Sage Days 65 in Chicago
When and where?
June 812, 2015, at Loyola University Chicago, in Chicago, Ill., USA.
Specifically, IES Building (#38), Rooms 123 & 124.
Tentative Schedule

Mon 
Tue 
Wed 
Thu 
Fri 
9:30 
Coffee & Light Breakfast 
Coffee 
Coffee 
Coffee 
Coffee 
9:45 

10:00 
open 

10:15 

10:30 

10:45 

11:00 
Project Intros 
Tutorial: Thiruvathukal+Albert 
Tutorial: 
Tutorial: Lauve 
Tutorial: open 
11:15 

11:30 
Tutorial: Doty 

11:45 

12:00 
Lunch 
Lunch / Free Afternoon 
Lunch 
Final Progress Reports 

12:15 
Lunch 

12:30 

12:45 


13:00 

13:15 

13:30 

13:45 

14:00 

14:15 

14:30 

14:45 

15:00 
Coffee 
Coffee 

15:15 

15:30 
Coffee 
Small groups (coding/tutorials) 
Small groups (coding/tutorials) 

15:45 

16:00 
Small groups (coding/tutorials) 

16:15 

16:30 

16:45 

17:00 
Progress Reports 
Progress Reports 

17:15 

17:30 
Progress Reports 



17:45 

18:00 


18:15 

18:30 

18:45 

19:00 
Main Focci
 We develop code for SAGE support of MVpolytopes and affine crystals.
 We develop code for SAGE support of combinatorial Hopf algebras.
We get newcomers to SAGE as up to speed as possible in a week!
(Personal) Goals for the Week
Participants should feel free to add to this list in advance of the meeting. Anonymous contributions are okay.
 Develop code for Hopf monoids in species (Lauve)
 Learn how to use SAGE in my classroom
Resume coding basic algebraic structure for KLRalgebras, quantum shuffle algebras, etc (Im, McNamara)
Start a wiki for combinatorial Hopf algebras, in the format of FindStat (Pang)
 Crystals of tableaux for the Lie superalgebra gl(mn) (Salisbury)
 improve NCGrobner basis calculations, implement dual QuasiSchur basis #18447 (Zabrocki)
 Noncommutative version of Faugere's F5 algorithm in Sage (King)
Quiver representation for cyclic quivers (Gunawan, King). See #18632
Code test for satisfaction of A_\inftyalgebra relations (Fansler)
 Help Mike, improve my sage abilities (Nantel)
 Get MV polytope code ready to include in sage (TingleyMuthiah)
Weight lattice realization for crystals (see #18453) (Schilling, Salisbury)
Implementation of Foata bijection on words #18628 (Schilling)
 Learn some patterns for organizing research code and computations (Muthiah)
Come up with general framework for constructing subHopf algebras of MalvenutoReutenauer that arise from lattice quotients on the weak order (see: Nathan Reading, Lattice congruences, fans and Hopf algebras, http://arxiv.org/abs/math/0402063). (Dilks)
Participants
 Darlayne Addabbo (U Illinois)
 Mark V. Albert (Loyola Chicago)
 N. Bergeron (York U)
 Kevin Dilks (U Minnesota)
 Steve Doty (Loyola Chicago)
 Merv Fansler (Millersville U)
 Gabriel Feinberg (Haverford College)
 Emily Gunawan (U Minnesota)
 Christine Haught (Loyola Chicago)
 Mee Seong Im (U Illinois and USMA)
 Jonathan Judge (UConn)
WonGeun Kim (CUNY)
 Simon King (FSU Jena, Germany)
 Michael Kratochvil (Loyola Chicago)
 Jonathan Lamar (U Colorado)
 Aaron Lauve (Loyola Chicago)
 Jake Levinson (U Michigan)
 Megan Ly (U Colorado Boulder)
Peter McNamara (U Queensland, Australia)
 Dinakar Muthiah (U Toronto)
 Amy Pang (LaCIM, UQAM)
Kyle Petersen (DePaul U, tentative)
 Viviane Pons (LRI, U ParisSud)
 Anup Poudel (Loyola)
 Franco Saliola (UQAM)
 Ben Salisbury (Central Michigan U)
 Anne Schilling (UC Davis)
 Adam Schultze (Loyola Chicago and SUNY Albany)
 George H. Seelinger (Loyola Chicago)
 Mark Shimozono (Virginia Tech)
Bridget Tenner (DePaul U, tentative)
 George Thiruvathukal (Loyola Chicago)
 Peter Tingley (Loyola Chicago)
 Panupong Vichitkunakorn (U Illinois)
 Mike Zabrocki (York U)
Abstracts
Monday 

Franco Saliola 
Let's Start Using Sage! 
A whirlwind tour of what Sage can and cannot do (and why you should care). 

Stephen Doty 
Getting Started with the Sagemath Cloud 
Sagemath Cloud is a recent project to make Sage (and much more: e.g., Python, R, LaTeX, Terminal) available in any modern browser, without the need to install anything on the computer. This will be an introduction, with no prerequisites. 

Dinakar Muthiah 
MV polytopes in finite and affine type 
MV polytopes provide a model for highest weight crystals in finite and affine type. Interest in MV polytopes comes from the variety of different contexts in which they appear: MV cycles in the affine Grassmannian, irreducible components in preprojective varieties, charactersupport for KLR modules, and PBW bases. They also can be constructed purely combinatorially. I will focus on the combinatorics of MV polytopes and briefly mention the other contexts in which they appear. I will also discuss the MV polytope code that we have already written and explain some of the tasks that remain. 

Nantel Bergeron 
Homogeneous, Noncommutative Gröbner Bases 
Computing a noncommutative Gröbner basis takes an extremely long time. I will present the algorithm and indicate where it could be parallelized... 

Tuesday 

Anne Schilling 
Algebraic Combinatorics in Sage: How to use it, make it, and get it into Sage 
We will very briefly discuss the history of combinatorics in Sage and give some examples on how to use some features like crystals, permutations and words. We will then implement some new missing features together and see how to get them into Sage. 

Mark A. & George T. 
Code collaboration in SAGE and other open source projects 
We will have a brief introduction to the typical organizational structures and technologies used by largescale open source projects and how one can contribute at various levels in each. This will be followed by a tutorial for working collaboratively on code to contribute directly to the SAGE environment. 

Mike Zabrocki 
How to program a combinatorial Hopf algebra (with bases) 
I will review the structure of the code for combinatorial Hopf algebras (symmetric functions/partitions, quasisymmetric functions/compositions, noncommutative symmetric functions/compositions, symmetric functions in noncommuting variables/set partitions) that are already in Sage and explain how to create a new combinatorial Hopf algebra on another set of combinatorial objects. I will also point out the ongoing work on open tickets to implement other combinatorial Hopf algebras (packed words #15611, FQSym, WQSym, PQSym #13793, PBT/LodayRonco #13855) 

Wednesday 

Ben Salisbury 
Affine crystals in Sage 
I will give a brief overview of affine crystals (both irreducible highest weight affine crystals and affine Verma crytals) before discussing certain implementations of these crystals in Sage. I will also point to some current Sage work in this area as well as possible extensions beyond. 

Peter T. & Emily P. 
Linear Algebra in Sage 
We will lead a session on figuring out how to get sage to do something. This will mostly consist of participants working together to try and figure stuff out. That stuff will be from linear algebra and, if things go well, random matrix theory. 

Thursday 

Simon King 
An F5 algorithm for modules over path algebra quotients and the computation of Loewy layers 
The F5 algorithm is a signature based algorithm to compute Gröbner bases for modules over polynomial rings. The F5 signature allows to exploit commutativity relations in order to avoid redundant computations. When considering modules over path algebra quotients, one can instead exploit the quotient relations to avoid redundancies. 

Aaron Lauve 
Convolution Powers: step by step 
I share my personal story (I want to say "natural progression" but I'm sure it's nothing of the kind) from perceived gap in the Sage code for Hopf algebras to sagetrac ticket submission. 

George Seelinger 
Orthogonal Idempotents in Semisimple Brauer Algebras 
I will describe my joint work with Doty and Lauve. Using Sage, we found a recursive description of primitive, pairwise orthogonal idempotents in a semisimple Brauer algebra. These are analogous to Young's seminormal idempotents for group algebras of the symmetric groups. 

Jonathan Judge 
Root Multiplicities for KacMoody Algebras in Sage 
Root multiplicities are fundamental data in the structure theory of KacMoody algebras. We will give a brief survey on root multiplicities that highlights the differences between finite, affine, and indefinite types. Then we will describe the two main ways that these multiplicities are computed, namely BermanMoody's formula and Peterson's recurrent formula. Lastly, we demonstrate an implementation of Peterson's recurrent formula in Sage. 

Friday 

open 
... 
Organizers
 ALBERT, Mark V. (Loyola Chicago  Computer Science)
 LAUVE, Aaron (Loyola Chicago  Mathematics)
 TINGLEY, Peter (Loyola Chicago  Mathematics)
List of projects people are working on
List compiled in the afternoon June 9, 2015:
Surface cluster algebra/quiver reps/infinite dim'l matrices
 Emily
 Darleen (need expert to look at code)
 Simon
Combinatorial Hopf Algebras
 Aaron L.
 Panupong
 Amy
 John
 Kevin (need expert to look at code)
 Nantel
 Mike
Associahedron
 Merve
Root mulitiplicities
 Jon
Super Characters
 Megan
 John
Inverse Foata Bijection
Fix DAHA Code/Extended affine Weyl groups
 Mark
Fix this morning's bug
 Franco
 Mike
Noncommutative Groebner bases
 Nantel
 Simon
 Vivianne
 Franco
Diagram Algebras
 George S.
 Steve D.
 Aaron L.
KLR/quantum shuffle/canonical bases
 Peter M.
 Peter T.
Spherical Varieties
 Won Geun Kim
MV Polytopes/PBW Crystals
 Adam S.
 Dinakar
 Peter
Weight function for affine crystals
 Ben
 Anne
Tutorials/Tutorial Requests
 Merv (Combinatorics)
 Jake (Abstract alg)
 Panupong (Contributing)
 John, Megan (contributing, cython)
 Fully packed loops (Vivianne)
 Mark, Albert (Abstract alg)
 Doty (cython, see Franco's web page)
 Simon (coercion)
 Franco (development in the cloud)
 Monkey Patch tutorial? (Dilks wants one)
Workshop dinner
The dinner will be at Goose Island Brew Pub, at the corner of [[https://www.google.com/maps/place/W+Willow+St+%26+N+Marcey+St,+Chicago,+IL+60642/@41.9130338,87.6543868,17z/data=!3m1!4b1!4m2!3m1!1s0x880fd321754a6fe5:0x16439cf7de1f697bN. Marcey and W. Willow]; near the North/Clybourn Red Line station.
Useful links
http://math.luc.edu/sagedays/: Main conference webpage (with information about housing)
Sage Development Images: Sage Math Cloud project with the development images
http://www.chitownfestivals.com: neighborhoods to explore, if you are around this weekend
Collaborative Development with GitTrac: documentation that explains how to use the helper git trac command, which simplifies many of the most common actions in collaboration on Sage (checking out a ticket; pulling new changes; pushing your changes; ...)