Alumni Events in the Department of Mathematics

Welcome to the Alumni Events listings for the Department of Mathematics.  Please feel free to leave your comments on any of the stories.

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Previous Events

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Current Alumni Projects

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Spring Reunion 2011

This year’s Spring Reunion took place on Saturday, May 28th

The event was well attended with over 30 participants.  The audience was treated to four talks from current faculty and distinguished alumni on a wide range of topics.

The presenters were:

  • Professor Kumar Murty, Chair, Department of Mathematics
    • “Opening Welcome and Updates on the Research and Programs in the Department of Mathematics”
  • Patrick Kaifos, PhD Candidate at Columbia University
    • “Models in Computational Neuroscience”
  • Dale Robichaud, SFA, Investment Financing
    • “Perspectives from a UofT Graduate: Mathematical Expectations in Financial Institutions”
  • Richard Cerezo, Recent Graduate of the Department of Mathematics
    • “Updates on New and Exciting Programs for Undergraduates in the Department of Mathematics”

Some pictures from the event can be found below:

Professor Kumar Murty
Chair of the Department of Mathematics

Richard Cerezo
Class of 2011

Patrick Kaifos illustrates a concept in his lecture
Speaker Patrick Kaifos

Audience members listen intently to the presentations

Speaker Dale Robichaud presents his topic to the audience

Audience members ask questions of the presenters

At the reception current undergraduate students
have conversations with recent graduates

Alumni participants speak with guest speaker
Dale Robichaud

Virginia Ise from the Alumni office speakers with speakers
and alumni

At the reception
Alumni speak with speaker Patrick Kaifos
A lovely spread of snacks and goodies at the reception

More images of alumni, recent graduates, honured speakers and current undergraduates at the reception


Spring Reunion 2010

On May 29, 2010 U of T graduates from years ending in 0 or 5 gathered at the University to celebrate for Spring Reunion and the Department of Mathematics was there to take part.

Entitled “A Celebration of Mathematics” the event saw a wide variety of alumni from both within and outside the Math Department enjoy a series of talks by members of the department.  Participants came from various backgrounds and degrees, from Engineering to History, but they all came for the same purpose, an interest in math.

The event started with an introduction session where participants spoke of their own personal experiences and interests in mathematics and what they were currently doing with their degrees.  Answers ranged from entrepreneurial endeavors to finance and accounting to song writing.

Introductions 1 Introductions 2 Introductions 3

The first formal talk was by the Chair of the Department, Professor Kumar Murty.  Professor Murty spoke of the history of the department, its current vision and its goals, challenges and successes.  His speech touched on the work of the department with the Fields Institute and with the University in general.

Professor Kumar Murty

The second talk was by Richard Cerezo, an undergraduate student in his fourth year of the Mathematics Specialist program.  He spoke of the people in the department who had shaped his studies and his life in general while studying here.  His talk was punctuated by images of the people who he identified with as influential to his time here in the department.  He then shared with the audience his future plans and how his math degree will help him to succeed.  A discussion then took place on the importance of critical thinking skills gained through mathematics in general society and the “real-world”.

Richard Cerezo

The afternoon’s final talk was presented by Professor Jeremy Quastel who gave the audience a small taste of his upcoming International Congress of Mathematicians (ICM) talk.  The title of the talk was “Exact solutions for models of random surface growth”.  In it Professor Quastel described his research into one dimensional surface growth.  He explained the KPZ universality class and the way researchers find exact solutions to the problem by using the limit of the weakly asymmetric simple exclusion process.  The talk was the most technical of the three and showed the branches between mathematics and physics and how they are used in “real world” applications.

Professor Jeremy Quastel

After the formal talks participants had a chance to mix and mingle and discuss topics.

After the Talks 1 After the Talks 2 After the Talks 3
After the Talks 4 We look forward to next year’s event! After the Talks


Spring Reunion 2007

On June 2, 2007, alumni from the Departments of Chemistry, Mathematics, and Physics returned to campus to celebrate Spring Reunion. A group of alumni was visiting the new home of the Department of Mathematics in the Bahen Centre on St. George Street, discovering that a rhombic triacontahedron is composed of acute and obtuse rhombohedra.

Professor Robert McCann from Mathematics presented his talk on “Spreading Populations, Draining Drops, and the Shape of Everything”.


December 2009 Alumni Reception

In December of 2009 we had a reception for our honoured alumni.  During this reception these alumni were treated to a series of 4 talks:

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Opening Comments
Professor Kumar Murty
Chair of the Department of Mathematics

It is a pleasure to welcome you to this first alumni networking event of the Department of Mathematics.

It is an occasion for us to share with you the achievements and aspirations of the Department. It is also an occasion for you to share with us the way in which Mathematics has shaped and is shaping and affecting your work and how we can bring these together to create a vision for the future of the Department.

The academic strength of the University of Toronto is well-known. Still, it might not be out of place to give you a snapshot of your Alma Mater. U of T researchers are the most cited amongst all Canadian Universities, with McGill a distant second. U of T is the third most published university in the world, behind Harvard and Tokyo and ahead of Stanford and Columbia. U of T gets twice as much research funding as most other Canadian schools and has generated more spinoff companies than any other Canadian university.

The Mathematics department at U of T is acknowledged as the leading mathematics department in Canada. We have world class expertise in many fields of mathematics, including automorphic forms, number theory, algebraic and symplectic geometry, knot theory, mathematical finance, mathematical physics and so on.

We teach more than 7000 undergraduates a year and 150 graduate students. Our students go on to distinguished careers in academia and industry and many of you here are a testament to that. We have done well. But we can do better.

A university is part of a community, not only a community of scholars but community in the sense of the larger society in which we live. As proper ventilation keeps a place fresh and healthy, there has to be a good exchange between society and the University. What kind of exchange? Mostly, it is an exchange of ideas by which both benefit. It is an exchange that helps us to together discuss, tackle and solve the fundamental problems facing us. And that brings us to the theme of today’s presentation.
We are facing a global economic situation which most of us, if not all of us, have never seen before. It is a situation that is having an immediate impact on people’s lives. Now, almost every one in this room has benefited from the study of mathematics. We are all aware to a certain extent of the ubiquity and power of mathematics. Can mathematics say anything about the situation we find ourselves in today?

Our speaker is Professor Luis Seco, Director of the Masters of Mathematical Finance Program. This program was designed by the Mathematics Department and instruction in this program is a combined effort of several departments and faculties.

Professor Seco got his Ph.D. from Princeton University in the field of PDE. It was only after his arrival in Toronto that he got interested in Math Finance. Now, he is a leader in the field, both academically and industrially.

Academically, he started RiskLab, the first research lab in the Mathematics Department and this Lab has produced a host of students and postdocs. Industrially, he has spun off a company which manages a large amount of money. Luis is uniquely positioned to be able to address the issue of the day: Mathematics and the Global Economy.

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Mathematics and the Global Economy
Professor Luis Seco
Department of Mathematics

In order to understand the role of mathematics in the global economy of today, it is useful to reflect on math and its history. In particular, I want to go back to the 1850′s, the decade when math started the process to shape itself as we know it today. The 50′s were an age of discovery. Joseph Fourier had discovered what will become the mp3 technology of our days. His approach was bold, and defied intuition to mathematicians of that age. In fact, Euler was a complete agnostic about his proposed discoveries. Many of the problems arose because the concept of the integral, which had been used successfully in engineering and physics since Newton, was realized to be based on very shaky ground. The attempts to put it on firm ground lead to a complete make over of mathematics; questions such as what a number is had to be addressed, for the first time ever. Mathematics had to stop what had been its role as a service provider to the other physical sciences, mostly Physics and Engineering, and devote all its energy to rebuild itself from the ground up. The result has been 100 years of intense abstract mathematical developments, during which new disciplines were born, such as Statistics and Probability, Set theory, Quantum Mechanics, Topology, and even traditional Differential Equations took on a complete new approach. And all of this in almost complete isolation, with occasional and exceptional love affairs with Physics. But over the last thirty years, all that body of knowledge generated since the 1850′s is exploding and finding partner disciplines to deploy its mathematical might.

The Nobel Prize awarded to John Pople and Walter Kohn in 1998 highlighted the importance of the advances in computational chemistry. John Nash won his Nobel Price in Economics for his work on game theory. One of these areas is finance. In 1973, Fisher Black, Myron Scholes and Robert Merton found a mathematical way to understand options markets. Their discovery was not immediately understood by the financial sector, which lacked the technical preparation at the time. But in the eighties, a new breed of young practitioners, many of them former unemployed particle physicists, found ways to used it in very profitable ways. The options and derivatives markets flourished, and eventually created the market crash of 1987.

The reaction of the business and government sectors what to increase regulation. The BIS treaty of 1991 called for risk management systems to be deployed at the banks by December 31, 1997. What was interesting in this regulation was its extraordinary level of mathematical sophistication.

But this did not stop the market from crashing once again in 1998, during the tumultuous summer were we were introduced to the Russian default and Monica Lewinsky, both events leading to the disappearance of available credit for a few months.

More regulation followed and, despite the tech bubble of the new millennium, markets plowed along and economic bonanza seemed to be firmly engrained in the financial system.

What had actually happened was that market sophistication, the creation of credit derivatives, provided many financial firms with what seemed a new way to conduct business, with little or no apparent risk. The financial services sector, which historically accounted for about 3% of the US economy, rose to over 20%. Risk was being transferred front, right and center, in such as way that it seemed to … disappear.

But it didn’t, risk was merely hiding.

Not many were surprised when the subprime bubble burst in 2007. In fact, what became clear last year is that mathematical sophistication had simply allowed risk to be hidden better and better. But almost everyone was surprised to see in 2008 the crisis to extend beyond the subprime, to the prime and super-prime areas, in such a way that the interconnectivity that allowed the financial systems to flourish during the last twenty years was now contributing to a domino-style collapse of the financial system worldwide.

Mathematics shares with the rest of the business part of the praise for the efficiency of the market that allowed credit to reach millions of consumers, and part of the blame for the demise of the credit market in 2008. What we are likely to see in a future of renewed regulation and reconstruction of financial markets is a continued relationship between mathematics and finance, from this day forward, for better or for worse, for richer, for poorer, in sickness and in health, to love and to cherish; from this day forward until death do us part.

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What role did Mathematics play in the current financial crisis?
Vallabh Muralikrishnan

Mathematical Finance has been one of the casualties of the current financial crisis.  Over the past year, the news media has berated “Quants” (as Mathematicians are known in the industry) and their esoteric models for supposedly misleading the market.  But how much of this blame is justified?The current financial crisis began in what is called the “structured credit products” market. The story here went something like this:There was a greater demand for funding in the economy than what could be provided solely by bank lending. Therefore, bankers set up legal entities to provide funding by issuing notes to investors. Some investors, such as hedge funds, were willing to tolerate high risks of loss while other investors, such as pension funds, demanded low risk. To appeal to this wide range of investors, bankers pooled several assets, such as loans, and then structured the cash flows from these assets in such a way that they were able create “safe” and “risky” notes to sell to different types of investors.

This is where mathematics was needed. Mathematical and statistical models were required to assess the risk of the notes issued to investors.

Specifically there was a need to model the correlation of defaults between assets in the pool that provided cash flows to the investors. The problem was that correlation estimates are notoriously unstable when modeling rare events such as defaults. Nevertheless, the “Quants” happily provided bankers with their best efforts at modeling correlations. This went on for years until bankers, investors, rating agencies, regulators, and all market participants began to trust these models. In 2007, unfortunately, the real world began to behave differently than what was predicted by the models. This led to even investors in “safe” notes to lose money, which in turn eventually led to the current financial crisis.
The models failed to predict reality. But the responsibility for failure lies with all market participants who directly or indirectly relied on these models. Mathematicians simply provided a tool. At a recent speech at the IACPM conference Professor Jarrow from Cornell University stated that having no model is better than having a bad model. Businessmen, however, seem to favor a bad model over no model at all.

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Simple Thoughts on the Current Global Financial Climate

David Miner, BSc, MBA. FCSI
David Miner & Associates

A few months ago while jogging with a friend, I commented that of my two degrees from the University of Toronto, my Bachelor of Science in mathematics was often more important to me in the investment industry than my Master of Business Administration in finance. Both degrees are important. The mathematics, however, enables some depth perception I would have never enjoyed otherwise.

Here are a few thoughts and beliefs, somewhat from a mathematical perspective, that may put a little light on the world today.

  1. The steady state of socio-economic systems such as the stock market and the economy is not straight line, but harmonic motion (like the swing of a pendulum). If all other factors were to remain unchanged, the stock market would still have its ups and downs. The economy would still see growth and contraction phases. In short, bear markets and recessions are as normal as air. There is little point in getting excited. Bear markets and recessions have happened repeatedly in the past and will happen repeatedly in the future.
  2. Since the early 1980′s, interesting work has been done on the mathematical application to the stock market of chaos theory and fractals. A lengthy discussion of chaos and fractals is beyond the scope of this article. Let it suffice that some appreciation of chaos theory and fractals would lead us to greater comfort with the jagged patterns of a stock market index over time. Call it nature, much like the weather that brings us both nice days and stormy days. By appreciating chaos theory and fractals, we understand the big picture better and expect periods of negative returns. We also understand that everything will work out okay.
  3. Since 1970, the Toronto Stock Market Total Return (i.e., dividends reinvested) has multiplied 38 times over. Simply stated, from early 1970 to the end of September 2008, you made 38 times your money in 38 years – not a bad investment! However, during that 38 years there were six periods when you would have seen your investments decline by a third. Typically, the declines lasted an average of ten months. Very simply, over long periods of time, the market goes up more than it goes down but we can expect it to go down from time to time.
  4. Market timing does not work. For it to work, both the sell and the buy have to be timed right. That simply never happens consistently. The market is too chaotic (and fickle!). The best plan to optimize return is stay invested – always. Because markets are chaotic, market timers are shown by a number of studies to have generally poor long-term investment performance.
    The four most costly words to investors are “This time is different”. Moving out of equity during periods of pessimism causes investors to effectively lose again when markets rebound.
  5. A significant portion of the selling in the stock market that we have seen in the last few months is a result of:
    a) Institutional selling (e.g., hedge funds selling to meet redemptions)
    b) Tax loss selling at the end of 2008
    c) Margin call selling (brokers are forced to sell out clients who are over leveraged)
    Selling for these purposes does not last forever, but does cause short-term downward pressure on stock prices like we have seen recently.
  6. There is about $3.5 Trillion in the U.S. sitting in money market funds earning virtually nothing. That amount is about 45% of the value of the S&P 500. When the stock market starts to show strength, some of that $3.5 Trillion will flow back into the stock market and add fuel to the next bull rally.
  7. There is new management at the White House effective January 20, 2009. I expect that a new president will create a better investment mood and climate going forward. (The last eight years in the White House have not been impressive.)
    It is also important to remember that the stock market is a leading indicator and starts to go up well before a recession is over. It is not unusual to se a stock market go up 25 percent or more before a recession is officially over. Never wait for “good” economic new before investing, because too much investment profit is missed.
  8. The sub-prime problems in the United States were an accident waiting to happen. Sadly, the bailout costs could have been used to install universal health care in the U.S., solve world hunger, and buy all of the sub-prime securities at book value. While capitalism can work well, we have experienced one of the worst cases of irresponsibility, short-sightedness, and greed of U.S. financial institutions. And this is not the first time major financial institutions have behaved badly. In the early 1980′s we experienced the Latin American debt crisis. The bailout was about $500 billion (and life went on). About twenty years ago, the United States suffered the S&L “crisis”. The bailout was about $400 billion (and life went on). We shall get through the current silliness and life will go on.
  9. The information flow from the stock market is excellent. We can get valuations of our portfolios instantly. Imagine how people might react if every day they were able to open up the newspaper and see the daily closing values of their houses. I expect many would experience high anxiety if they saw their house fluctuating a few thousand dollars a day. In housing, ignorance on day-to-day valuation is bliss. Perhaps we should apply the same attitude to our stock market holdings and not worry so much about short-term fluctuations.
  10. Feed-back loops profoundly affect markets and the economy. For example, if people expect a recession, they spend less. The result is recession. That situation is a negative feedback loop. A hot housing market pulls more speculators and more buying into the housing market. The housing market gets hotter. That situation is a positive feedback loop. Invariably, feedback loops run out of steam and situations return to a more normal state. We have recently experienced much negative feedback in both the stock market and the economy. Will the stock market and the economy get stronger? History tells us to expect positive outcome. And because of feedback loops, be very cautious of hot trends. Bubbles burst – always

In conclusion, I am reminded of a discussion with a friend during the recession in the early 1990′s. I asked him how the recession was affecting his business. He replied “Recession? Oh, that. We had a meeting and decided not to participate.” Indeed, most of us are little affected by the economy. We continue to work and pay our bills. If anything we are currently enjoying better prices at the fuel pump and cheaper vacation deals when we travel. And for those of us who invest, we are seeing excellent buying opportunities in equities that we probably will never see again. I compare it to a huge sale at the outlet mall, which in many ways is something to feel good about. After almost thirty-four years in the financial sector, I have become numb to the daily noise from the business media. It may be interesting, but it is noise and worrying is a waste of emotional energy.

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Bruce Trail Day

A Three Snake Day

On our annual Bruce Trail walk on the last weekend in September we saw three (actually four) snakes, some frogs, and a salamander. This indicates good weather and great spirits. These walks are ideal to meet and get to know fellow mathematicians. You can talk while you walk. You may talk a lot or avoid talk altogether because for the most part we walk in single file.

Our first walking on the Bruce Peninsula took place in 1972. Now some families are represented by three generations of enthusiastic walkers. Visitors to the department often join the hard-core hikers and new faculty regularly take this opportunity to meet colleagues casually. Our route which is close to Tobermory is on the whole rugged, but it has also less demanding stretches, and the last kilometre is now wheel chair accessible. So it is easy on the feet and after walking for six or seven hours this is a relief. Walkers are a welcoming crowd.Ragnar Buchweitz does the organization.Here are some photos.

E. W. E.

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