{"id":1606,"date":"2016-03-01T02:38:55","date_gmt":"2016-03-01T07:38:55","guid":{"rendered":"http:\/\/blogs.ams.org\/phdplus\/?p=1606"},"modified":"2016-03-01T10:07:29","modified_gmt":"2016-03-01T15:07:29","slug":"ipamania","status":"publish","type":"post","link":"https:\/\/blogs.ams.org\/phdplus\/2016\/03\/01\/ipamania\/","title":{"rendered":"IPAMania"},"content":{"rendered":"

I just spent a week working intensively with 5 people from very different backgrounds, whom I had mostly never met, on a problem that I’d never seen before Monday. And it was great, though I did need to sleep for 10 hours Saturday\u00a0night to even partially recover. What strange thing just happened to me? I went to the Workshop on Algebraic Geometry for Coding Theory and Cryptography at IPAM<\/a>.<\/p>\n

IPAM, the Institute for Pure and Applied Mathematics,\u00a0is a math institute funded primarily by the National Science Foundation, located on the campus of UCLA. \u00a0IPAM does semester-length thematic programs as well as one-week workshops. \u00a0Everett Howe, Kristin Lauter, and Judy Walker organized this\u00a0project-based research workshop to bring together pure and applied mathematicians and encourage collaboration in the overlap of these fields. The model was adopted from the Women in Numbers<\/a> workshops (see my last blog<\/a>). Participants were organized into 6 groups of 5-7 people each. A leaders or pair of co-leaders brought a research question for each group, hopefully one that could yield at least a little progress in a week of hard work. Participants did not generally have any special knowledge in their assigned problem, except for background readings sent by the leaders before the workshop. Each group was a mix of well-established researchers, early-career people like me, and often a few graduate students. The plan\u2014work hard, learn the problem, prove preliminary results, start a collaboration that will lead to a publishable paper in the next 3-6 months.<\/p>\n

\"My<\/a>

My group: me, Joachim Rosenthal (ETH), Jessalyn Bolkema (University of Nebraska, Lincoln), Heide Gluesing-Luerssen (University of Kentucky), Christine Kelley (University of Nebraska, Lincoln), Kristin Lauter (Microsoft Research).<\/p><\/div>\n

In the teaching world, I think a lot about active learning and how can I get my students to really engage with material though problem solving. I love this workshop model because it gives professional mathematicians the chance to learn new areas in one of same ways we think\u00a0our students learn best.<\/p>\n

My group studied\u00a0variants of the McEliece cryptosystem<\/a>. Devised in 1978 by Robert McEliece, this public key cryptosystem relies on the difficulty of decoding a random linear error-correcting code. In its original form it has never been broken. RSA, the most widely used public key cryptosystem in the world, was also devised (publicly) in 1978, making these two the longest-standing unbroken public key cryptosystems. However, currently nobody uses McEliece because the key sizes necessary for good security were seen as impractically large. Why use McEliece when RSA works so well?<\/p>\n

However, McEliece is increasingly relevant as technological advances make storing large keys less problematic and quantum computers loom on the horizon. Thanks to Shor\u2019s algorithm, a large-scale working quantum computer would make RSA and other currently used cryptosystems totally insecure. Government agencies are paying attention–NIST is planning to call for proposals for Post-Quantum cryptographic standards<\/a>. McEliece\u2019s system (as well as lattice-based systems and those based on multivariate polynomial problems) has not been found vulnerable to known quantum algorithms, so is a good post-quantum candidate. Many variants of McElice\u2019s system involve using algebraic-geometry codes or other highly structured codes. Of course, order is bad in cryptography, so these variants are often vulnerable to attacks that uncover or exploit their structure. Our group was exploring what variants of McEliece\u2019s original system could stand up to recent\u00a0attacks.<\/p>\n

Jumping into a problem like this with a bunch of people you\u2019ve never met, especially as an early-career person, could be horrible. If people don’t try to connect with the whole group, are afraid or unwilling to speak up, or are not really invested, the whole thing goes nowhere. My group was great, though. I credit this to our general willingness to ask questions and openly admit and discuss the things we didn\u2019t understand. Everybody’s\u00a0background knowledge was relevant to the topic but nobody felt that they should already know every piece. \u00a0It was the things that we didn\u2019t know that gave us room to work together. \u00a0I think that the presence of less experienced people encouraged more experienced people to ask extra questions, if only for the sake of others. Also, we developed our own private gameshow based on making up a disguising matrix and then guessing the dimension of the Schur product of the disguised code with itself. Endless hours of\u00a0fun! \u00a0Just wait for the app!<\/p>\n

\"Well-earned<\/a>

Well-earned workshop beers.<\/p><\/div>\n

It wasn’t all gameshows and group work. \u00a0During the early part of the week, each group leader gave a 45-minute overview of the topic for all the workshop participants. At the end of most days, someone from each group gave a 10-minute progress report to the full workshop. The most junior person in each group gave a 20-minute summary talk on the last day. Our topic was exciting to me but I was very intrigued by these other ideas as well. We were reminded\u00a0not to poach people\u2019s problems, which I agree is an important point to make. \u00a0However, we also had a lot of opportunities to talk to\u00a0pretty much everyone at the workshop and engage with them\u00a0a bit\u00a0about the other projects. \u00a0For example,\u00a0I learned about\u00a0potential applications of my some of my thesis work that I never would have heard of otherwise, since the papers are slightly out of my usual field. \u00a0I would not have met the person doing this work at a number theory conference.\u00a0\u00a0I think all these talks were a good idea not only because they gave the whole group repeated exposure to each problem, but also because the talks demanded that everyone buy into their group projects and stay engaged through the whole week. Less experienced people couldn\u2019t give up and advanced researchers couldn\u2019t check out or leave graduate students in the dust, because the graduate students were going to speak for the whole group at the end.<\/p>\n

\"Jessalyn<\/a>

Jessalyn Bolkema, a graduate student at the University of Nebraska, Lincoln, made an awesome final presentation for our group.<\/p><\/div>\n

With all the positive things I have to say about this week, it would be deceptive not to mention (again) that this workshop was totally exhausting. \u00a0I really couldn\u2019t keep up with emails from work or other responsibilities. \u00a0I was super tired and way behind in my teaching and other research work by the end of the week. Still, it was totally worthwhile. \u00a0I came in knowing a fair amount about algebraic curves over finite fields, and with some cryptography and basic coding theory background. \u00a0I left with much more concrete knowledge in our problem area than I’d ever have brought home from a normal, all-talks research conference.\u00a0 Even more exciting, I\u00a0got\u00a0a much better\u00a0sense of several really\u00a0interesting problems involving codes, algebraic geometry and cryptography, and saw the kinds of tools that people are using for these problems. \u00a0Best of all,\u00a0I spent a week with\u00a036 really cool\u00a0people. Now if I can only dig out from under my grading.<\/p>\n

\"BigGroupIPAM2\"<\/a>

The conference photo, taken by the wonderful Stacy Orozco, IPAM Program Coordinator.<\/p><\/div>\n

 <\/p>\n

<\/div>","protected":false},"excerpt":{"rendered":"

I just spent a week working intensively with 5 people from very different backgrounds, whom I had mostly never met, on a problem that I’d never seen before Monday. And it was great, though I did need to sleep for … Continue reading →<\/span><\/a><\/p>\n

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