Differences between revisions 20 and 95 (spanning 75 versions)

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)
Learn some patterns for organizing research code and computations (Muthiah)
Come up with general framework for constructing sub-Hopf algebras of Malvenuto-Reutenauer 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)
Monkey Patch tutorial? (Dilks wants one)

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	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 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)

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

Non-commutative Groebner bases - Nantel - Simon - Vivianne - Franco

Diagram Algebras - George S. - Steve D.

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)

Workshop dinner

The dinner will be at Goose Island Brew Pub, at the corner of N. 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

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-June 8-12, 2015, at Loyola University Chicago, in Chicago, Ill., USA.

== Web page ==

[[http://math.luc.edu/sagedays/]]

== Confirmed Speakers ==

 * Anne Schilling (UC Davis)
 * Dinakar Muthiah (U Toronto)
 * Mike Zabrocki (York U)
 * Franco Saliola (UQAM)
+June 8-12, 2015, at [[http://www.luc.edu/|Loyola University Chicago]], in Chicago, Ill., USA.

Specifically, IES Building [[http://www.luc.edu/media/lucedu/lsc.pdf|(#38)]], Rooms 123 & 124.


== Tentative Schedule ==

||<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)
 * Learn some patterns for organizing research code and computations (Muthiah)
 * Come up with general framework for constructing sub-Hopf algebras of Malvenuto-Reutenauer 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)

 * Monkey Patch tutorial? (Dilks wants one)
-Line 20:
+Line 82:
+ * Darlayne Addabbo (U Illinois)
-Line 22:
+Line 84:
+ * N. Bergeron (York U)
-Line 24:
+Line 87:
+ * Merv Fansler (Millersville U)
 * Gabriel Feinberg (Haverford College)
-Line 25:
+Line 90:
- * Mee Seong Im (U Illinois)
+ * Christine Haught (Loyola Chicago)
 * Mee Seong Im (U Illinois and USMA)
-Line 27:
+Line 93:
+ * WonGeun Kim (CUNY)
 * Simon King (FSU Jena, Germany)
 * Michael Kratochvil (Loyola Chicago)
 * Jonathan Lamar (U Colorado)
-Line 28:
+Line 98:
+ * Jake Levinson (U Michigan)
 * Megan Ly (U Colorado Boulder)
 * Peter McNamara (U Queensland, Australia)
-Line 30:
+Line 103:
+ * Kyle Petersen (DePaul U, tentative)
 * Viviane Pons (LRI, U Paris-Sud)
 * Anup Poudel (Loyola)
-Line 31:
+Line 107:
- * Ben Salisbury (U Central Michigan)
+ * Ben Salisbury (Central Michigan U)
-Line 33:
+Line 109:
+ * Adam Schultze (Loyola Chicago and SUNY Albany) 
 * George H. Seelinger (Loyola Chicago)
 * Mark Shimozono (Virginia Tech)
-Line 34:
+Line 113:
- * Kyle Petersen (DePaul U, tentative)
-Line 37:
+Line 115:
- * Yannic Vargas (UQAM)
-Line 40:
+Line 117:
+== 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;"> ''Orthogonal Idempotents in Semisimple Brauer Algebras'' ||
||||<( style="border:none;"> 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. <<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 48:
+Line 159:
+== 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

Non-commutative Groebner bases
- Nantel
- Simon
- Vivianne
- Franco

Diagram Algebras
- George S.
- Steve D.

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)


== Workshop dinner ==
The dinner will be at [[http://www.gooseislandbrewpubs.com/home-clybourn/|Goose Island Brew Pub]], at the corner of N. 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)
  * [[https://cloud.sagemath.com/projects/53b77207-8614-4086-a032-432af4b4cdbd/files/sage-dev-images/|Sage Development Images]]: Sage Math Cloud project with the development images
  * [[http://www.chitownfestivals.com]]: neighborhoods to explore, if you are around this weekend

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