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?
IdeaLab 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 postPhD 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 UrbanaChampaign

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 MalekMadani
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 forcegenerating mechanism of eukaryotic flagella and cilia has been wellstudied 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.
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 upsidedown 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 threebody problem (a three degree of freedom system after reductions) contains four invariant submanifolds of codimension 2: the collinear threebody problem and its three isosceles subproblems. These four subproblems 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 wellunderstood ways. Or perhaps such connections are blocked in some way. From the perspective of differential geometry, we have a Riemannian threemanifold 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.
Workshop Schedule
Monday, August 11, 2014
Time  Event  Location  Materials 

9:05  9:10  What is IdeaLab and how to make it work for you  Jeff Hoffstein, Brown University  11th Floor Lecture Hall  
9:10  9:40  Meet with Introductory Groups  11th Floor Lecture Hall  
9:40  10:40  Introductory Group Presentations  11th Floor Lecture Hall  
10:40  11:00  Coffee/Tea Break  11th Floor Collaborative Space  
11:00  12:00  Overview (Toward a more realistic model of ciliated and flagellated organisms)  11th Floor Lecture Hall  
11:00  12:00  Overview (High frequency vibrations and Riemannian geometry)  10th Floor Classroon  
12:00  1:15  Lunch@ICERM  11th Floor Collaborative Space  
1:15  2:45  Specialized Talk I (High frequency vibrations and Riemannian geometry)  11th Floor Lecture Hall  
1:15  2:45  Specialized Talk I(Toward a more realistic model of ciliated and flagellated organisms)  10th Floor Classroon  
2:45  3:15  Coffee/Tea Break  11th Floor Collaborative Space  
3:15  4:15  Specialized Talk II (High frequency vibrations and Riemannian geometry)  10th Floor Classroom  
3:15  4:15  Specialized Talk II(Toward a more realistic model of ciliated and flagellated organisms)  11th Floor Lecture Hall  
4:15  5:00  Questions, Discussion and Brainstorming (High frequency vibrations and Riemannian geometry)  10th Floor Classroom  
4:15  5:00  Questions, Discussion and Brainstorming (Toward a more realistic model of ciliated and flagellated organisms)  11th Floor Lecture Hall  
5:00  6:30  Welcome Reception  11th Floor Collaborative Space 
Tuesday, August 12, 2014
Time  Event  Location  Materials 

8:30  9:00  Touch base and light breakfast  11th Floor Collaborative Space  
9:00  11:00  Additional Brainstorming Session re: Projects and Group Formation (High frequency vibrations and Riemannian geometry)  11th Floor Conference Room  
9:00  11:00  Additional Brainstorming Session re: Projects and Group Formation (Toward a more realistic model of ciliated and flagellated organisms)  Meet with faculty leaders and form groups  10th Floor Classroom  
11:00  12:00  Work in Groups  
12:00  1:30  Break for Lunch & Free Time  
1:30  4:30  Working Groups  
4:30  5:00  Reconvene to touch base (Toward a more realistic model of ciliated and flagellated organisms)  10th Floor Classroom  
4:30  5:00  Reconvene to touch base (High frequency vibrations and Riemannian geometry)  11th Floor Conference Room 
Wednesday, August 13, 2014
Time  Event  Location  Materials 

8:30  9:00  Touch base and light breakfast  11th Floor Collaborative Space  
9:00  12:00  Working Groups  
12:00  1:30  Break for Lunch & Free Time  
1:30  4:30  Working Groups  
4:30  5:00  Reconvene to touch base (High frequency vibrations and Riemannian geometry)  10th Floor Classroom  
4:30  5:00  Reconvene to touch base (Toward a more realistic model of ciliated and flagellated organisms)  11th Floor Conference Room 
Thursday, August 14, 2014
Time  Event  Location  Materials 

8:30  9:00  Touch base and light breakfast  11th Floor Collaborative Space  
9:00  12:00  Working Groups  
12:00  1:30  Break for Lunch & Free Time  
1:30  4:30  Working Groups  
4:30  5:00  Reconvene to touch base (Toward a more realistic model of ciliated and flagellated organisms)  10th Floor Classroom  
4:30  5:00  Reconvene to touch base (High frequency vibrations and Riemannian geometry)  11th Floor Conference Room 
Friday, August 15, 2014
Time  Event  Location  Materials 

10:00  10:10  Opening Remarks  Homer Walker, Deputy Director, ICERM  11th Floor Lecture Hall  
10:10  11:25  Group Presentation 1  11th Floor Lecture Hall  
11:25  11:45  Coffee/Tea Break  11th Floor Collaborative Space  
11:45  1:00  Group Presentation 2  11th Floor Lecture Hall  
1:00  2:15  Lunch and Informal Discussions (lunch provided at ICERM)  11th Floor Lecture Hall  
2:15  3:30  Program Officer Panel  11th Floor Lecture Hall  
3:30  3:40  Group Photo in Lecture Hall  11th Floor Lecture Hall  
3:40  4:40  Afternoon for Discussions  11th Floor Collaborative Space 