Organizing Committee
 Henry Cohn
Microsoft Research New England  Jeffrey Hoffstein
Brown University  Christopher Jones
University of North Carolina at Chapel Hill  Pamela Martin
Indiana UniversityPurdue University  Bjorn Sandstede
Brown University  Joseph Silverman
Brown University
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?
The 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.
"I thought the program went very well. It was fun and interesting to try and work on a problem that was significantly outside my field with talented people who were also outside my field. I also thought the people in charge of our group did a very good job in fostering a fun atmosphere that encouraged us to try random attacks on a hard problem without worrying about that fact that any particular one would almost certainly fail (but hopefully might provide some insight eventually)."
 IdeaLab Participant
Confirmed Speakers & Participants
 Speaker
 Poster Presenter
 Attendee

Nate Ackerman
Harvard University

Folashade Agusto
Austin Peay State University

Thomas Bellsky
Arizona State University

Jesse Berwald
College of William and Mary

JeanFrançois Biasse
University of Waterloo

Peter Jaehyun Cho
University of Toronto

Henry Cohn
Microsoft Research New England

Graham Cox
University of North Carolina

Cameron Freer
Massachusetts Institute of Technology

Angelean Hendrix
North Carolina State University

Nadia Heninger
University of Pennsylvania

Jeffrey Hoffstein
Brown University

Sarah Iams
Bowdoin College

Christopher Jones
University of North Carolina at Chapel Hill

Hans Kaper
Argonne National Laboratory

Peter Koltai
TU München

Christian Kuehn
Cornell University

Benjamin LeVeque
Brown University

Deborah Lockhart
National Science Foundation

David LowryDuda
Brown University

Nishant Malik
University of North Carolina

Pamela Martin
Indiana UniversityPurdue University

Antara Mukherjee
The Citadel

Ekin Ozman
University of Texas at Austin

Andrew Pollington
National Science Foundation

Amanda Redlich
Bowdoin College

Adriana Salerno
Bates College

Bjorn Sandstede
Brown University

Timothy Sauer
National Science Foundation

Joseph Silverman
Brown University

Ivan Sudakov
University of Utah

Homer Walker
Worcester Polytechnic Institute

Esther Widiasih
University of Arizona

Ling Xu
University of Michigan, Ann Arbor
IdeaLab Topics
Tipping Points in Climate Systems (MPE2013 program)
The climate is changing and it is due to anthropogenic sources of carbonthat is agreed upon by the scientific community. But is there a possibility of abrupt change? On the whole, the large climate models do not predict such occurrences, but they also do not include the physical mechanisms that might trigger these tipping points in the modeling. So, how do we try to predict abrupt transitions? Is it even feasible?
There has been a considerable amount of mathematics devoted to rapid changes, dating back to catastrophe theory, and also to systems that enjoy varying timescales. This has laid the groundwork for an emerging area of tipping points in climate. But can we account for the potential climate tipping points with what amount to lowdimensional bifurcations? And, if we can, what are ways that this mathematical technology can be factored into the construction of large models?
There have, of course, been abrupt changes in the past, such as rapid warming after iceages. Can we learn from these? The technical approach here might be to assimilate the data into models. But the current techniques of data assimilation do not accommodate abrupt transitions. This can be viewed as the same issue arising in modeling: both modeling and data assimilation require relatively smooth evolution. But we must still be able to say something when it is not so smooth.
Towards Efficient Homomorphic Encryption
An encryption scheme is a method for efficiently computing an encrypted form e(x) of a given input x. It should be invertible, but computing the inverse must require a secret key. Roughly speaking, for the scheme to be secure it should be hard to learn anything useful about a series of inputs x_{1}, x_{2}, ... x_{n}, given just the corresponding series of outputs e(x_{1}), e(x_{2}), ... e(x_{n}). For over 30 years it was an open problem to find a secure encryption function e that was also a ring homomorphism, that is, that satisfied e(x + y) = e(x) + e(y) and e(xy) = e(x) e(y). To mention only one of the potential applications for such an encryption scheme, imagine calculations performed in the cloud on vast quantities of health data encrypted for privacy.
The first glimpse of a solution to this problem was given by a breakthrough discovery by Craig Gentry in 2009. The scheme he proposed was theoretically sound, given some plausible conjectures, but it was far too inefficient to be practical. There has been a great deal of work done on this since then, by many researchers, and today's schemes are orders of magnitudes more efficient in both time and meory than the original. Yet they are still far from practical, and new ideas are needed.
The object of this idea lab will be to gather together mathematicians from different backgrounds, without necessarily any prior experience with cryptography, to explore new approaches to this problem, both theoretical and computational.
Workshop Schedule
Monday, July 15, 2013
Time  Event  Location  Materials 

8:30  8:55  IdeaLab Registration  11th Floor Collaborative Space  
8:55  9:00  Welcome  ICERM Director  11th Floor Lecture Hall  
9:00  9:10  Young Researcher Introduction  Nate Leedom Ackerman, Harvard University  11th Floor Lecture Hall  
9:10  9:20  Young Researcher Introduction  Folashade Agusto, Austin Peay State University  11th Floor Lecture Hall  
9:20  9:30  Young Researcher Introduction  Thomas Bellsky, Arizona State University  11th Floor Lecture Hall  
9:30  9:40  Young Researcher Introduction  Jesse Berwald, College of William and Mary  11th Floor Lecture Hall  
9:40  9:50  Young Researcher Introduction  JeanFrancois Biasse, University of Calgary  11th Floor Lecture Hall  
9:50  10:00  Young Researcher Introduction  Peter Jaehyun Cho, University of Toronto  11th Floor Lecture Hall  
10:00  10:30  Coffee/Tea Break  11th Floor Collaborative Space  
10:30  10:40  Young Researcher Introduction  Graham Cox, University of North Carolina  11th Floor Lecture Hall  
10:40  10:50  Young Researcher Introduction  Cameron Eric Freer, Massachusetts Institute of Technology  11th Floor Lecture Hall  
10:50  11:00  Young Researcher Introduction  Angelean Hendrix, North Carolina State University  11th Floor Lecture Hall  
11:00  11:10  Young Researcher Introduction  Nadia Heninger, University of California, San Diego  11th Floor Lecture Hall  
11:10  11:20  Young Researcher Introduction  Sarah Iams, Bowdoin College  11th Floor Lecture Hall  
11:20  11:30  Young Researcher Introduction  Peter Koltai, TU München  11th Floor Lecture Hall  
11:30  11:40  Young Researcher Introduction  Christian Kuehn, Cornell University  11th Floor Lecture Hall  
11:40  11:50  Young Researcher Introduction  Nishant Malik, University of North Carolina  11th Floor Lecture Hall  
11:50  12:00  Young Researcher Introduction  Antara Mukherjee, The Citadel  11th Floor Lecture Hall  
12:00  12:10  Young Researcher Introduction  Ekin Ozman, University of Texas at Austin  11th Floor Lecture Hall  
12:10  12:20  Young Researcher Introduction  Amanda Redlich, Rutgers University  11th Floor Lecture Hall  
12:20  2:30  Break for Lunch and Free Time  
2:30  2:40  Young Researcher Introduction  Adriana Salerno, Bates College  11th Floor Lecture Hall  
2:40  2:50  Young Researcher Introduction  Ivan Sudakov, University of Utah  11th Floor Lecture Hall  
2:50  3:00  Young Researcher Introduction  Esther Widiasih, University of Arizona  11th Floor Lecture Hall  
3:00  3:10  Young Researcher Introduction  Ling Xu, Georgia State University  11th Floor Lecture Hall  
3:10  3:30  Coffee/Tea Break  11th Floor Collaborative Space  
3:30  4:15  Who, or what, will tip the big climate models?  Christopher KRT Jones, University of North Carolina  11th Floor Lecture Hall  
4:15  5:00  What is homomorphic encryption, and why do we want it?  Henry Cohn, Microsoft Research  11th Floor Lecture Hall  
5:00  6:30  Welcome Reception  11th Floor Collaborative Space 
Tuesday, July 16, 2013
Time  Event  Location  Materials 

8:30  10:00  An overview of public key cryptography, with a view towards homomorphic encryption  Joe Silverman, Brown University  11th Floor Lecture Hall  
8:30  10:00  Some cases of tipping points in the climate and paleoclimate record  Pamela Martin, Indiana UniversityPurdue University  11th Floor Conference Room  
10:00  10:30  Coffee/Tea Break  11th Floor Collaborative Space  
10:30  12:00  Homomorphic encryption: Where we are and where we'd like to go  Jeff Hoffstein, Brown University and Henry Cohn, Microsoft Research  11th Floor Lecture Hall  
10:30  12:00  An overview of possible mechanisms for tipping points  Bjorn Sandstede, Brown University  11th Floor Conference Room  
12:00  2:00  Break for Lunch and Free Time  
2:00  2:30  Break into 2 groups  
2:30  4:30  Working Groups  11th Floor Lecture Hall and Collaborative Spaces  
4:30  5:00  Reconvene to touch base 
Wednesday, July 17, 2013
Time  Event  Location  Materials 

9:00  12:00  Working Groups  11th Floor Lecture Hall and Collaborative Spaces  
12:00  2:00  Break for Lunch and Free Time  
2:00  4:30  Working Groups  11th Floor Lecture Hall and Collaborative Spaces  
4:30  5:00  Reconvene to touch base 
Thursday, July 18, 2013
Time  Event  Location  Materials 

9:00  12:00  Working Groups  11th Floor Lecture Hall and Collaborative Spaces  
12:00  2:00  Break for Lunch and Free Time  
2:00  4:30  Working Groups  11th Floor Lecture Hall and Collaborative Spaces  
4:30  5:00  Reconvene to touch base 
Friday, July 19, 2013
Time  Event  Location  Materials 

9:00  9:10  Opening Remarks  Jill Pipher, ICERM  11th Floor Lecture Hall  
9:10  10:25  Group Presentation 1  11th Floor Lecture Hall  
10:25  10:45  Coffee/Tea Break  11th Floor Collaborative Space  
10:45  12:00  Group Presentation 2  11th Floor Lecture Hall  
12:00  1:45  Lunch and Informal Discussions  (lunch provided at ICERM)  
1:45  3:00  Program Officer Panel  Hans Kaper, Argonne National Laboratory; Deborah Lockhart, National Science Foundation; Andrew Pollington, National Science Foundation; Timothy Sauer, National Science Foundation; Homer Walker, ICERM  11th Floor Lecture Hall  
3:00  3:10  IdeaLab Group Photo  11th Floor Lecture Hall  
3:10  5:00  Afternoon for Discussions 