Home /  MSRI-UP 2017: Solving Systems of Polynomial Equations


MSRI-UP 2017: Solving Systems of Polynomial Equations June 24, 2017 - August 06, 2017
Parent Program: --
Location: SLMath: Baker Board Room, Atrium
Organizers LEAD Federico Ardila (San Francisco State University), Duane Cooper (Morehouse College), Maria Mercedes Franco (Queensborough Community College (CUNY)), Herbert Medina (University of Portland), J. Maurice Rojas (Texas A & M University), Suzanne Weekes (SIAM - Society of Industrial and Applied Mathematics)

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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. 

In 2017, MSRI-UP will focus on Solving Systems of Polynomial Equations, a topic at the heart of almost every computational problem in the physical and life sciences. We will pay special attention to complexity issues, highlighting connections with tropical geometry, number theory, and the P vs. NP problem. The research program will be led by Prof. J. Maurice Rojas of Texas A&M University.

Students who have had a linear algebra course and a course in which they have had to write proofs are eligible to apply. Due to funding restrictions, only U.S. citizens and permanent residents may apply regardless of funding. Members of underrepresented groups are especially encouraged to apply.

Funding provided by:


MSRI-UP 2017: Solving Systems of Polynomial Equations

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General Description

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

  • participate in the mathematics research program under the direction of Prof. J. Maurice Rojas of Texas A&M University, 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 2017 should be submitted via MathPrograms, which lists the required application materials.  Due to funding restrictions, only U.S. citizens and permanent residents are eligible to apply, and the program cannot accept foreign students regardless of funding.  In addition, students who have already graduated or will have graduated with a bachelor's degree by August 31, 2017 are not eligible to apply.  Applications submitted by February 15, 2017 will receive full consideration. (Applications submitted after February 15, 2017 but by March 1, 2017 may still be considered in a second round of acceptances.) We expect to begin making offers for participation in late February or early March.

A complete application consists of five items, all of which should be submitted through the MathPrograms website.  These items are:

1. Transcripts.
Upload a copy of your transcripts showing courses and grades from all post-secondary institutions that you have attended. Initially, unofficial copies (as long as they are legible) of transcripts are acceptable, though we may request official transcripts upon acceptance to the program. Transcripts should contain Fall 2016 grades.

2. Statement of Interest.
Write a personal statement (300 - 800 words) addressing your interest in mathematics, science, and/or other disciplines, and why you would like to participate in the 2017 MSRI-UP. You may write in any style, but try to address the origins of your interest in mathematics and science, experiences (school-related and other) that have particularly stimulated you, obstacles you have faced along the way, and future educational and career plans and aspirations.  If you are currently attending a two-year institution, provide the name of the four-year institution to which you plan to transfer and the date when you plan to transfer in your statement.

3. List of Mathematics/Science Courses Taken with Grades.
Please list all mathematics and science courses taken, starting with the most recent.  State the Course Number, Course Title, Term Taken, Grade Received, and Institution where you took the course.
Example: MATH 201, Calculus 1, Spring 2015, B+, Carolina Community College 

4. Description of Previous Summer / Research Experiences.
Please list and give a brief description of all mathematics or science research or summer programs (high school or college), if any, in which you have participated. (Students who have not participated in any programs previously are encouraged to apply.)

5. Faculty Reference Letter of Recommendation. 
Please designate one Faculty Reference; this should be someone from whom you have taken a class or with whom you have done independent mathematical or scientific work. The person you identify as the Faculty Reference on the MathPrograms website will be notified to fill out an on-line form and upload a letter of recommendation. Although the person will be notified automatically by email, it is the student's responsibility to make sure the letter is uploaded on time. You may include a second letter if you think it will strengthen your application significantly.

For additional information, please contact the on-site director for the 2017 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, Notes/Handouts & Videos
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Jun 30, 2017
01:00 PM - 02:00 PM
  The Dehn-Sommerville Relations and the Catalan Matroid
Anastasia Chavez (Saint Mary's College of California)
Jul 07, 2017
01:00 PM - 02:00 PM
  Mathematical Models of the Retina and In Silico Experiments: Shedding Light on Vision Loss
Erika Camacho (Arizona State University)
Jul 14, 2017
01:00 PM - 02:00 PM
  Impact of Undergraduate Research on Student Learning at a Community College
Maria Mercedes Franco (Queensborough Community College (CUNY))
Jul 21, 2017
01:00 PM - 02:00 PM
  How to be "successful" in the mathematics world?
Alexander Diaz-Lopez (Villanova University)
Jul 28, 2017
01:00 PM - 02:00 PM
  Exponential Domination in Grids
Michael Young (Carnegie Mellon University)
Aug 04, 2017
09:00 AM - 09:15 AM
  Final Presentations: Opening Remarks
J. Maurice Rojas (Texas A & M University)
09:15 AM - 09:50 AM
  Counting the roots of a polynomial modulo p2
trajan hammonds (Carnegie Mellon University), Jeremy Johnson (California State Polytechnic University, Humboldt), Angela Patini (University of Pennsylvania)
10:00 AM - 11:20 AM
  On the maximal number of roots of a trinomial over a prime field
Jeshu Dastidar (San Francisco State University), Viviana Peña Márquez (Konrad Lorenz Fundación Universitaria), Ryan Pugh (Foothill College)
10:45 AM - 11:20 AM
  Applying discriminant chambers to structured polynomials
Amy Adair (Louisiana State University), Alex Mendez (University of Illinois at Urbana-Champaign), Diane Tchuindjo (Massachusetts Institute of Technology)
11:30 AM - 01:00 PM
01:00 PM - 01:35 PM
  Using lower binomials to approximate roots of trinomials
Harold Jimenez Polo (University of California, Berkeley), Esteban Madrigal (Harvard University), Carlos Osco Huaricapcha (San Francisco State University)
01:45 PM - 02:20 PM
  Topology of positive zero sets of bivariate pentanomials
Malachi Alexander (University of California, Santa Cruz), Ashley De Luna (California State Polytechnic University, Pomona), Christian McRoberts (Iowa State University)
02:30 PM - 03:05 PM
  Topology of positive zero sets of n-variate (n+4)-nomials
Davina Boykin (Valparaiso University), Sabrina Enriquez (University of Southern California), Noemi Valdez (Harvard University)
03:05 PM - 03:15 PM
  Closing Remarks
Federico Ardila (San Francisco State University)
03:15 PM - 04:00 PM
  Afternoon Tea