Toronto Math News

By: Anne Dranovski <a.dranovski@gmail.com>

Last month, five U of T students, myself included, attended the 2012 CUMC at UBC Okanagan campus, in quiet, clement and panoramic Kelowna.We were Reza Asad, Dylan Butson, Anne Dranovski, Mike Hongyoul Park, and Jonathon Zung. (Years 4, 3, 4, 2 and 3, respectively.)

In the three days leading up to the CUMC, three of us participated in an Optimization Workshop organized by UBC Okanagan’s Department ofMathematics and Computer Science — the University is known for its unrivaled graduate programs (MSc and PhD) in Optimization and Convex Analysis (OCANA).

The workshop was a very interesting, concise and fast-paced introduction to major topics in optimization. Namely, monotone operators, derivative free optimization, and variational analysis.

During the CUMC, all five of us gave talks. For most of us this was a first talk. Audience turnout and feedback was extremely positive. Reza Asad’s talk was even attended by Professor Heinz Bauschke of the workshop. The subjects of our talks were as follows.

• Reza Asad presented the Stiener symmetrization, which is a rearrangement or transformation of a set in the plane that comes in handy whenproving the isoperimetric inequality, as well as other functional inequalities, when applied to functions’ level sets, in mathematical physics and elsewhere.
• Dylan Butson introduced the stochastic integral, the heart of the stochastic calculus, which extends the Riemann-Stieltjes integral to random processes such as Brownian motion, and has important applications in mathematical finance. To learn more about topics in stochastic calculus and, more generally, in mathematical probability, follow the previous link.
• Mike Park reviewed Diophantine approximations, constructing examples of numbers which have very good rational approximations and, therefore,could not be algebraic. He also explained how to find good rational approximations using the theory of continued fractions.
• In a crafty application of the Borsuk-Ulam theorem, (following Alon and West 1986,) Jonathon Zung showed how two topologically inclinedthieves, having stolen a necklace with k different types of jewels, could cut up the necklace so that each receives the same number of jewels of each type.
• I gave a description of random polarizations, or two-point symmetrizations, on the sphere, which are also useful for proving inequalities in mathematical physics, and admit convergence results which generalize to more complicated rearrangements such as the Stiener symmetrization.

Collected speakers’ abstracts can be viewed here

On our second last day, Dylan Butson and I presented a bid to host next year’s CUMC. We were well-received, but lost honorably to UMontreal.

The CUMC was an incredible learning experience. I only wish more students from U of T were able to share in the week’s worth of non-stop math-musement. The good news is there will be ample opportunity for you to share math in conference-like settings with your peers before CUMC 2013, starting with a Mini Undergraduate Math Seminar (MUMS), to be held early September.

Students will speak about topics of interest in 25 minute long presentations. Please check the wiki for updates, and e-mail me your abstract and/or slides by August 31st if you would like to present.