### The School of Athens

January is a busy time for me with teaching, NSERC reviews, and my research and writing projects. With all that activity in mind, I am posting a short blog this week about Canada’s math institutes, intertwined with a few personal stories about them. Next week I will blog on Babai’s startling announcement of an error then fix to his quasipolynomial time graph isomorphism algorithm.

As Raphael’s painting *The School of Athens* in the featured image of this blog suggests, **scholars dig hanging out together**.

I completed my doctorate in 1998, and had the luxury of each of the four Canadian mathematics institutes at my disposal for the duration of my career. Since the new millennium, the institutes have become deeply ingrained into the fabric of Canadian mathematics. **The institutes are part of our DNA.** However, many of my non-mathematical colleagues have no clue about the existence or purpose of the institutes. My Ryerson STEM colleagues may have heard of Fields, but they don’t know about BIRS or PIMS, for example.

### Fields

My first exposure to a mathematical institute in Canada was to the Fields Institute for Research in the Mathematical Sciences (or Fields), which began in 1992 at the University of Waterloo (shortly before I started my Masters work). It moved to the University of Toronto in 1995, where it has resided on College Avenue ever since.

Whenever I walk/run/drive by Fields, I wonder if other passers-by realize the kind of deep mathematics that goes on there. Fields has evolved into one of the leading mathematical institutes in the world, hosting thematic programs, conferences, summer schools, and outreach activities. I spent some of my sabbatical year there in 2005, which was a terrifically productive experience. Since then, I have spoken there several times at Fields and it remains a thrill.

An early memory from graduate school days was a lecture by the famed logician Saharon Shelah. He wrote positive integers before each of his theorems, ranging from single digits to numbers like 836. I learned later these reference the numbering of his works, since he now has over 1,000!

### CRM

The first mathematical institute in Canada was the Centre de Recherches Mathématiques (CRM) in Montréal, founded in 1969, and recognized as an institute in 1984. CRM uses a model analogous to Fields, with thematic programs, conferences, and outreach.

The most recent Workshop on Algorithms and Models for the Web Graph conference that I co-chaired was there, and I’ve attended a number of workshops there such as Graph Searching in Canada (GRASCan) and GRAph Searching, Theory & Applications (GRASTA). CRM is located in the Andre-Aisenstadt building on the campus of Université de Montréal.

### PIMS

The Pacific Institute for the Mathematical Sciences (PIMS) began in 1996, and supports the western universities from its location in Vancouver. My interview with Nassif Ghoussoub outlines some of the fascinating origins of PIMS. Like Fields and CRM, PIMS has thematic programs and hosts a number of other activities.

As a freshly minted grad student, I have great memories from 2000 of a graph colouring and homomorphism workshop there. That’s where I first met graph homomorphism thought-leaders Pavol Hell and Jaroslov Nešetřil.

### BIRS

The Banff International Research Station (BIRS) has a different model than the other institutes, in that it is a self-contained retreat located outside a university. Participants in their three to five-day workshops live at BIRS in the Banff Centre: they sleep and eat there (and the buffet there is excellent even for vegans like myself, unfortunately for my waistline). BIRS is similar to the famous Oberwolfach Research institute for Mathematics in Germany. I’ve been at BIRS about a dozen times for various conferences, and I spent a week there with a colleague completing intense research together during our sabbaticals. Most recently, I was there for a great meeting on random geometric graphs, and every top expert in the field was present. Donald Trump’s election night happened while we there, and it made for “interesting” dinner conversation.

### AARMS

I would be remiss not mention AARMS. While the Atlantic Association for Research in the Mathematical Sciences (AARMS) has no physical building, it is an important association representing universities in the Atlantic provinces. AARMS supports research and conferences, and puts on a great annual summer school aimed at graduate students. The summer school features speakers delivering a month-long course in an AARMS-affiliated university (usually Dalhousie University, Memorial University, or University of New Brunswick).

I taught an AARMS summer school on the web graph in 2006, and the experience was terrific with strong students from across the country and beyond. The late Jon Borwein headed AARMS at the time, and my first book came about from lecture notes for that course. My co-author Jeannette Janssen recently completed her term as director of AARMS, which is now headed by Sanjeev Seahra.

AARMS deserves a building, if any rich benefactors are reading!

Anthony Bonato