Organizing Committee
Abstract

The Summer@ICERM faculty advisers will present a variety of research projects on the combinatorial and graph theoretical properties of DNA self-assembly. By modeling nanostructures with discrete graphs, efficient DNA self-assembly becomes a mathematical puzzle. Faculty will also guide the development of computational tools which can be used to aid in answering fundamental questions that arise in this field.

Throughout the eight-week program, students will be introduced to the research topic with interactive lectures. Afterward, students will work on their projects in assigned groups of two to four, supervised by faculty advisors and aided by teaching assistants. Students will meet daily, give regular talks about their findings, attend mini-courses, guest talks, and professional development seminars, practice coding, and Tex typesetting, and will acquire skills in free software development. Students will learn how to collaborate mathematically, working closely in their teams to write up their research into a paper.

Image for "Summer@ICERM 2023: Mathematical Modeling of DNA Self-Assembly"

Program Details

2023 Proposed Research Topics
  • Optimize design structures for families of graphs such as graphs with a lattice substructure and k-regular graphs.
  • Create, expand, and improve current software used to nd and check optimal solutions.
  • Determine relationships between optimizing bond-edge and tile types.
Detailed Project Descriptions (PDF)
Important Notes
  • Applicants must be matriculating undergraduate students at the time of the start of Summer@ICERM 2023.
  • Funding is available for 2-3 students who are not US citizens or permanent residents.
Funding Includes*
  • $4,000 stipend
  • Providence, RI room, board, and travel funding provided for in-person programming, pandemic permitting. (Brown students who choose not to live in the dorm will waive ICERM provided housing and meal funding.)
To Apply

Applications accepted via MathPrograms.org. Applications submitted by February 14, 2023, will receive full consideration.

Confirmed Speakers & Participants

Talks will be presented virtually or in-person as indicated in the schedule below.

  • Speaker
  • Poster Presenter
  • Attendee
  • Virtual Attendee
  • Leyda Almodóvar Velázquez
    Stonehill College
  • Toby Anderson
    Harvey Mudd College
  • Jacob Ashworth
    Rose-Hulman Institute of Technology
  • Lisa Baek
    Brown University
  • Grace Bielefeldt
    St. Olaf College
  • Ethan Bove
    Brown University
  • Katelyn Buck
    The University of Texas at Austin
  • Michael Cho
    Stanford University
  • Jo Ellis-Monaghan
    Saint Michael's College
  • Ryann Firestine
    Auburn University
  • Michaela Fitzgerald
    Stonehill College
  • Olivia Greinke
    Transylvania University
  • Luca Grossmann
    Tufts University
  • Janelle Hammond
    Stonehill College
  • Amanda Harsy Ramsay
    Lewis University
  • Iris Horng
    University of Pennsylvania
  • Catherine Jacobs
    Wellesley College
  • Cory Johnson
    California State University, San Bernardino
  • Amelia Julian
    Plymouth State University
  • Andrew Lavengood-Ryan
    Nevada State University
  • Holly Luebsen
    University of Texas at Austin
  • Fausto Navarro
    Johns Hopkins University
  • Iskandar Nazhar
    University of Massachusetts Amherst
  • Eric Redmon
    Marquette University
  • Steph Reyes
    Claremont Graduate University
  • Luis Santori
    University of Central Florida
  • Jessica Sorrells
    Converse University
  • Mitchell VonEschen
    Lawrence University
  • Xingyi Zhang
    Carleton College

Summer Schedule

Monday, June 12, 2023
  • 9:30 - 10:00 am EDT
    Welcome, Meet & Greet
    Welcome - 10th Floor Collaborative Space
  • 10:00 am - 12:30 pm EDT
    Scavenger Hunt
  • 12:45 - 2:00 pm EDT
    Lunch/Free Time
  • 2:00 - 3:00 pm EDT
    Goals of Summer
    10th Floor Collaborative Space
    • Leyda Almodóvar Velázquez, Stonehill College
    • Amanda Harsy, Lewis University
    • Cory Johnson, California State University, San Bernardino
    • Jessica Sorrells, Converse University
  • 3:00 - 3:30 pm EDT
    Coffee Break
    10th Floor Collaborative Space
  • 3:30 - 4:30 pm EDT
    Introduction to Graph Theoretical DNA Self-Assembly
    10th Floor Collaborative Space
    • Leyda Almodóvar Velázquez, Stonehill College
    • Amanda Harsy, Lewis University
    • Cory Johnson, California State University, San Bernardino
    • Jessica Sorrells, Converse University
Tuesday, June 13, 2023
  • 9:30 - 10:30 am EDT
    Introduction to Scenario 1
    10th Floor Collaborative Space
    • Cory Johnson, California State University, San Bernardino
    • Jessica Sorrells, Converse University
  • 11:00 am - 12:00 pm EDT
    Scenario 1 Group Work
    Group Work - 10th Floor Collaborative Space
  • 12:00 - 1:30 pm EDT
    Lunch/Free Time
  • 1:30 - 2:30 pm EDT
    Tools from Linear Algebra Minicourse
    10th Floor Collaborative Space
    • Amanda Harsy, Lewis University
    • Jessica Sorrells, Converse University
  • 2:30 - 3:00 pm EDT
    Coffee Break
    10th Floor Collaborative Space
  • 3:00 - 4:00 pm EDT
    Introduction to Scenario 2
    10th Floor Collaborative Space
    • Amanda Harsy, Lewis University
    • Cory Johnson, California State University, San Bernardino
  • 4:00 - 4:30 pm EDT
    Extra time/ wrap up
    - 10th Floor Collaborative Space
Wednesday, June 14, 2023
  • 9:30 - 10:30 am EDT
    Scenario 2 Group Work Session
    Group Work - 10th Floor Collaborative Space
  • 11:00 am - 12:00 pm EDT
    Additional Tools from Graph Theory Minicourse
    10th Floor Collaborative Space
    • Leyda Almodóvar Velázquez, Stonehill College
    • Cory Johnson, California State University, San Bernardino
  • 12:00 - 1:30 pm EDT
    Lunch/Free Time
  • 1:30 - 2:30 pm EDT
    Introduction to Scenario 3
    10th Floor Collaborative Space
    • Leyda Almodóvar Velázquez, Stonehill College
    • Jessica Sorrells, Converse University
  • 2:30 - 3:00 pm EDT
    Coffee Break
    10th Floor Collaborative Space
  • 3:00 - 4:00 pm EDT
    Scenario 3 Group Work Session
    Group Work - 10th Floor Collaborative Space
  • 4:00 - 4:30 pm EDT
    Extra time/ Wrap up
    - 10th Floor Collaborative Space
Thursday, June 15, 2023
  • 9:30 - 10:30 am EDT
    Overview of DNA Self-Assembly Research Projects
    10th Floor Collaborative Space
    • Leyda Almodóvar Velázquez, Stonehill College
    • Amanda Harsy, Lewis University
    • Cory Johnson, California State University, San Bernardino
    • Jessica Sorrells, Converse University
  • 11:00 am - 12:00 pm EDT
    Q&A about Scenarios 1, 2, and 3 / Discussion of Problem Sets
    Problem Session - 10th Floor Collaborative Space
    • Leyda Almodóvar Velázquez, Stonehill College
    • Amanda Harsy, Lewis University
    • Cory Johnson, California State University, San Bernardino
    • Jessica Sorrells, Converse University
  • 12:00 - 1:30 pm EDT
    Lunch/Free Time
  • 1:30 - 2:30 pm EDT
    Project Otions Q&A / Work Session
    10th Floor Collaborative Space
    • Leyda Almodóvar Velázquez, Stonehill College
    • Ryann Firestine, Auburn University
    • Michaela Fitzgerald, Stonehill College
    • Amanda Harsy, Lewis University
    • Cory Johnson, California State University, San Bernardino
    • Eric Redmon, Marquette University
    • Jessica Sorrells, Converse University
  • 2:30 - 3:00 pm EDT
    Coffee Break
    10th Floor Collaborative Space
  • 3:50 - 4:00 pm EDT
    Project Preference Surveys Due by 4:00 PM
    - 10th Floor Collaborative Space
  • 4:00 - 4:30 pm EDT
    Extra time/ Wrap up
    - 10th Floor Collaborative Space
Friday, June 16, 2023
  • 9:30 - 10:30 am EDT
    Project Assignments, Announcement & Introduction to Math Research
    10th Floor Collaborative Space
    • Leyda Almodóvar Velázquez, Stonehill College
    • Amanda Harsy, Lewis University
    • Cory Johnson, California State University, San Bernardino
    • Jessica Sorrells, Converse University
  • 10:30 - 11:00 am EDT
    Break
    Coffee Break - 10th Floor Collaborative Space
  • 11:00 am - 12:00 pm EDT
    Group Work
    10th Floor Collaborative Space
  • 12:00 - 1:30 pm EDT
    Lunch/Free Time
  • 1:30 - 3:00 pm EDT
    Group Work
    10th Floor Collaborative Space
  • 3:00 - 3:30 pm EDT
    Coffee Break
    10th Floor Collaborative Space
  • 3:30 - 4:00 pm EDT
    Group Work
    10th Floor Collaborative Space
Tuesday, June 20, 2023
  • 9:30 - 10:30 am EDT
    Introduction to Python & CoCalc
    10th Floor Collaborative Space
    • Jessica Sorrells, Converse University
  • 10:30 - 11:00 am EDT
    Break
    Coffee Break - 10th Floor Collaborative Space
  • 11:00 am - 12:00 pm EDT
    Introduction to Python & CoCalc
    10th Floor Collaborative Space
    • Jessica Sorrells, Converse University
  • 12:00 - 1:30 pm EDT
    Lunch/Free Time
  • 1:30 - 2:30 pm EDT
    Introduction to LaTeX & Overleaf
    10th Floor Collaborative Space
    • Amanda Harsy, Lewis University
    • Cory Johnson, California State University, San Bernardino
  • 2:30 - 3:00 pm EDT
    Coffee Break
    10th Floor Collaborative Space
  • 3:00 - 4:30 pm EDT
    Group Work
    10th Floor Collaborative Space
Wednesday, June 21, 2023
  • 9:30 - 10:30 am EDT
    Group Work
    10th Floor Collaborative Space
  • 10:30 - 11:00 am EDT
    Break
    Coffee Break - 10th Floor Collaborative Space
  • 11:00 am - 12:00 pm EDT
    Group Work
    10th Floor Collaborative Space
  • 12:00 - 1:30 pm EDT
    Lunch/Free Time
  • 1:30 - 2:30 pm EDT
    Group Work
    10th Floor Collaborative Space
  • 2:30 - 3:00 pm EDT
    Coffee Break
    10th Floor Collaborative Space
  • 3:00 - 4:30 pm EDT
    Group Work
    10th Floor Collaborative Space
Thursday, June 22, 2023
  • 9:30 - 10:30 am EDT
    Group Work
    10th Floor Collaborative Space
  • 10:30 - 11:00 am EDT
    Break
    Coffee Break - 10th Floor Collaborative Space
  • 11:00 am - 12:00 pm EDT
    Group Work
    10th Floor Collaborative Space
  • 12:00 - 1:30 pm EDT
    Lunch/Free Time
  • 2:30 - 3:00 pm EDT
    Coffee Break
    10th Floor Collaborative Space
  • 3:00 - 4:30 pm EDT
    Group Work
    10th Floor Collaborative Space
  • 6:00 - 6:45 pm EDT
    TBA
    11th Floor Lecture Hall
    • Jessisa Libertini, Brown University
Friday, June 23, 2023
  • 9:30 - 10:30 am EDT
    Group Presentations
    10th Floor Collaborative Space
  • 10:30 - 11:00 am EDT
    Break
    Coffee Break - 10th Floor Collaborative Space
  • 11:00 am - 12:00 pm EDT
    Group Presentations
    10th Floor Collaborative Space
  • 12:00 - 1:30 pm EDT
    Lunch/Free Time
  • 1:30 - 2:00 pm EDT
    Oscar Tutorial
    Tutorial - 10th Floor Collaborative Space
  • 2:00 - 2:30 pm EDT
    Group Work
    10th Floor Collaborative Space
  • 2:30 - 3:00 pm EDT
    Coffee Break
    10th Floor Collaborative Space
  • 3:00 - 4:30 pm EDT
    Group Work
    10th Floor Collaborative Space
Monday, June 26, 2023
  • 9:30 - 10:30 am EDT
    Group Work
    10th Floor Collaborative Space
  • 11:00 am - 12:00 pm EDT
    Group Work
    10th Floor Collaborative Space
  • 12:00 - 1:30 pm EDT
    Lunch/Free Time
  • 1:30 - 2:30 pm EDT
    Group Check-in Meetings
    Meeting - 10th Floor Collaborative Space
  • 2:30 - 3:00 pm EDT
    Coffee Break
    10th Floor Collaborative Space
  • 3:00 - 4:30 pm EDT
    Group Work
    Virtual
Tuesday, June 27, 2023
  • 9:30 - 11:30 am EDT
    Ethics I & II
    10th Floor Collaborative Space
  • 11:30 am - 1:00 pm EDT
    Lunch/Free Time
  • 1:00 - 2:00 pm EDT
    Research in Quantative Justice Panel
    Panel Discussion - 10th Floor Collaborative Space
  • 2:00 - 2:30 pm EDT
    Coffee Break
    10th Floor Collaborative Space
  • 2:30 - 4:30 pm EDT
    Group Work
    10th Floor Collaborative Space
Wednesday, June 28, 2023
  • 9:30 - 10:30 am EDT
    Group Work
    10th Floor Collaborative Space
  • 11:00 am - 12:00 pm EDT
    Group Work
    10th Floor Collaborative Space
  • 12:00 - 1:30 pm EDT
    Lunch/Free Time
  • 1:30 - 2:30 pm EDT
    Group Work
    10th Floor Collaborative Space
  • 2:30 - 3:00 pm EDT
    Coffee Break
    10th Floor Collaborative Space
  • 3:00 - 4:30 pm EDT
    Group Work
    10th Floor Collaborative Space
Thursday, June 29, 2023
  • 9:30 - 10:30 am EDT
    Group Check-in Meetings
    Meeting - 10th Floor Collaborative Space
  • 11:00 am - 12:00 pm EDT
    Group Work
    10th Floor Collaborative Space
  • 12:00 - 1:30 pm EDT
    Lunch/Free Time
  • 1:30 - 2:30 pm EDT
    Group Work
    10th Floor Collaborative Space
  • 2:30 - 3:00 pm EDT
    Coffee Break
    10th Floor Collaborative Space
  • 3:00 - 4:30 pm EDT
    Group Work
    10th Floor Collaborative Space
Friday, June 30, 2023
  • 9:30 - 10:30 am EDT
    Group Presentations
    10th Floor Collaborative Space
  • 11:00 am - 12:00 pm EDT
    Group Presentations
    10th Floor Collaborative Space
  • 12:00 - 1:30 pm EDT
    Lunch/Free Time
  • 1:30 - 2:30 pm EDT
    Group Presentations
    10th Floor Collaborative Space
  • 2:30 - 3:00 pm EDT
    Coffee Break
    10th Floor Collaborative Space
  • 3:00 - 4:30 pm EDT
    Group Work
    10th Floor Collaborative Space
Wednesday, July 5, 2023
  • 9:30 - 10:30 am EDT
    Group Work
    10th Floor Collaborative Space
  • 11:00 am - 12:00 pm EDT
    Group Work
    10th Floor Collaborative Space
  • 12:00 - 1:30 pm EDT
    Lunch/Free Time
  • 1:30 - 2:30 pm EDT
    Group Work
    10th Floor Collaborative Space
  • 2:30 - 3:00 pm EDT
    Coffee Break
    10th Floor Collaborative Space
  • 3:00 - 4:30 pm EDT
    Group Work
    10th Floor Collaborative Space
Thursday, July 6, 2023
  • 9:30 - 10:30 am EDT
    Group Check-in Meetings
    Meeting - 10th Floor Collaborative Space
  • 11:00 am - 12:00 pm EDT
    Group Work
    10th Floor Collaborative Space
  • 12:00 - 1:30 pm EDT
    Lunch/Free Time
  • 1:30 - 2:30 pm EDT
    Group Work
    10th Floor Collaborative Space
  • 2:30 - 3:00 pm EDT
    Coffee Break
    10th Floor Collaborative Space
  • 3:00 - 4:30 pm EDT
    Group Work -Suggested: Prepare Weekly Presentation
    Group Work - 10th Floor Collaborative Space
Friday, July 7, 2023
  • 9:30 - 10:30 am EDT
    Group Presentations
    10th Floor Collaborative Space
  • 11:00 am - 12:00 pm EDT
    Group Presentations
    10th Floor Collaborative Space
  • 12:00 - 1:30 pm EDT
    Lunch/Free Time
  • 1:30 - 2:00 pm EDT
    Brief Presentation Feedback
    10th Floor Collaborative Space
  • 2:00 - 2:30 pm EDT
    Group Work
    10th Floor Collaborative Space
  • 2:30 - 3:00 pm EDT
    Coffee Break
    10th Floor Collaborative Space
  • 3:00 - 4:30 pm EDT
    Group Work - Suggested: Strategize for nex week
    Group Work - 10th Floor Collaborative Space
Monday, July 10, 2023
  • 9:30 - 10:30 am EDT
    Group Work
    10th Floor Collaborative Space
  • 11:00 am - 12:00 pm EDT
    Group Work
    10th Floor Collaborative Space
  • 12:00 - 1:30 pm EDT
    Lunch/Free Time
  • 1:30 - 2:30 pm EDT
    Group Work
    10th Floor Collaborative Space
  • 2:30 - 3:00 pm EDT
    Coffee Break
    10th Floor Collaborative Space
  • 3:00 - 4:30 pm EDT
    Group Work
    10th Floor Collaborative Space
Tuesday, July 11, 2023
  • 9:30 - 10:30 am EDT
    Group Check-in Meetings
    Meeting - 10th Floor Collaborative Space
  • 11:00 am - 12:00 pm EDT
    Group Work
    10th Floor Collaborative Space
  • 12:00 - 1:30 pm EDT
    Lunch/Free Time
  • 1:30 - 2:30 pm EDT
    Group Work
    10th Floor Collaborative Space
  • 2:30 - 3:00 pm EDT
    Coffee Break
    10th Floor Collaborative Space
  • 3:00 - 4:30 pm EDT
    Group Work
    10th Floor Collaborative Space
Wednesday, July 12, 2023
  • 9:30 - 10:30 am EDT
    Group Work
    10th Floor Collaborative Space
  • 11:00 am - 12:00 pm EDT
    Group Work
    10th Floor Collaborative Space
  • 12:00 - 1:30 pm EDT
    Lunch/Free Time
  • 1:30 - 2:30 pm EDT
    Group Work
    10th Floor Collaborative Space
  • 2:30 - 3:00 pm EDT
    Coffee Break
    10th Floor Collaborative Space
  • 3:00 - 3:30 pm EDT
    Group Work
    10th Floor Collaborative Space
  • 3:30 - 4:30 pm EDT
    The geometric nature of polynomial equations
    10th Floor Collaborative Space
Thursday, July 13, 2023
  • 9:30 - 10:30 am EDT
    Group Check-in Meetings
    Meeting - 10th Floor Collaborative Space
  • 11:00 am - 12:00 pm EDT
    Group Work
    10th Floor Collaborative Space
  • 12:00 - 1:30 pm EDT
    Lunch/Free Time
  • 1:30 - 2:30 pm EDT
    Group Work
    10th Floor Collaborative Space
  • 2:30 - 3:00 pm EDT
    Coffee Break
    10th Floor Collaborative Space
  • 3:00 - 4:30 pm EDT
    Suggested: Prepare Weekly Presentation
    Group Work - 10th Floor Collaborative Space
  • 6:30 - 8:00 pm EDT
    Movie Night
    Movie Night - 11th Floor Lecture Hall
Friday, July 14, 2023
  • 9:30 - 10:30 am EDT
    Group Presentations
    10th Floor Collaborative Space
  • 11:00 am - 12:00 pm EDT
    Group Presentations
    10th Floor Collaborative Space
  • 12:00 - 1:30 pm EDT
    Lunch/Free Time
  • 1:30 - 2:00 pm EDT
    Brief Presentation Feedback
    10th Floor Collaborative Space
  • 2:00 - 2:30 pm EDT
    Group Work
    10th Floor Collaborative Space
  • 2:30 - 3:00 pm EDT
    Coffee Break
    10th Floor Collaborative Space
  • 3:00 - 4:30 pm EDT
    Suggested: Strategize for next week
    Group Work - 10th Floor Collaborative Space
Monday, July 17, 2023
  • 9:30 - 10:30 am EDT
    Group Work
    10th Floor Collaborative Space
  • 11:00 am - 12:00 pm EDT
    Group Work
    10th Floor Collaborative Space
  • 12:00 - 1:30 pm EDT
    Lunch/Free Time
  • 1:30 - 2:30 pm EDT
    Group Work
    10th Floor Collaborative Space
  • 2:30 - 3:00 pm EDT
    Yellow Pig Day
    Coffee Break - 10th Floor Collaborative Space
  • 3:00 - 4:30 pm EDT
    Group Work
    10th Floor Collaborative Space
Tuesday, July 18, 2023
  • 9:30 - 10:30 am EDT
    Group Check-In Meetings
    Meeting - 10th Floor Collaborative Space
  • 11:00 am - 12:00 pm EDT
    Group Work
    10th Floor Collaborative Space
  • 12:00 - 1:30 pm EDT
    Lunch/Free Time
  • 1:30 - 2:30 pm EDT
    Group Work
    10th Floor Collaborative Space
  • 2:30 - 3:00 pm EDT
    Coffee Break
    10th Floor Collaborative Space
  • 3:00 - 3:30 pm EDT
    Group Work
    10th Floor Collaborative Space
  • 3:30 - 4:30 pm EDT
    Output of a pot with exactly one bond-edge type
    10th Floor Collaborative Space
    • Andrew Lavengood-Ryan, Nevada State University
Wednesday, July 19, 2023
  • 10:00 am - 12:00 pm EDT
    Group Work
    10th Floor Collaborative Space
  • 12:00 - 1:30 pm EDT
    Lunch/Free Time
  • 1:30 - 2:30 pm EDT
    Group Work
    10th Floor Collaborative Space
  • 2:30 - 3:00 pm EDT
    Coffee Break
    10th Floor Collaborative Space
  • 3:00 - 4:30 pm EDT
    Group Work
    10th Floor Collaborative Space
  • 5:00 - 6:00 pm EDT
    Group Work
    10th Floor Collaborative Space
  • 6:00 - 7:00 pm EDT
    Panel Discussion
    10th Floor Collaborative Space
    • Panelists
    • Andrew Lavengood-Ryan, Nevada State University
    • José Pabón, New Jersey Institute of Technology
    • Rachel Roca, Michigan State University
Thursday, July 20, 2023
  • 9:30 - 10:30 am EDT
    Group Check-In Meetings
    Meeting - 10th Floor Collaborative Space
  • 11:00 am - 12:00 pm EDT
    Group Work
    10th Floor Collaborative Space
  • 12:00 - 1:30 pm EDT
    Lunch/Free Time
  • 1:30 - 2:30 pm EDT
    Group Work
    10th Floor Collaborative Space
  • 2:30 - 3:00 pm EDT
    Coffee Break
    10th Floor Collaborative Space
  • 3:00 - 4:30 pm EDT
    Group Work
    10th Floor Collaborative Space
Friday, July 21, 2023
  • 9:30 - 10:30 am EDT
    Group Presentations
    10th Floor Collaborative Space
  • 11:00 am - 12:00 pm EDT
    Group Presentations
    10th Floor Collaborative Space
  • 12:00 - 1:30 pm EDT
    Lunch/Free Time
  • 1:30 - 2:00 pm EDT
    Brief Presentation Feeback
    10th Floor Collaborative Space
  • 2:00 - 2:30 pm EDT
    Group Work
    10th Floor Collaborative Space
  • 2:30 - 3:00 pm EDT
    Coffee Break
    10th Floor Collaborative Space
  • 3:00 - 4:30 pm EDT
    Group Work
    10th Floor Collaborative Space
Monday, July 24, 2023
  • 9:30 - 10:30 am EDT
    Group Work
    10th Floor Collaborative Space
  • 11:00 am - 12:00 pm EDT
    Group Work
    10th Floor Collaborative Space
  • 12:00 - 1:30 pm EDT
    Lunch/Free Time
  • 1:30 - 2:30 pm EDT
    Group Work
    10th Floor Collaborative Space
  • 2:30 - 3:00 pm EDT
    Coffee Break
    10th Floor Collaborative Space
  • 3:00 - 3:30 pm EDT
    Group Work
    10th Floor Collaborative Space
  • 3:30 - 4:30 pm EDT
    Metamodeling and uncertainty quantification of a simulation chain for urban air quality
    10th Floor Collaborative Space
    • Janelle Hammond, Stonehill College
Tuesday, July 25, 2023
  • 9:30 - 10:30 am EDT
    Group Check-in Meetings
    Meeting - 10th Floor Collaborative Space
  • 11:00 am - 12:00 pm EDT
    Group Work
    10th Floor Collaborative Space
  • 12:00 - 1:30 pm EDT
    Lunch/Free Time
  • 1:30 - 2:30 pm EDT
    Group Work
    10th Floor Collaborative Space
  • 2:30 - 3:00 pm EDT
    Coffee Break
    10th Floor Collaborative Space
  • 3:00 - 4:30 pm EDT
    Group Work
    10th Floor Collaborative Space
Wednesday, July 26, 2023
  • 9:30 - 10:30 am EDT
    Group Work
    10th Floor Collaborative Space
  • 11:00 am - 12:00 pm EDT
    Group Work
    10th Floor Collaborative Space
  • 12:00 - 1:30 pm EDT
    Lunch/Free Time
  • 1:30 - 2:30 pm EDT
    Group Work
    10th Floor Collaborative Space
  • 2:30 - 3:00 pm EDT
    Coffee Break
    10th Floor Collaborative Space
  • 3:00 - 4:30 pm EDT
    Group Work
    10th Floor Collaborative Space
  • 5:00 - 6:00 pm EDT
    PowerPoint Party
    - 10th Floor Collaborative Space
Thursday, July 27, 2023
  • 9:30 - 10:30 am EDT
    Group Work
    10th Floor Collaborative Space
  • 11:00 am - 12:00 pm EDT
    Group Work
    10th Floor Collaborative Space
  • 12:00 - 1:30 pm EDT
    Lunch/Free Time
  • 1:30 - 2:30 pm EDT
    Practice Run for Final Presentations
    Group Presentations - 10th Floor Collaborative Space
  • 2:30 - 3:00 pm EDT
    Coffee Break
    10th Floor Collaborative Space
  • 3:00 - 4:30 pm EDT
    Practice Run for Final Presentations
    Group Presentations - 10th Floor Collaborative Space
Friday, July 28, 2023
  • 9:30 - 10:30 am EDT
    Suggested: Make Revisions to Final Presentation
    Group Work - 10th Floor Collaborative Space
  • 11:00 am - 12:00 pm EDT
    Group Work
    10th Floor Collaborative Space
  • 12:00 - 1:30 pm EDT
    Lunch/Free Time
  • 1:30 - 2:30 pm EDT
    Group Work
    10th Floor Collaborative Space
  • 2:30 - 3:00 pm EDT
    Coffee Break
    10th Floor Collaborative Space
  • 3:00 - 4:30 pm EDT
    Suggested: Strategize for next week
    Group Work - 10th Floor Collaborative Space
Monday, July 31, 2023
  • 9:00 - 10:00 am EDT
    Algorithmic Generation of DNA Self-Assembly Graph
    11th Floor Lecture Hall
    • Grace Bielefeldt, St. Olaf College
    • Iris Horng, University of Pennsylvania
    • Holly Luebsen, University of Texas at Austin
    • Mitchell VonEschen, Lawrence University
    Abstract
    With recent advancements in the field of nanotechnology, there has been increasing interest in self-assembling nanostructures. These are constructed through the process of branched junction DNA molecules bonding with each other without external guidance. Using a flexible tile-based model, we represent molecules as vertices of a graph and cohesive ends of DNA strands as complementary half-edges allowing the molecules to bond with each other. Due to the unpredictability of DNA self-assembly in a laboratory setting and the risk of undesirable products being incidentally constructed, predicting what structures can be produced from a given list of components, referred to as a “pot of tiles,” is useful but has been proven NP-hard. Our project introduces an algorithm to computationally generate and visualize at least one valid graph given a pot of tiles. By adjusting a number of construction parameters, we can produce graphs of various orders and proportions of tiles.
  • 10:00 - 11:00 am EDT
    Optimal Constructions for DNA Self-Assembly of k-Regular Graphs
    11th Floor Lecture Hall
    • Lisa Baek, Brown University
    • Ethan Bove, Brown University
    • Michael Cho, Stanford University
    • Xingyi Zhang, Carleton College
    Abstract
    Within biology, it is of interest to construct DNA complexes of a certain shape. These complexes can be represented abstractly in the language of graph theory, where edges are understood to be strands of DNA joined at junctions, represented by vertices. Because guided construction of such structures is inefficient, design strategies for DNA self-assembly are desirable. Branched DNA molecules are referred to as tiles, each consisting of flexible unpaired cohesive ends with the ability to form bond-edges. We thus consider the minimum number of tiles and bond-edge types to construct a graph G (corresponding to a DNA target structure) without allowing the formation of smaller graphs, or non-isomorphic graphs of the same size. In this paper, we specifically investigate the case where G is k-regular. We introduce the concept of (un)swappable graphs, using the property to establish lower bounds on bond-edge and tile types in the unswappable case. We also introduce a method of generating upper bounds using a vertex-cover model. We apply both of these methods to prove new bounds on a number of regular families, including crown graphs, prism graphs, Kneser graphs, Johnson graphs, Antiprism Graphs and Archimedean solid graphs.
  • 11:00 am - 12:00 pm EDT
    Exploring Relationships Between Optimal Flexible Tile and Bond-Edge Types of Self-Assembling DNA
    11th Floor Lecture Hall
    • Toby Anderson, Harvey Mudd College
    • Olivia Greinke, Transylvania University
    • Iskandar Nazhar, University of Massachusetts Amherst
    • Luis Santori, University of Central Florida
    Abstract
    DNA self-assembly is an emerging area of study within the field of biology and nanotechnology with applications in targeted drug delivery, biomolecular computing, and biosensing. Branched molecules of DNA bond to each other with complementary strands of base pairs to form a target nanostructure. Using a flexible tile model, these structures can be modeled mathematically as graphs that are constructed from vertices with extending half-edges. These vertices are referred to as tiles, and their extending half-edges are labeled with bond-edge types that represent different extending sequences of DNA base pairs. Most mathematical research using the flexible tile model seeks to find optimal constructions for various graphs and graph families in an effort to maximize laboratory efficiency within three scenarios of increasing restriction. Our research focuses on searching for underlying relationships between the minimum number of bond-edge types and tile types needed to construct a graph across these scenarios. Building on previous work, we explore a variety of low-order graphs and present optimal constructions for all graphs of order five and below in all scenarios. In addition, we present results for various lattice graphs, particularly hexagonal lattices, and web graphs.
  • 12:00 - 1:30 pm EDT
    Lunch/Free Time
  • 1:30 - 2:30 pm EDT
    Group Work
    10th Floor Collaborative Space
  • 2:30 - 3:00 pm EDT
    Coffee Break
    Virtual
  • 3:00 - 4:00 pm EDT
    Group Work
    10th Floor Collaborative Space
  • 4:00 - 4:30 pm EDT
    Reception with Spring 2021 Reunion Group
    Reception - 11th Floor Collaborative Space
Tuesday, August 1, 2023
  • 9:15 - 9:30 am EDT
    Group Photo (Immediately After Talk)
    11th Floor Collaborative Space
  • 9:30 - 10:30 am EDT
    Multi-dimensional Graphs Modeling Self-Assembling DNA Nanostructures
    11th Floor Lecture Hall
    • Katelyn Buck, The University of Texas at Austin
    • Catherine Jacobs, Wellesley College
    • Amelia Julian, Plymouth State University
    Abstract
    Employing tools from graph theory and linear algebra, we model the biological process of the creation of nanostructures from self-assembling DNA complexes. We represent $k$-armed branch junction molecules with tiles which are vertices in a graph with half-edges. The half-edges depict the cohesive-end types of a DNA strand. We aim to determine the minimum number of tiles and cohesive-end types necessary to form the complete complex of a given multi-dimensional graph structure. The problem of modeling DNA self-assembly is particularly challenging when considering graph families which change in multiple dimensions. In this research, we present the minimum number of tiles and cohesive-end types necessary to create the stacked book graphs, the square lattice graphs, and the Mongolian tent graphs, under different laboratory constraints.
  • 10:30 - 11:30 am EDT
    Algorithmic Pot Generation for DNA Self-Assembly
    11th Floor Lecture Hall
    • Jacob Ashworth, Rose-Hulman Institute of Technology
    • Luca Grossmann, Tufts University
    • Fausto Navarro, Johns Hopkins University
    Abstract
    Recent advancements in microbiology have motivated the study of the production of nano-structures with applications such as biomedical computing and molecular robotics. One way to construct these structures is to allow small DNA molecules to join together with complementary DNA branches. A practical question is: given a target nanostructure, what is the optimal set of DNA molecules that can assemble such a structure? We use a flexible-tile graph theoretic model to develop algorithmic approaches, which, given an undirected graph representing a target structure, finds the optimal collection of smaller structures which can construct that graph under certain constraints. Our exploration into these algorithmic approaches has also lead to several mathematical results.
  • 11:30 am - 1:30 pm EDT
    Lunch/Free Time
  • 1:30 - 2:30 pm EDT
    What's Next?
    10th Floor Collaborative Space
    • Leyda Almodóvar Velázquez, Stonehill College
    • Amanda Harsy, Lewis University
    • Cory Johnson, California State University, San Bernardino
    • Jessica Sorrells, Converse University
  • 2:30 - 3:00 pm EDT
    Coffee Break
    Virtual
  • 3:30 - 4:30 pm EDT
    Group Work
    10th Floor Collaborative Space
Wednesday, August 2, 2023
  • 9:30 - 10:30 am EDT
    Group Work
    10th Floor Collaborative Space
  • 11:00 am - 12:00 pm EDT
    Group Work
    10th Floor Collaborative Space
  • 12:00 - 1:30 pm EDT
    Lunch/Free Time
  • 1:30 - 2:30 pm EDT
    Self-Assembly with DNA Origami
    10th Floor Collaborative Space
    • Jo Ellis-Monaghan, Saint Michael's College
  • 2:30 - 3:00 pm EDT
    Coffee Break
    Virtual
  • 3:00 - 4:30 pm EDT
    Group Work
    10th Floor Collaborative Space
Thursday, August 3, 2023
  • 9:30 - 10:30 am EDT
    Group Work
    10th Floor Collaborative Space
  • 11:00 am - 12:00 pm EDT
    Group Work
    11th Floor Collaborative Space
  • 12:00 - 1:30 pm EDT
    Lunch/Free Time
  • 2:30 - 3:00 pm EDT
    Coffee Break
    Virtual
  • 3:00 - 4:30 pm EDT
    Group Work
    10th Floor Collaborative Space
Friday, August 4, 2023
  • 9:30 - 10:30 am EDT
    Summer Research Symposium Set Up
    - Sayles Hall
  • 10:30 am - 1:00 pm EDT
    Summer Research Symposium
    - Sayles Hall
  • 1:00 - 1:30 pm EDT
    Lunch/Free Time

All event times are listed in ICERM local time in Providence, RI (Eastern Daylight Time / UTC-4).

All event times are listed in .

Other Summer@ICERM Events

Summer@ICERM 2012: Geometry and Dynamics
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Summer@ICERM 2013: Geometry and Dynamics
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Summer@ICERM 2014: Polygons and Polynomials
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Summer@ICERM 2015: Computational Dynamics and Topology
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Summer@ICERM 2016: Dynamics and Stochastics
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Summer@ICERM 2017: Topological Data Analysis
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Summer@ICERM 2018: Low Dimensional Topology and Geometry
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Summer@ICERM 2019: Computational Arithmetic Dynamics
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Summer@ICERM 2021: Computational Polygonal Billiards
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Summer@ICERM 2022: Computational Combinatorics
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