##### Organizing Committee

- Henry Cohn
*Microsoft Research New England* - Jeffrey Hoffstein
*Brown University* - Christopher Jones
*University of North Carolina at Chapel Hill* - Pamela Martin
*Indiana University-Purdue 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 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.

*"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

- Nate Ackerman
- Folashade Agusto
- Thomas Bellsky
- Jesse Berwald
- Jean-François Biasse
- Peter Jaehyun Cho
- Henry Cohn
- Graham Cox
- Cameron Freer
- Angelean Hendrix
- Nadia Heninger
- Jeffrey Hoffstein
- Sarah Iams
- Christopher Jones
- Hans Kaper
- Peter Koltai
- Christian Kuehn
- Benjamin LeVeque
- Deborah Lockhart
- David Lowry-Duda
- Nishant Malik
- Pamela Martin
- Antara Mukherjee
- Ekin Ozman
- Andrew Pollington
- Amanda Redlich
- Adriana Salerno
- Bjorn Sandstede
- Timothy Sauer
- Joseph Silverman
- Ivan Sudakov
- Homer Walker
- Esther Widiasih
- Ling Xu

#### IdeaLab Topics

##### Tipping Points in Climate Systems (MPE2013 program)

The climate is changing and it is due to anthropogenic sources of carbon-that 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 time-scales. 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 low-dimensional 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 ice-ages. 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`, given just the corresponding series of outputs

_{n}`e(x`,

_{1})`e(x`, ...

_{2})`e(x`. For over 30 years it was an open problem to find a secure encryption function

_{n})`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 - Jean-Francois 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 University-Purdue 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 |