Proving the QUE Conjecture

Recently Roman Holowinsky, a former post-doc student here in the Department, alongside Soundararajan, a Professor of Mathematics at Standford University, were profiled in the AIMath newsletter.

Their work on proving the Quantum Unique Ergodicity (QUE) conjecture was featured. The conjecture focuses on how waves are influenced by the geometry of their enclosure, like sound waves in a concert hall. At one end the waves spread out evenly, at the other end there are “whispering zones”.

The pair showed that for certain shapes that come from number theory the waves always spread out evenly leaving no “whispering zones”.

The full article, which includes links to the full papers and other research by the pair, can be found here: http://www.aimath.org/news/que/

Roman Holowinsky was a post doctoral fellow here at the University of Toronto from 2007 – 2009. He was a visitor to the Fields Institute in 2008, is currently working at the Institute for Advanced Study (IAS) at Princeton and will be a tenure track professor at The Ohio State University starting in July 2010. He specilizes in Analytical Number Theory.

We wish Roman all the best in his research and congratulate him on his work.

Making Spheres from Cubes

If you spin a cube quickly on its axis, can you turn it into a sphere?  Anyone studying geometry or geometric theory would tell you no. Rubix, however, has attempted to do just that turning their famous, multi-coloured Cube into the new sphere and the Math Department’s own Conan Wu was there to test it out.

An article in the Toronto Star back in July featured Wu puzzling over the new Rubix sphere and attempting to solve it.  After only a few hours, two precisely, she had it solved.  She then worked at speeding her time up to a mere 15 minutes, most likely a new record in Canada.

At 20 years old Wu has already

successfully finished her undergraduate degree, a four year program in only two, and is now attending graduate school.

We wanted to get some more information from this wonder of mathematics, and Rubix Cube solver, so we sat down with Conan to get some more information.

Why do you like the Rubik’s Cube so much?

Well…in fact, I don’t like it ‘that much’. It’s true that I have played with it when I was a kid, and I like puzzles such as Rubik’s cube. But I’m not a ‘cubing fan’. I just sometimes use it to ‘find something to do for my hands while thinking about math problems’.

Why did you get involved with mathematics?

Why not? It’s naturally the most beautiful subject in the world. I’ve enjoyed doing mathematics for as long as I can remember.

What year did you start/graduate your undergraduate program?

I started September 2007 and graduated August 2009

What was your main field of study/interest?

Dynamical systems and possibly some kind of metric geometry although I’m still exploring.

Where are you now/what are you studying?

Northwestern University doing my PhD in mathematics.

What is your favorite part of math?

In general, I think mathematics is fascinating because it’s (at least from my point of view) independent of the physical world. i.e. people do math because it’s interesting in its own right, and typically we don’t care about what does the theory do to the rest of the world. Mathematics is pretty much the unique subject with this property.

Why did you choose to come to UofT?

Honestly, my childhood dream was to go to MIT. One thing leads to another and I ended up in UofT.

But now I truly believe UofT is indeed the perfect place for me. One thing I liked the most about our department was the flexibility of our undergraduate program. i.e. instead of sticking with definite requirements and rules, they are willing to modify the program as long as the student is capable of doing more advanced stuff. For example, when I first came in as a high school student, I was allowed to take 8 math courses per semester, including graduate courses; I was also given the oppotunity to TA a third year pure math course while I was only a sophomore. I don’t think this could happen anywhere else in the world.

Do you have any other hobbies/interests?

Traveling, photography, drawing and painting, practicing magic tricks.

Anything else you’d like to tell us?

Although I have officially graduated from UofT, but I have kept in touch with various faculty members here. In particular I come back to Toronto every month to meet and work with some of my professors. I think through the undergrad program, I have built many mathematical connections with our department, some of which may last a lifetime. I wish to sincerely thank our department for providing me all the right opportunities.

We would like to sincerely thank Conan for taking the time to speak with us and we wish her all the best in her continued studies and hope she continues to keep in touch!

Click here to read the full Toronto Star article