Algebraic combinatorics is an area of mathematics that studies objects that have combinatorial and algebraic properties. An example of such object is the ring of symmetric functions. In algebraic combinatorics, we use algebraic methods to answer combinatorial questions, and conversely, apply combinatorial techniques to problems in algebra.

Let  be commuting variables, a polynomial  is symmetric if =  for all permutations . The space of all symmetric polynomials forms a ring, . This simply says that if we multiply two symmetric functions we get another symmetric function.  has several distinguished bases that are indexed by partitions. One of the most important bases is Schur's basis: . The objective of the summer is to learn about and work on open problems involving symmetric polynomials. 

The academic and research portion of the 2013 MSRI-UP will be led by Prof. Rosa Orellana from Dartmouth College.

Bibliography

General Description

During the summer, each of the 18 student participants will:

• participate in the mathematics research program under the direction of Dr. Rosa Orellana, Dartmouth College, a post-doc and two graduate students
• complete a research project done in collaboration with other MSRI-UP students
• give a presentation and write a technical report on his/her research project
• attend a series of colloquium talks given by leading researches in their fields
• attend workshops aimed at developing skills and techniques needed for research careers in the mathematical sciences and
• learn techniques that will maximize a student's likelihood of admissions to graduate programs as well as the likelihood of winning fellowships
• receive a $3100 stipend, lodging, meals and round trip travel to Berkeley, CA.

After the summer, each student will:

• have an opportunity to attend a national mathematics or science conference where students will present their research
• be part of a network of mentors that will provide continuous advice in the long term as the student makes progress in his/her studies
• be contacted regarding future research opportunities

Application Materials

Applications for MSRI-UP 2013 should be submitted via the MathPrograms listing, which lists the required application materials.  Due to funding restrictions, only U.S. citizens and permanent residents are eligible to apply, and the proram cannot accept foreign students regardless of funding.  In addition, students who have already graduated or will have graduated with a bachelor's degree by June 16, 2013 are not eligible to apply.  Applications that are complete by March 3, 2013 are guaranteed full consideration.

Email: msriup@msri.org (Primary)

The directors of MSRI-UP are:

• Dr. Ivelisse Rubio - iverubio@gmail.com - 2013 on-site director
• Dr. Herbert Medina - hmedina@lmu.edu
• Dr. Duane Cooper - dcooper@morehouse.edu
• Dr. Suzanne Weekes - sweekes@wpi.edu
• Dr. Ricardo Cortez - rcortez@tulane.edu

Previous Years:

• 2012 MSRI-UP: Enumerative Combinatorics
• 2011 MSRI-UP: Mathematical Finance
• 2010 MSRI-UP: Elliptic curves and Applications
• 2009 MSRI-UP: Coding Theory
• 2008 MSRI-UP: Experimental Mathematics
• 2007 MSRI-UP: Computational Science and Mathematics