Research Experiences for Undergraduate Faculty (REUF)

Institute for Computational and Experimental Research in Mathematics (ICERM)

https://icerm.brown.edu/reuf/reuf2023/
August 7, 2023 - August 11, 2023
Monday, August 7, 2023
  • 9:00 - 9:20 am EDT
    Check In
    11th Floor Collaborative Space
  • 9:20 - 9:30 am EDT
    Welcome
    11th Floor Lecture Hall
    • Brendan Hassett, ICERM/Brown University
  • 9:30 - 10:00 am EDT
    Welcome to REUF / Introduction
    Program Overview - 11th Floor Lecture Hall
    • Leslie Hogben, American Institute of Mathematics (AIM) & Iowa State U
    • Ulrica Wilson, ICERM/Morehouse College
  • 10:00 - 10:30 am EDT
    Project 1 Introduction - Maximum likelihood degree of stochastic block models
    11th Floor Lecture Hall
    • Project Leader
    • Elizabeth Gross, University of Hawai'i at Mānoa
    Abstract
    A popular class of statistical models studied in algebraic statistics are log-linear models. Log-linear models are popular since they have a monomial parameterization and correspond to toric ideals. Toric ideals are polynomial ideals generated by binomials with lots of combinatorial structure, making them great objects for exploration at varying levels of depth. For our project, we will focus on log-linear models that appear in network analysis, in particular, stochastic block models, which are used for clustering tasks in networks. We will study the geometry of maximum likelihood estimation for these models, specifically the maximum likelihood degree. The maximum likelihood degree is the number of complex solutions to the system of likelihood equations, and thus, for part of our project we will explore different computational software to solve such systems and different techniques to bound the number of solutions.
  • 10:30 - 11:00 am EDT
    Coffee Break
    11th Floor Collaborative Space
  • 11:00 - 11:30 am EDT
    Project 2 Introduction - A New Variation on Happy Numbers
    11th Floor Lecture Hall
    • Project Leader
    • Helen Grundman, Bryn Mawr College
    Abstract
    The happy function maps a positive integer (expressed in base 10) to the sum of the squares of its digits. A happy number is a positive integer that, under repeated applications of the happy function, maps to 1. The iterative behavior of the happy function and its many variations has been the subject of study for over 75 years. In this project, we'll study a new variation on the classic happy function, working to establish results paralleling those known for the classic happy function and/or its other variations.
  • 11:30 am - 12:00 pm EDT
    Project 3 Introduction - BRACKETS: A NEW METHOD FOR INTEGRATION
    11th Floor Lecture Hall
    • Project Leader
    • Victor Moll, Tulane University
    Abstract
    The evaluation of integrals is one of the subjects taught in Calculus courses. Even tough this appears to be an elementary subject, there is no complete algorithm to compute every integral. The project will be based on a new method to evaluate definite integrals. This is called the method of brackets, invented by Ivan Gonzalez at his Physics Ph.D. thesis at Universidad Santa Maria, Valparaiso, Chile in the context of Feynman diagrams. These diagrams explain the interaction of elementary particles and their parametrization produces very complicated integrals. The evaluation of this integrals give all the fundamental properties of particles. This is a heuristic method, based on a small number of rules, some of which have established rigorously. The project will involve a combinations of symbolic computation and also some theory needed to prove the rules of the method. This is a remarkable method: it reduces the evaluation of definite integrals to the solution of a system of linear equations, usually of very small size.
  • 12:00 - 2:00 pm EDT
    Lunch/Free Time
  • 2:00 - 2:15 pm EDT
    Selection of Project Groups
    Group Work - 11th Floor Lecture Hall
  • 2:15 - 3:30 pm EDT
    Group Work
    Assigned Group Work Space
  • 3:30 - 4:00 pm EDT
    Coffee Break
    11th Floor Collaborative Space
  • 4:00 - 5:00 pm EDT
    Group Work
    Assigned Group Work Space
  • 5:00 - 6:30 pm EDT
    Reception
    11th Floor Collaborative Space
Tuesday, August 8, 2023
  • 9:00 - 9:15 am EDT
    Announcements
    Meeting - 11th Floor Lecture Hall
  • 9:15 - 10:00 am EDT
    Group Work
    Assigned Group Work Space
  • 10:00 - 10:30 am EDT
    Coffee Break
    11th Floor Collaborative Space
  • 10:30 am - 12:00 pm EDT
    Group Work
    Assigned Group Work Space
  • 12:00 - 2:00 pm EDT
    Lunch/Free Time
  • 2:00 - 2:15 pm EDT
    Announcements
    Meeting - 11th Floor Lecture Hall
  • 2:15 - 3:00 pm EDT
    Group Work
    Assigned Group Work Space
  • 3:00 - 3:30 pm EDT
    Coffee Break
    11th Floor Collaborative Space
  • 3:30 - 5:00 pm EDT
    Group Work
    Assigned Group Work Space
Wednesday, August 9, 2023
  • 9:00 - 9:15 am EDT
    Interim group reports
    Meeting - 11th Floor Lecture Hall
  • 9:15 - 9:20 am EDT
    Group Photo (Immediately After Interim group reports)
    Group Photo (Immediately After Talk) - 11th Floor Lecture Hall
  • 9:20 - 10:00 am EDT
    Group Work
    Assigned Group Work Space
  • 10:00 - 10:30 am EDT
    Coffee Break
    11th Floor Collaborative Space
  • 10:30 am - 12:00 pm EDT
    Group Work
    Assigned Group Work Space
  • 12:00 - 2:00 pm EDT
    Lunch/Free Time
  • 2:00 - 2:15 pm EDT
    Announcements
    Meeting - 11th Floor Lecture Hall
  • 2:15 - 3:00 pm EDT
    Group Work
    Assigned Group Work Space
  • 3:00 - 3:30 pm EDT
    Coffee Break
    11th Floor Collaborative Space
  • 3:30 - 5:00 pm EDT
    Group Work
    Assigned Group Work Space
Thursday, August 10, 2023
  • 9:00 - 10:30 am EDT
    Group Discussion - Undergraduate Research
    Meeting - 11th Floor Lecture Hall
  • 10:30 - 11:00 am EDT
    Coffee Break
    11th Floor Collaborative Space
  • 11:00 am - 12:00 pm EDT
    Group Work
    11th Floor Lecture Hall
  • 12:00 - 2:00 pm EDT
    Lunch/Free Time
  • 2:00 - 2:15 pm EDT
    Announcements
    Meeting - 11th Floor Lecture Hall
  • 2:15 - 3:00 pm EDT
    Group Work
    Assigned Group Work Space
  • 3:00 - 3:30 pm EDT
    Coffee Break
    11th Floor Collaborative Space
  • 3:30 - 5:00 pm EDT
    Group Work
    Assigned Group Work Space
Friday, August 11, 2023
  • 9:00 - 9:15 am EDT
    Announcements
    Meeting - 11th Floor Lecture Hall
  • 9:15 - 10:00 am EDT
    Group Work
    Assigned Group Work Space
  • 10:00 - 10:30 am EDT
    Coffee Break
    11th Floor Collaborative Space
  • 10:30 am - 12:00 pm EDT
    Group Work
    Assigned Group Work Space
  • 12:00 - 2:00 pm EDT
    Lunch/Free Time
  • 2:00 - 2:30 pm EDT
    Group Presentations - 1
    Group Presentations - 11th Floor Lecture Hall
  • 2:30 - 3:00 pm EDT
    Coffee Break
    11th Floor Collaborative Space
  • 3:00 - 3:30 pm EDT
    Group Presentations - 2
    Group Presentations - 11th Floor Lecture Hall
  • 3:30 - 4:00 pm EDT
    Group Presentations - 3
    Group Presentations - 11th Floor Lecture Hall

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