## Pi Day Thursday and the March Break Math Camp

Today is Pi Day, and as part of the March Break Math Camp that the department is running the students are celebrating this fascinating and mysterious number with activities, investigations and, of course, pie.  Apple pie to be exact.  We’ve even been featured in a Toronto Star article about the day.

The March Break Math Camp, open to students in Grades 4 – 10, has seen 57 students participate in a week of hands-on, interactive activities designed to introduce and excite them about the various fields of mathematics.  From number theory to geometry to building geodesic domes and optimizations.   The camp has also drawn from a partnership with the Canadian Math Kangaroo Competition to provide students with competition based problems and content.  Today they celebrate Pi with discussions of circles and the fascinating number ratio itself.

In addition, the camp will see guest speakers from the Department of Mathematics give talks to students on optimization, Mobius strips, origami and math, the board game Blockus and how Google works.

Grade 9/10 students building Geodesic Domes

Grade 7/8 students built circles from string, meter sticks and math!

## Math Mentorship Underway

On January 31st the Department of Mathematics welcomed 18 Grade 11 and 12 students to participate in a Mentorship program with our Graduate students and postdoctoral fellows.

So far the topics covered have been far ranging and of various interests.  A sampling of topics:

• Optimal Transport
• Topics in abstract algebra starting with some basic groups and rings theory building to some notions of geometry (e.g., projective spaces and affine varieties over complex numbers) with the ultimate goal to learn the intuition behind blowing-up and resolution of singularities, and producing graphs or animations of simple resolutions of curve singularities
• Issues in the foundations of mathematics such as the difference between countable and uncountable sets, and “constructing” most of the basic mathematical objects (the integers, rational numbers, real numbers, complex numbers) starting from just the empty set
• Number theory starting from the basics of congruences, Little Fermat Theorem, Euler function, Integer points inside polygons and ellipses and some other relatively elementary theorems
• Calculus of Young tableaux with applications to combinatorics and symmetric polynomials

… and much more.

We are looking forward to seeing their poster presentations in April on the fascinating mathematics they have learned.

## Invited Talk at SIAM

Professor Adrian Nachman had the honour of being chosen to give the SIAM Invited Address at the SIAM Sessions of the Joint Mathematics Meeting which took place in San Diego on January 9 – 12, 2013.

Further information on the seminar, including Professor Nachman’s talk, can be found at the SIAM website (http://www.siam.org/meetings/jmm13/index.htm).

## 2013 André-Aisenstadt Prize in Math Announced

Our congratulations go to Professor Spyros Alexakis for being awarded the highly prestigious André-Aisenstadt Prize in Mathematics for 2013.

This is the 3rd year in a row a member of the Department of Mathematics at the University of Toronto has been awarded this prize by the CRM and the 6th time since it’s inception in 1992.

The official announcement from the CRM can be found here

Full information on the prize and it’s history can be found here

Our congratulations to Professor Alexakis on this remarkable achievement!

## James Arthur’s Monograph (Draft) on Endoscopic Classifications of Representations Released

From James Arthur:

“This is an uncorrected complete draft of my monograph on the endoscopic classification of representations. I will spend the next couple of months checking and correcting it, and then send the final version to the American Mathematical Society for publication in its Colloquium Publications series”.

## Fulkerson Prize Winner

Our hearty congratulations go to László Lovász and Balázs Szegedy this year’s Fulkerson Prize winners.

The Fulkerson Prize is one of the most prestigious prizes in discrete math and it is awarded every three years.

From their website: “This award is sponsored jointly by the Mathematical Optimization Society (formerly the Mathematical Programming Society)  and the American Mathematical Society (AMS). Up to three awards of US\$1500 are presented at each (triennial) International Symposium of the MPS.”

This year it went to László Lovász and Balázs Szegedy for their paper on the “Limits of dense graph sequences”

A full list of winners, including this year’s, can be found here

The prize was announced on August 18, 2012 at the  International Symposium on Mathematical Programming in Berlin.

## Update on the 2012 CUMC

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.

## Department Highlighted in Fields Notes

For it’s involvement in the Mathematics Pavilion at this year’s Science Rendezvous the department received a nod and a two page spread of photos from this year’s event.

For the past three years the Math department has had an ever growing pavilion at Science Rendezvous.  This near exponential growth has been in good part due to the efforts of the Fields Institute and their generous usage of space and resources.  This year’s event saw over 300 visitors and allowed them to freely tour the Fields Institute and be up close and personal with a wide variety of math activities and personel.

We look forward to next year’s event and the continued growth of this wonderful pavilion.

## Math Kangaroo Featured in CMS Notes

The CMS notes recently ran an article written by the board members of the Canadian Math Kangaroo competition detailing the potential competition like this have for popularizing the field of Mathematics for our up-and-coming mathematicians.

The article provides an overview of the competition, sample problems and background on the competition.  It also talks of how the competition helps to involve and inspire students to be involved with mathematics in a context outside the typical classroom.

The full article can be found here (starting on page 8 )

This year the GTA section of the competition saw over 900 students participate across the three UofT campuses (UTSC, UTM and St George) and had over 50 staff and students volunteer to make it a success.

More information on UofT’s involvement with the competition can be found here

## Canadian IMO Team Strikes Gold…

… and Silver and Bronze!

This year’s Canadian IMO (International Mathematics Olympiad) had a clean-up year for medals at this year’s competition.  The team, coached by Lindsey Shorser (an instructor with the Math Department), along with David Arthur, Ralph Furmaniak, and Alex Fink, won 6 medals (one for each of the team members).  In addition, the team leader was Jacob Tsimerman, who was a former U of T undergraduate math specialist.

In total the Canadian team walked away with 3 gold medals, 1 silver and 2 bronze medals.  This success ranks Canada 5th in the world out of 100 countries which is the best standing Canada has received since it started participating in the IMO in 1981.

The full story, complete with a picture of the team and a breakdown of the medals, can be found here

Further Stories

Our congratulations go to the team, its leaders and its coaches!  Great work!