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MSRI-UP 2013: Algebraic Combinatorics June 15, 2013 - July 28, 2013
Registration Deadline: July 28, 2013 almost 4 years ago
To apply for Funding you must register by: March 15, 2013 over 4 years ago
Parent Program: --
Location: MSRI: Baker Board Room, Commons Room, Atrium
Organizers Duane Cooper (Morehouse College), Ricardo Cortez (Tulane University), Herbert Medina (Loyola Marymount University), LEAD Ivelisse M. Rubio (University of Puerto Rico), Suzanne Weekes (Worcester Polytechnic Institute)

The MSRI Undergraduate Program (MSRI--UP) is a comprehensive summer program designed for undergraduate students who have completed two years of university-level mathematics courses and would like to conduct research in the mathematical sciences.  The main objective of the MSRI-UP is to identify talented students, especially those from underrepresented groups, who are interested in mathematics and make available to them meaningful research opportunities, the necessary skills and knowledge to participate in successful collaborations, and a community of academic peers and mentors who can advise, encourage and support them through a successful graduate program.

MSRI-UP 2013: Algebraic Combinatorics

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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.


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:

Previous Years:

Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
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Jul 26, 2013
08:45 AM - 09:00 AM
  Opening Remarks
09:00 AM - 09:45 AM
  On the Schur Positivity of Differences of Products of Schur Functions
10:00 AM - 10:45 AM
  Permutation Patterns for Real-Valued Functions
11:00 AM - 11:45 AM
  The Algebra of Set Partitions
12:00 PM - 01:00 PM
01:00 PM - 01:45 PM
  The lattice of set partitions and transition matrices of symmetric functions
02:00 PM - 02:45 PM
  Chromatic Symmetric Functions of Trees and Unicycles
03:00 PM - 03:45 PM
  Number of permutations with same peak set for signed permutations
04:00 PM - 04:30 PM
  Closing Remarks