3. Postdoctoral Program - MSRI

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5. Undergraduate Program (MSRI-UP) 5.1 Description of Undergraduate Program Research Topic: Elliptic Curves and Applications Date: June 12, 2010 to July 25, 2010 Organizers: Ivelisse Rubio, Duane Cooper*, Ricardo Cortez, Herbert Medina, Suzanne Weekes The MSRI-UP summer program is designed for undergraduate students who have completed two years of university-level mathematics courses and would like to conduct research in the mathematical sciences. 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. The academic portion of the 2010 program will be led by Dr. Edray Goins. During the summer, each of the 18 student participants � participated in the mathematics research program under the direction of Dr. Goins, � completed a research project done in collaboration with other MSRI-UP students, � gave a presentation and wrote a technical report on his/her research project, � attended a series of colloquium talks given by leading researches in their fields, � attended workshops aimed at developing skills and techniques needed for research careers in the mathematical sciences, 93
� acquired techniques that will maximize a student's likelihood of admissions to graduate programs as well as the likelihood of winning fellowships, and � received a $3000 stipend, lodging, meals, and roundtrip travel to Berkeley, CA. After the summer, each student � had an opportunity to attend a national mathematics or science conference where students presented their research, � became part of a network of mentors that provides continuous advice in the long term as the student makes progress in his/her studies, and � was contacted regarding future research opportunities. The main objective of MSRI-UP 2010 was to identify talented students, especially those from underrepresented groups, who are interested in mathematics and to 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 objective was designed to contribute significantly toward meeting the program goal of increasing the number of graduate degrees in the mathematical sciences, especially doctorates, earned by U.S. citizens and permanent residents by cultivating heretofore untapped mathematical talent within the U.S. Black, Hispanic/Latino, and Native American communities. MSRI is delighted to announce that two of the students who participated in the MSRI-UP 2007 were awarded 2010 NSF Graduate Research Fellowships. They are Talea Mayo and Gina Pomann. Topic: Elliptic Curves and Applications An elliptic curve E is an arithmetic-algebraic object: It is simultaneously a nonsingular projective curve with an affine equation, which allows one to perform arithmetic on its points, and a finitely generated abelian group, which allows one to apply results from abstract algebra. The goal for this summer was to learn about elliptic curves and give applications by using their properties to study problems in other fields. Students completed a short course for two (2) weeks to cover any necessary background from abstract algebra and discrete mathematics. For the remainder of the program, the students broke up into smaller groups and worked on research projects. They had a choice of one of the following projects: Project 1: ABC Conjecture This deceptively simple question was first outlined in 1985 by Joseph Oesterlé and David Masser. Consider three relatively prime positive integers A, B, C, such that A+B=C. Let rad(ABC) denote the product of the distinct prime factors of ABC. Computational evidence suggests that it is rare to have C > rad(ABC). To be more precise, given any positive number e, there should only exist finitely many (A:B:C) such that the quantity q(A:B:C) = log(C)/log(rad(ABC)) is greater than 1+e. 94
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Final Report, 2005-2010 and Annual
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6. Appendix - Final Reports .......
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• Spring 2008: Representation The
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place the highest value on the oppo
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which establishes the relation betw
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Public Understanding of Mathematics
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1.3 Scientific Programs and their A
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The first week of May 2010 coincide
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The goal of this program was, throu
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"An illustration of the tropical Ab
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• lead to new breakthroughs in th
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Other mathematical breakthroughs th
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• Advice on preparing for intervi
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An off-site workshop partially fund
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1.7 Other Scientific Workshops Hot
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experienced circle leaders. Togethe
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2. Program and Workshop Data 2.1 Pr
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Jöricke Burglind Institut des Haut
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Smith Ivan Centre for Mathematical
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Home Institution Classified by Stat
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2.4 Workshop Participant List (See
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Home Institution Classified by Stat
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2.7 Program Publication List Last N
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Page 50 and 51: Lekili Yanki Geometric composition
Page 52 and 53: Draisma Jan The tropical projective
Page 54 and 55: Krasner Daniel Patterns in sl(2)-li
Page 56 and 57: Sarkar Sucharit Murasugi sums Matt
Page 58 and 59: Falk Michael Feichtner Eva Tropical
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Page 64 and 65: Here are additional details on the
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Page 70 and 71: Katz, Eric Lopez de Medrano, Lucia
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Page 74 and 75: Sazdanovic, Radmila Wehrli, Stephan
Page 76 and 77: Angeltveit, Vigleik Crofts, Scott H
Page 78 and 79: 3.2 Postdoctoral Fellow Placement L
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Page 104 and 105: 2 2. Participants The response to o
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Page 108 and 109: 6 While at MSRI, Gathmann extended
Page 110 and 111: 8 In conclusion, my postdoc at MSRI
Page 112 and 113: 10 -with Christian Haase, who staye
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Page 116 and 117: 14 Josephine Yu PhD: UC Berkeley, 2
Page 118 and 119: 16 6. Alex Fink was an invited spea
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Page 126 and 127: field. Nevertheless, some of it is
Page 128 and 129: developments which occurred in this
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Page 136 and 137: Mark spend his time at MSRI working
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Page 146 and 147: 2 REPORT ON THE MSRI WORKSHOP “HO
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4 REPORT ON THE MSRI WORKSHOP “HO
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Homology Theory of Knots and Links
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Complementary Program August 17, 20
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Complementary Program 2009-10 Postd
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Complementary Program Demographic S
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MID YEAR REPORT - DECEMBER 2009 VIG
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California. We talked about several
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EXTERNAL POSTDOCTORAL FELLOW REPORT
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on. While his research area is some
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POSTDOCTORAL FELLOW REPORT December
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[1] (with Garcia-Puente, Martin del
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REPORT FROM MENTOR June 2010 Year e
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I have also begun working on relate
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2 Professional Travel Sep. 6 - 26,
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REPORT FROM MENTOR June 2010 Karl h
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POSTDOCTORAL FELLOW REPORT June 201
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REPORT FROM MENTOR June 2010 ------
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Postdoctoral Program supported by t
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RO(S 1 )-graded homotopy groups of
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MSRI POSTDOCTORAL FELLOWSHIP REPORT
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2 TRISTRAM BOGART and its facets ar
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To Whom It May Concern: During the
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MSRI FELLOWSHIP FINAL REPORT SCOTT
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As his mentor at UCSC, I had freque
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- UC Davis Combinatorics Seminar -
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Christopher J. Hillar University of
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G. Isely, C. Hillar, and F. Sommer,
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Postdoc Report for: Dr. Christopher
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2 NSF REPORT FOR ERIC KATZ linear s
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Year-End Report 2010-11 NSF Math In
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Jan. 25 - 28, 2011 Recruitment Visi
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MSRI POSTDOCTORAL FELLOWSHIP REPORT
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Final report: mentoring Sikimeti Ma
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eginning of the Fall semester, and
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MSRI FINAL REPORT JARED SPECK 1. Ba
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External Postdoctoral Fellows 2009-
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External Postdoctoral Fellows 2009-
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2 connections to geometry, topology
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Connections for Women: Tropical Geo
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Participant List MSRI Workshop: Con
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Connections for Women: Tropical Geo
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2 Combinatorics, Several Complex Va
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Introductory Workshop: Tropical Geo
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Currently Available Videos � Sam
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Name Institution Hering, Milena Uni
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Introductory Workshop: Tropical Geo
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analysis. The clarity of Payne’s
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Tropical Geometry in Combinatorics
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Name Institution Kharlamov, Viatche
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Tropical Geometry in Combinatorics
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Above satisfactory 35 73% Somewhat
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Tropical structures in geometry and
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Research Workshop: Tropical Structu
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Research Workshop: Tropical Structu
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Algebraic Structures in the Theory
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2 WORKSHOP REPORT toric fibrations,
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Algebraic Structures in the Theory
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Wednesday November 18, 2009 09:00AM
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Participant List MSRI Workshop: Alg
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Name Institution Smith, Ivan Centre
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Research Workshop: Symplectic and C
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Detailed review: We will now discus
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Symplectic and Contact Topology and
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Research Workshop: Symplectic and C
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Final Report MSRI Connections for W
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Connections : Symplectic and Contac
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Currently Available Videos � Siki
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Milin, Isidora University of Illino
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Final Report Introductory Workshop
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at a variety of levels. Since a hig
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Introductory Workshop: Symplectic a
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Participant List MSRI Workshop: Int
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Park, Jongil Seoul National Univers
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Symplectic and Poisson Geometry in
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Symplectic and Poisson Geometry in
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Symplectic Geometry, Noncommutative
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09:00AM - 10:00AM Registration 10:0
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REPORT ON THE MSRI WORKSHOP “HOMO
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of the theory via webs and foams mo
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Schedule Connections for Women: Hom
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Connections for Women: Homology The
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04/29/2010 Connections for Women: H
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REPORT ON THE MSRI WORKSHOP “INTR
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INTRODUCTORY WORKSHOP, FINAL REPORT
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Introductory Workshop: Homology The
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Connections for Women: Homology The
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Research Workshop: Homology Theorie
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Schedule Research Workshop: Homolog
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Currently Available Videos Research
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Research Workshop: Homology Theorie
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04/29/2010 Research Workshop: Homol
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comprehensive lectures explaining t
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Hot Topics: Black Holes in Relativi
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Currently Available Videos � Miha
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Shao, Shuanglin Institute for Advan
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MATHEMATICAL SCIENCES RESEARCH INST
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MPDI Summer Institute 2009: Final R
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school teachers (in the case of sim
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in length)? The audience would be e
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Evaluation #1 1. What were the bene
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6. Do you have to report to an admi
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your class because your way of teac
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employee with a summary of what you
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what have you learned in this insti
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Evaluation #9 (signed Kelly L.) 1.
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therefore should not be given the j
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would you like them organized? Plea
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Evaluation #11 1. What were the ben
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Evaluation #12 (signed Jake Disston
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ideas are insignificant in light of
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manipulative and pictorial level. F
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Yes.. I would like to talk to 4 - 6
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No, but I have continued to make my
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5. Are you planning to work with co
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(1) change the order of my curricul
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I will show my 6th grade teacher co
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to teaching and planning. Perhaps b
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III - Develop a lesson on similarit
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4. What are you going to implement/
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matics? * How are people teaching t
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Evaluation #23 (I guess this is Cla
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Evaluation #24 1. What were the ben
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2010 Mathematical Sciences Research
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During the 2007-2009 summers, 46 st
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MSRI-UP peers promoted mathematical
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The outcome of all the students’
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school in mathematics.” They prov
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16. Evidence Already Pointing to Lo
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II. Research Projects 1. Your resea
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5. Is there a workshop, discussion
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V. Non-Academic Aspects of MSRI-UP
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MSRI-UP 2010 Calendar, Weeks 1 and
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MSRI-UP 2010 Calendar, Weeks 5 and
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In 1945 Stanislaw Ulam posed a ques
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2.2 Circle Theorem 2. Let r ∈ Q w
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parabola is (a) The parabola and tw
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Proof. For each 1 ≤ i < j ≤ 4 w
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2.5 Non-Concyclic Points on a Parab
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⎛ ⎜ 1 ⎜ 0 ⎜ 0 ⎜ 0 ⎜ 0
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following rational points: n23 = Y1
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Toric Varieties Cox, David Invited
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Toric varieties Held: June 15-26, 2
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the graduate participants to hear a
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This lecture series addressed topic
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Participant List MSRI Workshop: Sym
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Example of a Summer Graduate Worksh
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Random Matrix theory July 6, 2009 t
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Random Matrix Theory Held: July 6 -
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Participant List MSRI Workshop: Ran
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Below is the list of topics conside
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stability estimates for the inverse
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Participant List MSRI Workshop: Inv
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The Arithmetic of L-Functions IAS/P
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ackground material on group represe
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Computational Theory of Real Reduct
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3. Postdoctoral Program - MSRI

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