC Santa Cruz11th Floor Lecture Hall
10:00 - 10:30am EDTCoffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15am EDTWebs, foams, knot invariants, and representation theory - David Rose, University of North Carolina at Chapel Hill11th Floor Lecture Hall
11:30 - 12:15pm EDTAnimating the deformation of Lattices - Edmund Harriss, University of Arkansas and Pierre Arnoux, Université d'Aix-Marseille11th Floor Lecture Hall 
12:30 - 2:30pm EDTBreak for Lunch / Free Time  
2:30 - 3:15pm EDTThe Surprising Pedagogical Value and Versatility of Cayley Graphs - Nathan Carter, Bentley University11th Floor Lecture Hall
3:30 - 4:15pm EDTHyperbolic surfaces, cutting sequences, and continued fractions - Claire Merriman, Ohio State University11th Floor Lecture Hall
4:30 - 6:00pm EDTWelcome Reception11th Floor Collaborative Space 
6:00 - 7:00pm EDTMath + Art Panel11th Floor Lecture Hall 
Tuesday, October 22, 2019
TimeEventLocationMaterials
9:00 - 9:45am EDTHoneycombs, puzzles, and moment polytopes - Allen Knutson, Cornell University11th Floor Lecture Hall
10:00 - 10:30am EDTCoffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15am EDTApollonian Circle Packings- Arithmetic, Illustrated - Elena Fuchs, University of California, Davis11th Floor Lecture Hall
11:30 - 12:15pm EDTWallpaper and Rings of Integers in Quadratic Number Fields - Frank A. Farris, Santa Clara University11th Floor Lecture Hall
12:30 - 2:00pm EDTBreak for Lunch / Free Time  
2:00 - 2:45pm EDTTowards computation and visualization of symmetries of locally-finite infinite vertex-transitive graphs - Michal Ferov University of Newcastle, Australia11th Floor Lecture Hall
3:00 - 3:30pm EDTShow'n'tell11th Floor Lecture Hall
3:30 - 5:00pm EDTPoster Session & Coffee/Tea Break11th Floor Collaborate Space 
Wednesday, October 23, 2019
TimeEventLocationMaterials
9:00 - 9:45am EDTPrime spirals and rational approximations - Grant Sanderson, 3Blue1Brown11th Floor Lecture Hall
10:00 - 10:30am EDTCoffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15am EDTContinued fractions in imaginary quadratic fields - Daniel Martin, University of Colorado11th Floor Lecture Hall
11:30 - 12:15pm EDTSupercharacters and their superpowers- the graphic nature of exponential sums - Stephan Garcia, Pomona College11th Floor Lecture Hall
12:30 - 12:40pm EDTWorkshop Group Photo11th Floor Lecture Hall 
12:40 - 2:30pm EDTBreak for Lunch / Free Time  
2:30 - 3:15pm EDTNumbers that Inspire - Margaret Kepner, Independent Artist11th Floor Lecture Hall
3:30 - 4:00pm EDTCoffee/Tea Break11th Floor Collaborate Space 
4:00 - 4:45pm EDTShow'n'tell11th Floor Lecture Hall
Thursday, October 24, 2019
TimeEventLocationMaterials
9:00 - 9:45am EDTVisualizing Algebraic Numbers and Other Countable Sets - David Moore, UC San Diego11th Floor Lecture Hall
10:00 - 10:30am EDTCoffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15am EDTSphere packings, rational curves, and Coxeter graphs - Arthur Baragar, University of Nevada Las Vegas11th Floor Lecture Hall
11:30 - 12:15pm EDTGalaxy Leggings, Truth Serum, & the Visibility Cloak - Olena Shmahalo, Quanta Magazine11th Floor Lecture Hall
12:30 - 2:30pm EDTBreak for Lunch / Free Time  
2:30 - 3:15pm EDTSeeing the Monodromy Group of a Blaschke Product - Elias Wegert, TU Bergakademie Freiberg11th Floor Lecture Hall
3:30 - 4:00pm EDTCoffee/Tea Break11th Floor Collaborate Space 
4:00 - 4:45pm EDTProjective and Non-abelian SET - Catherine Hsu, University of Bristol11th Floor Lecture Hall
Friday, October 25, 2019
TimeEventLocationMaterials
9:00 - 9:45am EDTOn the fractal objects that arise from iteration of various zeta functions, L functions, and one modular form - David Rainford, No academic affiliation11th Floor Lecture Hall
10:00 - 10:30am EDTCoffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15am EDTWhen a picture is a proof - Emily Peters, Loyola University Chicago11th Floor Lecture Hall
11:30 - 12:15pm EDTAlgebraic relations and integrality of limit sets of maximal cusp groups - David Wright, Oklahoma State University11th Floor Lecture Hall
12:30 - 2:00pm EDTBreak for Lunch / Free Time  
2:00 - 2:45pm EDTEuclidean Algorithm in Circle-Sphere Packings - Arseniy Sheydvasser Graduate Center, CUNY11th Floor Lecture Hall
3:00 - 3:45pm EDTDimers, Minecraft and Algebraic Combinatorics - Benjamin Young, University of Oregon11th Floor Lecture Hall
4:00 - 4:30pm EDTCoffee/Tea Break11th Floor Collaborate Space 

Associated Semester Workshops

Illustrating Mathematics
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Program Opener: Meet, Make and Design
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Math + Art Panel
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Illustrating Geometry and Topology
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Math + Art Panel
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Computational Textiles Working Group
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Math + Art Panel
Image for "Math + Art Panel"
Math + Art Panel
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Illustrating Dynamics and Probability
Image for "Illustrating Dynamics and Probability"
Math + Art Panel
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Lecture Videos

Euclidean Algorithm in Circle-Sphere Packings

Arseniy Sheydvasser
City University of New York, Graduate Center
October 25, 2019

When a picture is a proof

Emily Peters
Loyola University Chicago
October 25, 2019

Projective and Non-abelian SET

Catherine Hsu
University of Bristol
October 24, 2019

Seeing the Monodromy Group of a Blaschke Product

Elias Wegert
Freiberg University of Mining and Technology
October 24, 2019

Galaxy Leggings, Truth Serum, & the Visibility Cloak

Olena Shmahalo
Simons Foundation / Quanta Magazine
October 24, 2019

Sphere packings, rational curves, and Coxeter graphs

Arthur Baragar
University of Nevada Las Vegas
October 24, 2019

Numbers that Inspire

Margaret Kepner
Independent
October 23, 2019

Apollonian Circle Packings- Arithmetic, Illustrated

Elena Fuchs
University of Illinois at Urbana-Champaign
October 22, 2019

Animating the deformation of Lattices

Edmund Harriss
University of Arkansas
Pierre Arnoux
Université d'Aix-Marseille
October 21, 2019

Webs, foams, knot invariants, and representation theory

David Rose
University of North Carolina at Chapel Hill
October 21, 2019

Number Theory by design

Marty Weissman
University of California, Santa Cruz
October 21, 2019