Organizing Committee
  • Ricardo Cortez
    Tulane University
  • Mark Levi
    Pennsylvania State University
  • Michael Minion
    Stanford University
  • Richard Montgomery
    University of California - Santa Cruz
Abstract

Interested in discussing cutting edge research ideas with both peers and leaders in their field?

Interested in broadening your professional network across the mathematical sciences?

Interested in the opportunity to present your ideas and hear about funding opportunities from program officers?

Idea-Lab invites 20 early career researchers (postdoctoral candidates and assistant professors) to ICERM for a week during the summer. The program will start with brief participant presentations on their research interests in order to build a common understanding of the breadth and depth of expertise. Throughout the week, organizers or visiting researchers will give comprehensive overviews of their research topics. Organizers will create smaller teams of participants who will discuss, in depth, these research questions, obstacles, and possible solutions. At the end of the week, the teams will prepare presentations on the problems at hand and ideas for solutions. These will be shared with a broad audience including invited program officers from funding agencies.

IdeaLab applicants should be at an early stage of their post-PhD career. A CV, research statement, and two reference letters are required.

"The best part of the program was meeting and getting to know the other participants - everyone involved was enthusiastic and friendly, and having such a wide range of expertise made it a safe space in which to admit to not knowing particular things and to ask questions and learn from one another. The topic gave us a common ground from which to spark scientific discussions which were both educational and fun."
-- IdeaLab Participant

Confirmed Speakers & Participants

  • Roza Aceska
    Ball State University
  • Alessandro Arsie
    University of Toledo
  • Brian Benson
    University of Illinois at Urbana-Champaign
  • Yougan Cheng
    University of Minnesota
  • Ricardo Cortez
    Tulane University
  • William Cousins
    Massachusetts Institute of Technology
  • Jim Curry
    National Science Foundation
  • Marcelo Disconzi
    Vanderbilt University
  • Amit Einav
    University of Cambridge
  • Fariba Fahroo
    DARPA
  • Cristi Guevara
    Mexican Petroleum Institute
  • Eric Hall
    University of Massachusetts Amherst
  • Silvia Jiménez Bolaños
    Colgate University
  • Madison Krieger
    Brown University
  • Mark Levi
    Pennsylvania State University
  • Lina Ma
    Purdue University
  • Reza Malek-Madani
    Office of Naval Research
  • Michael Minion
    Stanford University
  • Alexey Miroshnikov
    University of Massachusetts
  • Richard Montgomery
    University of California - Santa Cruz
  • Tomoki Ohsawa
    University of Michigan
  • Sarah Olson
    Worcester Polytechnic Institute
  • Thomas Russell
    National Science Foundation
  • Emily Russell
    Harvard University
  • Jason Teutsch
    University of Chicago
  • Léon Tine
    Institut Camille Jordan, Universite Lyon 1
  • Guowei Yu
    University of Toronto
  • Longhua Zhao
    Case Western Reserve University

IdeaLab Topics

Toward a more realistic model of ciliated and flagellated organisms

The biological world at the scale of cellular organisms is full of fascinating examples of fluid motion that is generated or affected by its interaction with elastic structures. Examples are the fluid motion around "swimming" bacteria and sperm, and the ciliary function in the respiratory system. A common feature of these phenomena is the interaction of elastic flexible membranes or filaments with a surrounding fluid, where the forces generated by the elastic structures and their motion are coupled by the fluid dynamics.

The development of computational methods for the accurate simulation of thin filaments in a fluid has reached maturity. At the same time, the force-generating mechanism of eukaryotic flagella and cilia has been well-studied biologically. However, the vast majority of numerical models of flagellar and ciliary motions do not yet include a proper representation of the internal microtubule structure of flagella.

By bringing together mathematicians with a variety of backgrounds, the goal of this IdeaLab is to brainstorm on possible approaches to introduce a more faithful representation of the internal structure of flagella into a computational model that can be used to study a variety of flows generated by microorganisms.

Simulation of flow streamlines generated by an organism with one rotating flagellum bundle near a plane wall.
Escherichia coli cell with flagella Content credit: CDC/Peggy S. Hayes. Photo credit: Elizabeth H. White, M.S.
High frequency vibrations and Riemannian geometry

We will discuss several specific projects at the interface of mechanics, geometry and analysis.

The fascinating phenomenon of stabilization by vibration suggests one group of problems. The most famous example of such a stabilization is the Kapitsa pendulum in which the upside-down unstable equilibrium of the standard pendulum becomes a stable equilibrium when the pendulum's pivot is vibrated vertically at a high enough frequency. See, for instance, the YouTube video below.

This effect led to the invention of the cyclotron and of the Paul trap, for which W. Paul received the 1989 Nobel Prize in physics. Another effect in the same spirit is the stabilization of a viscous fluid by vibration. A surface of molasses in an appropriately vibrating container can be made to form a vertical wall! One proposed activity will be to recast these problems in terms of differential geometry, as the study of geodesics on vibrating manifolds. This recasting has not been widely explored despite its important applications.

In celestial mechanics vibrational stablization questions also arise. For example, the equal mass planar three-body problem (a three degree of freedom system after reductions) contains four invariant submanifolds of codimension 2: the collinear three-body problem and its three isosceles sub-problems. These four sub-problems are much better understood than the full planar problem. Oscillations orthogonal to their submanifolds have the potential of connecting the submanifolds in interesting and not well-understood ways. Or perhaps such connections are blocked in some way. From the perspective of differential geometry, we have a Riemannian three-manifold which contains 4 distinguished totally geodesic surfaces. What can we say about the growth or oscillation of the normal mode (orthogonal to the surface) of the Jacobi equation for geodesics lying in one of these surfaces? How does this understanding of normal modes lead to a better understanding of the full geodesic flow?

The discussion will greatly benefit from collaboration of people with diverse interests ranging from geometry to differential equations to mechanics.

The collinear problem forms a planar slice of the full planar three-body problem. Figure courtesy of Rick Moeckel.

Workshop Schedule

Monday, August 11, 2014
TimeEventLocationMaterials
9:05 - 9:10What is IdeaLab and how to make it work for you - Jeff Hoffstein, Brown University11th Floor Lecture Hall 
9:10 - 9:40Meet with Introductory Groups11th Floor Lecture Hall 
9:40 - 10:40Introductory Group Presentations11th Floor Lecture Hall 
10:40 - 11:00Coffee/Tea Break11th Floor Collaborative Space 
11:00 - 12:00Overview (Toward a more realistic model of ciliated and flagellated organisms)11th Floor Lecture Hall 
11:00 - 12:00Overview (High frequency vibrations and Riemannian geometry)10th Floor Classroon 
12:00 - 1:15Lunch@ICERM11th Floor Collaborative Space 
1:15 - 2:45Specialized Talk I (High frequency vibrations and Riemannian geometry)11th Floor Lecture Hall 
1:15 - 2:45Specialized Talk I(Toward a more realistic model of ciliated and flagellated organisms)10th Floor Classroon 
2:45 - 3:15Coffee/Tea Break11th Floor Collaborative Space 
3:15 - 4:15Specialized Talk II (High frequency vibrations and Riemannian geometry)10th Floor Classroom 
3:15 - 4:15Specialized Talk II(Toward a more realistic model of ciliated and flagellated organisms)11th Floor Lecture Hall 
4:15 - 5:00Questions, Discussion and Brainstorming (High frequency vibrations and Riemannian geometry)10th Floor Classroom 
4:15 - 5:00Questions, Discussion and Brainstorming (Toward a more realistic model of ciliated and flagellated organisms)11th Floor Lecture Hall 
5:00 - 6:30Welcome Reception11th Floor Collaborative Space 
Tuesday, August 12, 2014
TimeEventLocationMaterials
8:30 - 9:00Touch base and light breakfast11th Floor Collaborative Space 
9:00 - 11:00Additional Brainstorming Session re: Projects and Group Formation (High frequency vibrations and Riemannian geometry)11th Floor Conference Room 
9:00 - 11:00Additional Brainstorming Session re: Projects and Group Formation (Toward a more realistic model of ciliated and flagellated organisms) - Meet with faculty leaders and form groups10th Floor Classroom 
11:00 - 12:00Work in Groups  
12:00 - 1:30Break for Lunch & Free Time  
1:30 - 4:30Working Groups  
4:30 - 5:00Reconvene to touch base (Toward a more realistic model of ciliated and flagellated organisms)10th Floor Classroom 
4:30 - 5:00Reconvene to touch base (High frequency vibrations and Riemannian geometry)11th Floor Conference Room 
Wednesday, August 13, 2014
TimeEventLocationMaterials
8:30 - 9:00Touch base and light breakfast11th Floor Collaborative Space 
9:00 - 12:00Working Groups  
12:00 - 1:30Break for Lunch & Free Time  
1:30 - 4:30Working Groups  
4:30 - 5:00Reconvene to touch base (High frequency vibrations and Riemannian geometry)10th Floor Classroom 
4:30 - 5:00Reconvene to touch base (Toward a more realistic model of ciliated and flagellated organisms)11th Floor Conference Room 
Thursday, August 14, 2014
TimeEventLocationMaterials
8:30 - 9:00Touch base and light breakfast11th Floor Collaborative Space 
9:00 - 12:00Working Groups  
12:00 - 1:30Break for Lunch & Free Time  
1:30 - 4:30Working Groups  
4:30 - 5:00Reconvene to touch base (Toward a more realistic model of ciliated and flagellated organisms)10th Floor Classroom 
4:30 - 5:00Reconvene to touch base (High frequency vibrations and Riemannian geometry)11th Floor Conference Room 
Friday, August 15, 2014
TimeEventLocationMaterials
10:00 - 10:10Opening Remarks - Homer Walker, Deputy Director, ICERM11th Floor Lecture Hall 
10:10 - 11:25Group Presentation 111th Floor Lecture Hall 
11:25 - 11:45Coffee/Tea Break11th Floor Collaborative Space 
11:45 - 1:00Group Presentation 211th Floor Lecture Hall 
1:00 - 2:15Lunch and Informal Discussions (lunch provided at ICERM)11th Floor Lecture Hall 
2:15 - 3:30Program Officer Panel 11th Floor Lecture Hall 
3:30 - 3:40Group Photo in Lecture Hall11th Floor Lecture Hall 
3:40 - 4:40Afternoon for Discussions11th Floor Collaborative Space