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Home » MSRI-UP 2015: Geometric Combinatorics Motivated by the Social Sciences

MSRI-UP

MSRI-UP 2015: Geometric Combinatorics Motivated by the Social Sciences June 13, 2015 - July 26, 2015
Location: MSRI: Baker Board Room, Atrium
Organizers Federico Ardila (San Francisco State University), LEAD Duane Cooper (Morehouse College), Herbert Medina (Loyola Marymount University), Ivelisse M. Rubio (University of Puerto Rico), Suzanne Weekes (Worcester Polytechnic Institute)
Speaker(s)

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Description

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.
 

The academic and research portion of the 2015 MSRI-UP will be led by Prof. Francis Su from Harvey Mudd College.

 

In only the last 75 years or so has mathematics enjoyed a symbiotic relationship with the social sciences. On one hand, mathematics can be used to model questions in the social sciences; on the other hand, the social sciences motivate new mathematical questions. Game theory was born out of a question to model human interaction and decision-making.

 

As an example, the space of preferences is often a geometric space whose combinatorial structure encodes player preferences in interesting ways. It many 'fair division' problems (e.g., how to divide a cake fairly among several people) the space of preferences is often a convex polytope, and in a voting theory the space of preferences (the political spectrum) is commonly modeled as a line but could be something else as well.

 

In this REU we will consider mathematical problems motivated by 'fair division' questions and voting theory, using a mix of techniques from combinatorics, convex geometry, and analysis. Students who have had a course in which they have had to write proofs and also linear algebra or discrete mathematics are eligible to apply. It can be helpful, though not necessary, to have some exposure to economics, game theory, or a course in programming. 

General Description

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

  • participate in the mathematics research program under the direction of Dr. Francis Su, Harvey Mudd 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 2015 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, 2015 are not eligible to apply.  The application link will be available on this page starting November 29, 2014. Applications submitted by February 15, 2015 will receive full consideration. (Applications submitted after February 15, 2015 but by March 1, 2015 may still be considered in a second round of acceptances.) We hope to begin making offers for participation in late February or early March.

For additional information, please contact the on-site director for the 2015 MSRI-UP.

The directors of MSRI-UP are:

Previous Years:

Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
Schedule
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Jul 24, 2015
Friday
09:30 AM - 10:15 AM
  Double-n Circular Societies
Edwin Baeza (Purdue University), Nikaya Smith (University of North Carolina), Sarah Yoseph (Claremont Graduate University)
10:15 AM - 11:00 AM
  An Analogue of the Median Voter Theorem for Approval Voting
Ethan Bush (University of Michigan, Flint), Kyle Duke (James Madison University), Miles Stevens (Morehouse College)
11:00 AM - 11:45 AM
  A Matroid Generalization of Sperner's Lemma
Gabriel Andrade (University of Massachusetts Amherst), Andres Rodriguez (San Francisco State University), Alberto Ruiz Sandoval (University of Puerto Rico)
11:45 AM - 01:15 PM
  Lunch Break
01:15 PM - 02:00 PM
  Committee Selection with Approval Voting and Hypercubes
Caleb Bugg (Morehouse College), Gabriel Elvin (University of California, Los Angeles)
02:00 PM - 02:45 PM
  The Banquet Seating Problem
Michelle Rosado, Michelle Rosado (University of Puerto Rico), Ashley Scruse (Clark Atlanta University), Alexis Jane Torre (University of Arizona)
02:45 PM - 03:30 PM
  A Volume Argument for Tucker's Lemma
Beauttie Kuture (Pomona College), Oscar Leong (Swarthmore College), Christopher Loa (University of Tennessee)
03:30 PM - 04:30 PM
  Tea