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June 8-12, 2015, at Loyola University Chicago, in Chicago, Ill., USA. June 8-12, 2015, at [[http://www.luc.edu/|Loyola University Chicago]], in Chicago, Ill., USA.
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== Web page == Specifically, IES Building [[http://www.luc.edu/media/lucedu/lsc.pdf|(#38)]], Rooms 123 & 124.
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[[http://math.luc.edu/sagedays/]]
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== Confirmed Speakers == == Tentative Schedule ==
Line 14: Line 13:
 * Anne Schilling (UC Davis)
 * Dinakar Muthiah (U Toronto)
 * Mike Zabrocki (York U)
 * Franco Saliola (UQAM)		 ||<tablewidth="80%"> &nbsp; ||<:17%> '''Mon''' ||<:17%> '''Tue''' ||<:18%> '''Wed''' ||<:16%> '''Thu''' ||<:17%> '''Fri''' ||
|| 9:30 ||<|2 #FFFF66> Coffee & Light Breakfast ||<|2 #FFFF66> Coffee ||<|2 #FFFF66> Coffee ||<|2 #FFFF66> Coffee ||<|2 #FFFF66> Coffee ||
|| 9:45 ||
|| 10:00 ||<|4 #BBBBFF> [[#Saliola|Saliola]] ||<|4 #BBBBFF> [[#Schilling|Schilling]] ||<|4 #BBBBFF> [[#Salisbury|Salisbury]] ||<|4 #BBBBFF> [[#King|King]] ||<|4 #BBBBFF> open ||
|| 10:15 ||
|| 10:30 ||
|| 10:45 ||
|| 11:00 ||<|2 #6666FF> Project Intros ||<|4> Tutorial: [[#Mark|Thiruvathukal+Albert]] ||<|4> Tutorial: <<BR>>[[#Tingley|Tingley+Peters]] ||<|4> Tutorial: [[#Lauve|Lauve]] ||<|4> Tutorial: open ||
|| 11:15 ||
|| 11:30 ||<|3> Tutorial: [[#Doty|Doty]] ||
|| 11:45 ||
|| 12:00 ||<|8 #FFFFBB> Lunch ||<|28> Lunch / Free Afternoon ||<|8 #FFFFBB> Lunch ||<|3 #66FF66> Final Progress Reports ||
|| 12:15 ||<|7 #FFFFBB> Lunch ||
|| 12:30 ||
|| 12:45 ||<|26> ||
|| 13:00 ||
|| 13:15 ||
|| 13:30 ||
|| 13:45 ||
|| 14:00 ||<|3 #BBBBFF> [[#Muthiah|Muthiah]] ||<|4 #BBBBFF> [[#Zabrocki|Zabrocki]] ||<|2 #BBBBFF> [[#Seelinger|Seelinger]] ||
|| 14:15 ||
|| 14:30 ||<|2 #BBBBFF> [[#Judge|Judge]] ||
|| 14:45 ||<|3 #BBBBFF> [[#Bergeron|Bergeron]] ||
|| 15:00 ||<|2 #FFFF66> Coffee ||<|2 #FFFF66> Coffee ||
|| 15:15 ||
|| 15:30 ||<|2 #FFFF66> Coffee ||<|6> Small groups (coding/tutorials) ||<|6> Small groups (coding/tutorials) ||
|| 15:45 ||
|| 16:00 ||<|6> Small groups (coding/tutorials) ||
|| 16:15 ||
|| 16:30 ||
|| 16:45 ||
|| 17:00 ||<|2 #66FF66> Progress Reports ||<|2 #66FF66> Progress Reports ||
|| 17:15 ||
|| 17:30 ||<|2 #66FF66> Progress Reports ||<|10> ||<|8> ||
|| 17:45 ||
|| 18:00 ||<|8> ||
|| 18:15 ||
|| 18:30 ||
|| 18:45 ||
|| 19:00 ||<:> [[http://www.gooseislandbrewpubs.com/home-clybourn/|Goose Island Brew Pub]] ||


== Main Focci ==
 * We develop code for SAGE support of MV-polytopes 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 KLR-algebras, quantum shuffle algebras, etc (Im, McNamara)
 * Start a wiki for combinatorial Hopf algebras, in the format of [[http://www.findstat.org|FindStat]] (Pang)
 * Crystals of tableaux for the Lie superalgebra gl(m|n) (Salisbury)
 * improve NC-Grobner basis calculations, implement dual Quasi-Schur basis #18447 (Zabrocki)
 * Non-commutative version of Faugere's F5 algorithm in Sage (King)
 * Quiver representation for ''cyclic'' quivers (Gunawan, King). See [[http://trac.sagemath.org/ticket/18632|#18632]]
 * Code test for satisfaction of $A_\infty$-algebra relations (Fansler)
 * Help Mike, improve my sage habilities (Nantel)
 * Get MV polytope code ready to include in sage (Tingley-Muthiah)
 * Weight lattice realization for crystals (see [[http://trac.sagemath.org/ticket/18453|#18453]]) (Schilling, Salisbury)
 * Implementation of Foata bijection on words [[http://trac.sagemath.org/ticket/18628|#18628]] (Schilling)
Line 20: Line 79:
 * Darlayne Addabbo (U Illinois)
Line 22: Line 81:
 * N. Bergeron (York U)
 * Kevin Dilks (U Minnesota)
Line 23: Line 84:
 * Mee Seong Im (U Illinois)  * Merv Fansler (Millersville U)
 * Gabriel Feinberg (Haverford College)
 * Emily Gunawan (U Minnesota)
 * Christine Haught (Loyola Chicago)
 * Mee Seong Im (U Illinois and USMA)
Line 25: Line 90:
 * WonGeun Kim (CUNY)
 * Simon King (FSU Jena, Germany)
 * Michael Kratochvil (Loyola Chicago)
 * Jonathan Lamar (U Colorado)
Line 26: Line 95:
 * Jake Levinson (U Michigan)
 * Megan Ly (U Colorado Boulder)
 * Peter McNamara (U Queensland, Australia)
Line 28: Line 100:
 * Kyle Petersen (DePaul U, tentative)
 * Viviane Pons (LRI, U Paris-Sud)
 * Anup Poudel (Loyola)
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 * Ben Salisbury (U Central Michigan, tentative)  * Ben Salisbury (Central Michigan U)
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 * Adam Schultze (Loyola Chicago and SUNY Albany)
 * George H. Seelinger (Loyola Chicago)
 * Mark Shimozono (Virginia Tech)
Line 32: Line 110:
 * George Thiruvathukal (Loyola Chicago, tentative)  * George Thiruvathukal (Loyola Chicago)
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 * Yannic Vargas (UQAM)  * Panupong Vichitkunakorn (U Illinois)
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 * Panupong Vichitkunakorn (U Illinois)
 * Kevin Dilks (U Minnesota)
 * Emily Gunawan (U Minnesota)
 

== Abstracts ==
||||<tablewidth="80%" style="background-color: #d63366; text-align: left; color: #FFFFFF; border:none;"> '''Monday''' ||
||<style="width: 15%; text-align: left; border-left:none; border-right:none;"> <<Anchor(Saliola)>>'''Franco Saliola''' ||<style="width: 65%; text-align: left; border-left:none; border-right:none;"> ''Let's Start Using Sage!'' ||
||||<( style="border:none;"> A whirlwind tour of what Sage can and cannot do (and why you should care).<<BR>>&nbsp; ||
||<style="text-align: left; border-left:none; border-right:none;"> <<Anchor(Doty)>>'''Stephen Doty''' ||<style="text-align: left; border-left:none; border-right:none;"> ''Getting Started with the Sagemath Cloud'' ||
||||<( style="border:none;"> 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.<<BR>>&nbsp; ||
||<style="text-align: left; border-left:none; border-right:none;"> <<Anchor(Muthiah)>>'''Dinakar Muthiah''' ||<style="text-align: left; border-left:none; border-right:none;"> ''MV polytopes in finite and affine type'' ||
||||<( style="border:none;"> 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, character-support 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.<<BR>>&nbsp; ||
||<style="text-align: left; border-left:none; border-right:none;"> <<Anchor(Bergeron)>>'''Nantel Bergeron''' ||<style="text-align: left; border-left:none; border-right:none;"> ''Homogeneous, Non-commutative Gröbner Bases'' ||
||||<( style="border:none;"> Computing a non-commutative Gröbner basis takes an extremely long time. I will present the algorithm and indicate where it could be parallelized...<<BR>>&nbsp; ||
||||<style="background-color: #d63366; text-align: left; color: #FFFFFF; border:none;"> '''Tuesday''' ||
||<style="text-align: left; border-left:none; border-right:none;"> <<Anchor(Schilling)>>'''Anne Schilling''' ||<style="text-align: left; border-left:none; border-right:none;"> ''Algebraic Combinatorics in Sage: How to use it, make it, and get it into Sage'' ||
||||<( style="border:none;"> 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.<<BR>>&nbsp; ||
||<style="text-align: left; border-left:none; border-right:none;"> <<Anchor(Mark)>>'''Mark A. & George T.''' ||<style="text-align: left; border-left:none; border-right:none;"> ''Code collaboration in SAGE and other open source projects'' ||
||||<( style="border:none;"> We will have a brief introduction to the typical organizational structures and technologies used by large-scale 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.<<BR>>&nbsp; ||
||<style="text-align: left; border-left:none; border-right:none;"> <<Anchor(Zabrocki)>>'''Mike Zabrocki''' ||<style="text-align: left; border-left:none; border-right:none;"> ''How to program a combinatorial Hopf algebra (with bases)'' ||
||||<( style="border:none;"> I will review the structure of the code for combinatorial Hopf algebras (symmetric functions/partitions, quasi-symmetric functions/compositions, non-commutative symmetric functions/compositions, symmetric functions in non-commuting 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/Loday-Ronco #13855)<<BR>>&nbsp; ||
||||<style="background-color: #d63366; text-align: left; color: #FFFFFF; border:none;"> '''Wednesday''' ||
||<style="text-align: left; border-left:none; border-right:none;"> <<Anchor(Salisbury)>>'''Ben Salisbury''' ||<style="text-align: left; border-left:none; border-right:none;"> ''Affine crystals in Sage'' ||
||||<( style="border:none;"> 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.<<BR>>&nbsp; ||
||<style="text-align: left; border-left:none; border-right:none;"> <<Anchor(Tingley)>>'''Peter T. & Emily P.''' ||<style="text-align: left; border-left:none; border-right:none;"> ''Linear Algebra in Sage'' ||
||||<( style="border:none;"> 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.<<BR>>&nbsp; ||
||||<style="background-color: #d63366; text-align: left; color: #FFFFFF; border:none;"> '''Thursday''' ||
||<style="text-align: left; border-left:none; border-right:none;"> <<Anchor(King)>>'''Simon King''' ||<style="text-align: left; border-left:none; border-right:none;"> ''An F5 algorithm for modules over path algebra quotients and the computation of Loewy layers'' ||
||||<( style="border:none;"> 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. <<BR>>&nbsp;<<BR>>For my applications, it is important that Gröbner bases are actually not more than a by-product of the F5 algorithm. Indeed, the F5 signature provides additional information: If the quotient algebra is a basic algebra and if a negative degree monomial ordering is used, then the F5 signature allows to read off the Loewy layers of the module.<<BR>>&nbsp; ||
||<style="text-align: left; border-left:none; border-right:none;"> <<Anchor(Lauve)>>'''Aaron Lauve''' ||<style="text-align: left; border-left:none; border-right:none;"> ''Convolution Powers: step by step'' ||
||||<( style="border:none;"> 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 sage-trac ticket submission.<<BR>>&nbsp; ||
||<style="text-align: left; border-left:none; border-right:none;"> <<Anchor(Seelinger)>>'''George Seelinger''' ||<style="text-align: left; border-left:none; border-right:none;"> ''TBA'' ||
||||<( style="border:none;"> ...<<BR>>&nbsp; ||
||<style="text-align: left; border-left:none; border-right:none;"> <<Anchor(Judge)>>'''Jonathan Judge''' ||<style="text-align: left; border-left:none; border-right:none;"> ''Root Multiplicities for Kac-Moody Algebras in Sage'' ||
||||<( style="border:none;"> Root multiplicities are fundamental data in the structure theory of Kac-Moody 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 Berman-Moody's formula and Peterson's recurrent formula. Lastly, we demonstrate an implementation of Peterson's recurrent formula in Sage.<<BR>>&nbsp; ||
||||<style="background-color: #d63366; text-align: left; color: #FFFFFF; border:none;"> '''Friday''' ||
||<style="text-align: left; border-left:none; border-right:none;"> '''open''' ||<style="text-align: left; border-left:none; border-right:none;"> ''...'' ||
Line 47: Line 156:

== Web page ==

[[http://math.luc.edu/sagedays/]] (with information about housing)

Sage Days 65 in Chicago

When and where?

June 8-12, 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

Saliola

Schilling

Salisbury

King

open

10:15

10:30

10:45

11:00

Project Intros

Tutorial: Thiruvathukal+Albert

Tutorial:
Tingley+Peters

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

Muthiah

Zabrocki

Seelinger

14:15

14:30

Judge

14:45

Bergeron

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

Goose Island Brew Pub

Main Focci

  • We develop code for SAGE support of MV-polytopes 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 KLR-algebras, 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(m|n) (Salisbury)
  • improve NC-Grobner basis calculations, implement dual Quasi-Schur basis #18447 (Zabrocki)
  • Non-commutative version of Faugere's F5 algorithm in Sage (King)

  • Quiver representation for cyclic quivers (Gunawan, King). See #18632

  • Code test for satisfaction of A_\infty-algebra relations (Fansler)

  • Help Mike, improve my sage habilities (Nantel)
  • Get MV polytope code ready to include in sage (Tingley-Muthiah)

  • Weight lattice realization for crystals (see #18453) (Schilling, Salisbury)

  • Implementation of Foata bijection on words #18628 (Schilling)

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 Paris-Sud)
  • 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, character-support 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, Non-commutative Gröbner Bases

Computing a non-commutative 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 large-scale 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, quasi-symmetric functions/compositions, non-commutative symmetric functions/compositions, symmetric functions in non-commuting 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/Loday-Ronco #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.
 
For my applications, it is important that Gröbner bases are actually not more than a by-product of the F5 algorithm. Indeed, the F5 signature provides additional information: If the quotient algebra is a basic algebra and if a negative degree monomial ordering is used, then the F5 signature allows to read off the Loewy layers of the module.
 

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 sage-trac ticket submission.
 

George Seelinger

TBA

...
 

Jonathan Judge

Root Multiplicities for Kac-Moody Algebras in Sage

Root multiplicities are fundamental data in the structure theory of Kac-Moody 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 Berman-Moody'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)

Web page

http://math.luc.edu/sagedays/ (with information about housing)

days65 (last edited 2015-07-29 20:57:38 by ptingley)