Lfunctions—vast generalizations of the Riemann zeta function— are fundamental objects of study in number theory. In the 1980's the idea emerged that it could be useful to tie together a family of related Lfunctions in one variable to create a "double Dirichlet series," which could be used to study the average behavior of the original family of Lfunctions. Double Dirichlet series soon became multiple Dirichlet series. It has gradually emerged that the local structure of these multiple Dirichlet series shows a rich connection to combinatorial representation theory.
This program will explore this interface between automorphic forms and combinatorial representation theory, and will develop computational tools for facilitating investigations. On the automorphic side, Whittaker functions on padic groups and their covers are the fundamental objects. Whittaker functions and their relatives are expressible in terms of combinatorial structures on the associated Lgroup, its flag variety, or Schubert varieties. In the combinatorial theory crystal graphs, Demazure characters, the Schubert calculus and KazhdanLusztig theory all enter.
Recent progress in combinatorial representation theory has been facilitated by the development of computer programs by the SageCombinat group within the opensource mathematical software Sage. These tools have evolved in response to the research needs of the developers, but through a disciplined development process are general enough to have already found applications beyond their original intent. A major component of the program will be the further development and application of these resources, and it is hoped that they may be used to investigate the connection to multiple Dirichlet series and related combinatorics.



Please note that on date the ICERM IT Staff will be holding Technology Tutorials to familiarize our visitors with the technology ICERM has to offer.
Special Talks & Lecture Series (see full schedule for more information)This page will show upcoming seminars that will be scheduled by organizers, speakers, and participants of the Spring 2013 semester program Automorphic Forms, Combinatorial Representation Theory and Multiple Dirichlet Series. Walkins are welcomed and encouraged for these seminars. Please check back regularly for updates.
We provide an iCal link for those attendees who wish to sync their own devices and/or calendars to our schedule.
Thursday  January 31, 2013  

Time  Description  Speaker  Location  Abstracts  Slides 
10:00  11:00  ICERM Information Technology Resources  Isani Cayetano, ICERM  11th Floor Lecture Hall  
3:30  4:00  Coffee/Tea Break  11th Floor Collaborative Space  
4:00  5:00  Postdoc/Grad Student Seminar Organizational Meeting  11th Floor Lecture Hall 
Friday  February 1, 2013  

Time  Description  Speaker  Location  Abstracts  Slides 
3:30  4:00  Coffee/Tea Break  11th Floor Collaborative Space  
4:00  5:00  Sage coding sprint and help desk  11th Floor Lecture Hall 
Monday  February 4, 2013  

Time  Description  Speaker  Location  Abstracts  Slides 
9:30  10:30  Multiple Dirichlet series I  Solomon Friedberg, Boston College  11th Floor Lecture Hall  
10:45  11:45  Crystals I  Anne Schilling, University of California, Davis  11th Floor Lecture Hall  
1:00  2:20  Representations of affine KacMoody groups over local and global fields  Alexander Braverman, Brown University  10th Floor Classroom  
2:30  3:30  Padic special functions and automorphic forms I  Benjamin Brubaker, Massachusetts Institute of Technology and University of Minnesota; Daniel Bump, Stanford University  11th Floor Lecture Hall  
3:30  4:00  Coffee/Tea Break  11th Floor Collaborative Space 
Thursday  February 7, 2013  

Time  Description  Speaker  Location  Abstracts  Slides 
11:00  11:45  Office Hours: Crystals  Travis Scrimshaw, UC Davis  11th Floor Lecture Hall  
2:45  3:30  Office Hours: padic special functions and automorphic forms  Xin Shen, University of Minnesota  11th Floor Lecture Hall  
3:30  4:00  Coffee/Tea Break  11th Floor Collaborative Space 
Thursday  February 14, 2013  

Time  Description  Speaker  Location  Abstracts  Slides 
9:00  9:50  Open presentation/coding sprints  11th Floor Lecture Hall  
10:00  10:30  Coffee/Tea Break  11th Floor Collaborative Space  
10:30  11:20  Introduction to Version Control (Mercurial & Git)  Chris Berg, University of Quebec  11th Floor Lecture Hall  
11:30  12:20  Tutorial IV: Contributing to Sage  Vincent Delecroix, UniversitÃ© de Paris VII (Denis Diderot); and Franco Saliola, University of Quebec  11th Floor Lecture Hall  
12:30  2:30  Break for Lunch & Free Time  
2:30  3:20  Open presentation/coding sprints  11th Floor Lecture Hall  
3:20  3:30  Survey Distribution  11th Floor Lecture Hall  
3:30  4:00  Coffee/Tea Break  11th Floor Collaborative Space  
4:00  4:50  Graduate Student software demos + status reports  11th Floor Lecture Hall 
Friday  February 15, 2013  

Time  Description  Speaker  Location  Abstracts  Slides 
9:00  9:50  Open presentation/coding sprints  11th Floor Lecture Hall  
10:00  10:30  Coffee/Tea Break  11th Floor Collaborative Space  
11:00  11:30  The category framework  Nicolas Thiery, UniversitÃ© de Paris XI (ParisSud)  11th Floor Lecture Hall  
11:30  12:00  The debugger  Nicolas Thiery, UniversitÃ© de Paris XI (ParisSud)  11th Floor Lecture Hall  
12:30  2:30  Break for Lunch & Free Time  
2:30  3:20  Final Status Reports  11th Floor Lecture Hall  
3:30  4:00  Coffee/Tea Break  11th Floor Collaborative Space  
4:00  4:50  Coding Sprints  11th Floor Lecture Hall 
Wednesday  February 20, 2013  

Time  Description  Speaker  Location  Abstracts  Slides 
11:00  12:50  Representations of affine KacMoody groups over local and global fields  Alexander Braverman, Brown University  10th Floor Classroom  
3:30  4:00  Coffee/Tea Break  11th Floor Collaborative Space  
4:00  5:00  Postdoc & Grad Student Seminar II  11th Floor Lecture Hall 
Thursday  February 21, 2013  

Time  Description  Speaker  Location  Abstracts  Slides 
3:30  4:00  Coffee/Tea Break  11th Floor Collaborative Space 
Friday  February 22, 2013  

Time  Description  Speaker  Location  Abstracts  Slides 
3:30  4:00  Coffee/Tea Break  11th Floor Collaborative Space 
Thursday  February 28, 2013  

Time  Description  Speaker  Location  Abstracts  Slides 
3:30  4:00  Coffee/Tea Break  11th Floor Collaborative Space 
Monday  March 11, 2013  

Time  Description  Speaker  Location  Abstracts  Slides 
1:00  2:20  Representations of affine KacMoody groups over local and global fields  Alexander Braverman, Brown University  11th Floor Lecture Hall  
3:30  4:00  Coffee/Tea Break  11th Floor Collaborative Space  
5:00  7:00  Public Lecture: Scratching the Surface in Dynamic Visual Effects  Robert Bridson, UBC Computer Science, Vancouver Canada  Dynamic Visual Effects 
Wednesday  March 13, 2013  

Time  Description  Speaker  Location  Abstracts  Slides 
11:00  12:20  Representations of affine KacMoody groups over local and global fields  Alexander Braverman, Brown University  11th Floor Lecture Hall  
3:30  4:00  Coffee/Tea Break  11th Floor Collaborative Space  
4:00  5:00  Postdoc & Grad Student Seminar II  11th Floor Lecture Hall 
Thursday  March 14, 2013  

Time  Description  Speaker  Location  Abstracts  Slides 
3:30  4:00  Coffee/Tea Break  11th Floor Collaborative Space 
Friday  March 15, 2013  

Time  Description  Speaker  Location  Abstracts  Slides 
3:30  4:00  Coffee/Tea Break  11th Floor Collaborative Space 
Tuesday  March 19, 2013  

Time  Description  Speaker  Location  Abstracts  Slides 
1:15  2:30  Postdoc & Grad Student Seminar I  11th Floor Lecture Hall  
3:30  4:00  Coffee/Tea Break  11th Floor Collaborative Space 
Thursday  March 21, 2013  

Time  Description  Speaker  Location  Abstracts  Slides 
3:30  4:00  Coffee/Tea Break  11th Floor Collaborative Space 
Friday  March 22, 2013  

Time  Description  Speaker  Location  Abstracts  Slides 
3:30  4:00  Coffee/Tea Break  11th Floor Collaborative Space 
Tuesday  March 26, 2013  

Time  Description  Speaker  Location  Abstracts  Slides 
1:15  2:30  Postdoc & Grad Student Seminar I  11th Floor Lecture Hall  
3:30  4:00  Coffee/Tea Break  11th Floor Collaborative Space 
Wednesday  March 27, 2013  

Time  Description  Speaker  Location  Abstracts  Slides 
3:30  4:00  Coffee/Tea Break  11th Floor Collaborative Space  
4:00  5:00  Postdoc & Grad Student Seminar II  11th Floor Lecture Hall 
Thursday  March 28, 2013  

Time  Description  Speaker  Location  Abstracts  Slides 
3:30  4:00  Coffee/Tea Break  11th Floor Collaborative Space 
Friday  March 29, 2013  

Time  Description  Speaker  Location  Abstracts  Slides 
3:30  4:00  Coffee/Tea Break  11th Floor Collaborative Space 
Monday  April 1, 2013  

Time  Description  Speaker  Location  Abstracts  Slides 
1:00  2:20  Representations of affine KacMoody groups over local and global fields  Alexander Braverman, Brown University  11th Floor Lecture Hall  
3:30  4:00  Coffee/Tea Break  11th Floor Collaborative Space 
Wednesday  April 3, 2013  

Time  Description  Speaker  Location  Abstracts  Slides 
11:00  12:20  Representations of affine KacMoody groups over local and global fields  Alexander Braverman, Brown University  11th Floor Lecture Hall  
3:30  4:00  Coffee/Tea Break  11th Floor Collaborative Space  
4:00  5:00  Postdoc & Grad Student Seminar II  11th Floor Lecture Hall 
Thursday  April 4, 2013  

Time  Description  Speaker  Location  Abstracts  Slides 
3:30  4:00  Coffee/Tea Break  11th Floor Collaborative Space  
3:30  4:30  CareerLAB: Preparing and applying for nonacademic jobs  11th Floor Conference Room 
Friday  April 5, 2013  

Time  Description  Speaker  Location  Abstracts  Slides 
3:30  4:00  Coffee/Tea Break  11th Floor Collaborative Space 
Monday  April 8, 2013  

Time  Description  Speaker  Location  Abstracts  Slides 
3:30  4:00  Coffee/Tea Break  11th Floor Collaborative Space 
Wednesday  April 10, 2013  

Time  Description  Speaker  Location  Abstracts  Slides 
1:00  3:00  Sage Mini Days  Travis Scrimshaw, University of California, Davis  11th Floor Lecture Hall  
3:30  4:00  Coffee/Tea Break  11th Floor Collaborative Space  
4:00  5:00  Postdoc & Grad Student Seminar II  11th Floor Lecture Hall 
Friday  April 12, 2013  

Time  Description  Speaker  Location  Abstracts  Slides 
3:30  4:00  Coffee/Tea Break  11th Floor Collaborative Space 
Monday  April 22, 2013  

Time  Description  Speaker  Location  Abstracts  Slides 
1:00  2:20  Representations of affine KacMoody groups over local and global fields  Alexander Braverman, Brown University  11th Floor Lecture Hall  
3:30  4:00  Coffee/Tea Break  11th Floor Collaborative Space 
Wednesday  April 24, 2013  

Time  Description  Speaker  Location  Abstracts  Slides 
11:00  12:20  Representations of affine KacMoody groups over local and global fields  Alexander Braverman, Brown University  11th Floor Lecture Hall  
12:20  12:30  Long Term Visitor Group Photo  11th Floor Lecture Hall  
3:30  4:00  Coffee/Tea Break  11th Floor Collaborative Space  
4:00  5:00  Postdoc & Grad Student Seminar II  11th Floor Lecture Hall 
Thursday  April 25, 2013  

Time  Description  Speaker  Location  Abstracts  Slides 
3:30  4:00  Coffee/Tea Break  11th Floor Collaborative Space 
Friday  April 26, 2013  

Time  Description  Speaker  Location  Abstracts  Slides 
3:30  4:00  Coffee/Tea Break  11th Floor Collaborative Space 
Monday  April 29, 2013  

Time  Description  Speaker  Location  Abstracts  Slides 
1:00  2:20  Representations of affine KacMoody groups over local and global fields  Alexander Braverman, Brown University  11th Floor Lecture Hall  
3:30  4:00  Coffee/Tea Break  11th Floor Collaborative Space 
Wednesday  May 1, 2013  

Time  Description  Speaker  Location  Abstracts  Slides 
3:30  4:00  Coffee/Tea Break  11th Floor Collaborative Space  
4:00  5:00  Postdoc & Grad Student Seminar II: Metaplectic Demazure Operators.  Anna PuskÃ¡s, Columbia University  11th Floor Lecture Hall 
Thursday  May 2, 2013  

Time  Description  Speaker  Location  Abstracts  Slides 
3:30  4:00  Coffee/Tea Break  11th Floor Collaborative Space 
Friday  May 3, 2013  

Time  Description  Speaker  Location  Abstracts  Slides 
3:30  4:00  Coffee/Tea Break  11th Floor Collaborative Space 
Sage is a mathematics software system developed by and for the mathematics community,
whose mission is to create a viable free open source alternative to Magma, Maple, Mathematica and Matlab.
Its wide span of features, in particular in number theory, combinatorics, and representation theory,
together with its friendly community based development, fosters collaborations across disciplines,
from the design and implementation of new computer exploration tools to research.
This workshop will bring together experienced Sage and SageCombinat
developers and experts of multiple Dirichlet series and computational algebraic combinatorics.
Like every workshop in the Sage Days series, it
will welcome whoever wants to discover Sage, learn more about it, or contribute to it.
As the first meeting for the ICERM Semester Program on "Automorphic Forms,
Combinatorial Representation Theory and Multiple Dirichlet Series", this workshop will focus on Sage
training and on the design and planning of new computational features of central interest for the semester,
around Weyl groups, Hecke algebras and their representations, crystals, posets, combinatorial data visualization, etc.
The workshop will consist of mathematical presentations, presentations on
Sage and coding sprints.
The mathematical presentations will include talks introducing the relevant mathematics for the entire
audience and more advanced talks for interested participants. The Sage presentations will begin with
introductory tutorials and progress to more advanced topics, including software development in Sage.
There will be ample time allotted for design discussions and coding sprints to implement the developed algorithms.



Dates  Title  Organizers 

February 11  15, 2013  Sage Days: Multiple Dirichlet Series, Combinatorics, and Representation Theory  Franco Saliola, Anne Schilling, Nicolas Thiery 
Tutorial Video Links  

Description  Speaker  
Crystals III  Arun Ram, University of Melbourne  

Multiple Dirichlet series III  Gautam Chinta, City College, CUNY  
Thursday  February 14, 2013  

Time  Description  Speaker  Location  Abstracts  Slides 
9:00  9:50  Open presentation/coding sprints  11th Floor Lecture Hall  
10:00  10:30  Coffee/Tea Break  11th Floor Collaborative Space  
10:30  11:20  Introduction to Version Control (Mercurial & Git)  Chris Berg, University of Quebec  11th Floor Lecture Hall  
11:30  12:20  Tutorial IV: Contributing to Sage  Vincent Delecroix, UniversitÃ© de Paris VII (Denis Diderot); and Franco Saliola, University of Quebec  11th Floor Lecture Hall  
12:30  2:30  Break for Lunch & Free Time  
2:30  3:20  Open presentation/coding sprints  11th Floor Lecture Hall  
3:20  3:30  Survey Distribution  11th Floor Lecture Hall  
3:30  4:00  Coffee/Tea Break  11th Floor Collaborative Space  
4:00  4:50  Graduate Student software demos + status reports  11th Floor Lecture Hall 
Friday  February 15, 2013  

Time  Description  Speaker  Location  Abstracts  Slides 
9:00  9:50  Open presentation/coding sprints  11th Floor Lecture Hall  
10:00  10:30  Coffee/Tea Break  11th Floor Collaborative Space  
11:00  11:30  The category framework  Nicolas Thiery, UniversitÃ© de Paris XI (ParisSud)  11th Floor Lecture Hall  
11:30  12:00  The debugger  Nicolas Thiery, UniversitÃ© de Paris XI (ParisSud)  11th Floor Lecture Hall  
12:30  2:30  Break for Lunch & Free Time  
2:30  3:20  Final Status Reports  11th Floor Lecture Hall  
3:30  4:00  Coffee/Tea Break  11th Floor Collaborative Space  
4:00  4:50  Coding Sprints  11th Floor Lecture Hall 
Schubert calculus is the modern approach to classical problems in enumerative algebraic geometry, specifically on flag varieties and their many generalizations. Crystals are combinatorial tools based on quantum groups which arise in the study of representations of Lie algebras. Whittaker functions are special functions on Lie groups or padic groups, for example GL(n,F) where F might be the real or complex numbers, or a padic field. The area of intersection between these three topics is combinatorial representation theory. Common tools such as Demazure operators, the Bruhat partial order, and Macdonald polynomials appear in all three areas. Some connections between these three areas are quite new. This workshop will explore these connections.



Dates  Title  Organizers 

March 48, 2013  Whittaker Functions, Schubert calculus and Crystals  Sara Billey, Daniel Bump, Cristian Lenart 
Thursday  February 28, 2013  

Time  Description  Speaker  Location  Abstracts  Slides 
3:30  4:00  Coffee/Tea Break  11th Floor Collaborative Space 
Recent years have seen a flurry of activity in the field of Weyl group multiple Dirichlet series. Surprising and unexpected connections between these multiple Dirichlet series and several different fields of mathematics have emerged. This workshop will survey recent results and set the stage for future developments which further interrelate analytic number theory, automorphic forms and combinatorial representation theory.
Particular focus will be given to applications of Weyl group multiple Dirichlet series to the following areas:



Dates  Title  Organizers 

April 15  19, 2013  Combinatorics, Multiple Dirichlet Series and Analytic Number Theory  Gautam Chinta, Adrian Diaconu, Dorian Goldfeld, Ozlem Imamoglu 