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.

Algebraic numbers in the complex plane.
Image credit: Stephen J. Brooks, (rendering by David Moore)

Confirmed Speakers & Participants

  • Speaker
  • Poster Presenter
  • Attendee

Workshop Schedule

Monday, October 21, 2019
TimeEventLocationMaterials
8:30 - 8:55Registration - ICERM 121 South Main Street, Providence RI 0290311th Floor Collaborative Space 
8:55 - 9:00Welcome - ICERM Director11th Floor Lecture Hall 
9:00 - 9:45Number Theory by design - Martin Weissman, UC Santa Cruz11th Floor Lecture Hall
10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15Webs, foams, knot invariants, and representation theory - David Rose, University of North Carolina at Chapel Hill11th Floor Lecture Hall
11:30 - 12:15Animating the deformation of Lattices - Edmund Harriss, University of Arkansas and Pierre Arnoux, Université d'Aix-Marseille11th Floor Lecture Hall 
12:30 - 2:30Break for Lunch / Free Time  
2:30 - 3:15The Surprising Pedagogical Value and Versatility of Cayley Graphs - Nathan Carter, Bentley University11th Floor Lecture Hall
3:30 - 4:15Hyperbolic surfaces, cutting sequences, and continued fractions - Claire Merriman, Ohio State University11th Floor Lecture Hall
4:30 - 6:00Welcome Reception11th Floor Collaborative Space 
6:00 - 7:00Math + Art Panel11th Floor Lecture Hall 
Tuesday, October 22, 2019
TimeEventLocationMaterials
9:00 - 9:45Honeycombs, puzzles, and moment polytopes - Allen Knutson, Cornell University11th Floor Lecture Hall
10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15Apollonian Circle Packings- Arithmetic, Illustrated - Elena Fuchs, University of California, Davis11th Floor Lecture Hall
11:30 - 12:15Wallpaper and Rings of Integers in Quadratic Number Fields - Frank A. Farris, Santa Clara University11th Floor Lecture Hall
12:30 - 2:00Break for Lunch / Free Time  
2:00 - 2:45Towards computation and visualization of symmetries of locally-finite infinite vertex-transitive graphs - Michal Ferov University of Newcastle, Australia11th Floor Lecture Hall
3:00 - 3:30Show'n'tell11th Floor Lecture Hall
3:30 - 5:00Poster Session & Coffee/Tea Break11th Floor Collaborate Space 
Wednesday, October 23, 2019
TimeEventLocationMaterials
9:00 - 9:45Prime spirals and rational approximations - Grant Sanderson, 3Blue1Brown11th Floor Lecture Hall
10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15Continued fractions in imaginary quadratic fields - Daniel Martin, University of Colorado11th Floor Lecture Hall
11:30 - 12:15Supercharacters and their superpowers- the graphic nature of exponential sums - Stephan Garcia, Pomona College11th Floor Lecture Hall
12:30 - 12:40Workshop Group Photo11th Floor Lecture Hall 
12:40 - 2:30Break for Lunch / Free Time  
2:30 - 3:15Numbers that Inspire - Margaret Kepner, Independent Artist11th Floor Lecture Hall
3:30 - 4:00Coffee/Tea Break11th Floor Collaborate Space 
4:00 - 4:45Show'n'tell11th Floor Lecture Hall
Thursday, October 24, 2019
TimeEventLocationMaterials
9:00 - 9:45Visualizing Algebraic Numbers and Other Countable Sets - David Moore, UC San Diego11th Floor Lecture Hall
10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15Sphere packings, rational curves, and Coxeter graphs - Arthur Baragar, University of Nevada Las Vegas11th Floor Lecture Hall
11:30 - 12:15Galaxy Leggings, Truth Serum, & the Visibility Cloak - Olena Shmahalo, Quanta Magazine11th Floor Lecture Hall
12:30 - 2:30Break for Lunch / Free Time  
2:30 - 3:15Seeing the Monodromy Group of a Blaschke Product - Elias Wegert, TU Bergakademie Freiberg11th Floor Lecture Hall
3:30 - 4:00Coffee/Tea Break11th Floor Collaborate Space 
4:00 - 4:45Projective and Non-abelian SET - Catherine Hsu, University of Bristol11th Floor Lecture Hall
Friday, October 25, 2019
TimeEventLocationMaterials
9:00 - 9:45On 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 - 10:30Coffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15When a picture is a proof - Emily Peters, Loyola University Chicago11th Floor Lecture Hall
11:30 - 12:15Algebraic relations and integrality of limit sets of maximal cusp groups - David Wright, Oklahoma State University11th Floor Lecture Hall
12:30 - 2:00Break for Lunch / Free Time  
2:00 - 2:45Euclidean Algorithm in Circle-Sphere Packings - Arseniy Sheydvasser Graduate Center, CUNY11th Floor Lecture Hall
3:00 - 3:45Dimers, Minecraft and Algebraic Combinatorics - Benjamin Young, University of Oregon11th Floor Lecture Hall
4:00 - 4:30Coffee/Tea Break11th Floor Collaborate Space 

Request Reimbursement

Acceptable Costs
  • 1 roundtrip between your home institute and ICERM
  • Flights on U.S. or E.U. airlines – economy class to either Providence airport (PVD) or Boston airport (BOS)
  • Ground Transportation to and from airports and ICERM.
Unacceptable Costs
  • Flights on non-U.S. or non-E.U. airlines
  • Flights on U.K. airlines
  • Seats in economy plus, business class, or first class
  • Change ticket fees of any kind
  • Multi-use bus passes
  • Meals or incidentals
Advance Approval Required
  • Personal car travel to ICERM from outside New England
  • Multiple-destination plane ticket; does not include layovers to reach ICERM
  • Arriving or departing from ICERM more than a day before or day after the program
  • Multiple trips to ICERM
  • Rental car to/from ICERM
  • Flights on a Swiss, Japanese, or Australian airlines
  • Arriving or departing from airport other than PVD/BOS or home institution's local airport
  • 2 one-way plane tickets to create a roundtrip (often purchased from Expedia, Orbitz, etc.)
Reimbursement Request Form

https://icerm.brown.edu/money/

Refer to the back of your ID badge for more information. Checklists are available at the front desk.

Reimbursement Tips
  • Scanned original receipts are required for all expenses
  • Airfare receipt must show full itinerary and payment
  • ICERM does not offer per diem or meal reimbursement
  • Allowable mileage is reimbursed at prevailing IRS Business Rate and trip documented via pdf of Google Maps result
  • Keep all documentation until you receive your reimbursement!
Reimbursement Timing

6 - 8 weeks after all documentation is sent to ICERM. All reimbursement requests are reviewed by numerous central offices at Brown who may request additional documentation.

Reimbursement Deadline

Submissions must be received within 30 days of ICERM departure to avoid applicable taxes. Submissions after thirty days will incur applicable taxes. No submissions are accepted more than six months after the program end.

Associated Semester Workshops

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

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

Pierre Arnoux
Université d'Aix-Marseille
Edmund Harriss
University of Arkansas
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