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## Biography

Appointed a University Professor in 2002 Professor Friedlander is widely recognized as an international leader in one of the purest branches of mathematics – analytic number theory, and a leader in the theory of prime numbers and L-functions. The exploration of prime numbers is among the oldest endeavours in pure and abstract knowledge and new insights are generally achieved only after decades, or even centuries, of research.

Professor Friedlander's talents were recognized early and many of his earlier results are now tools of the trade for scientists working in this area. However, in a discipline in which it is commonly accepted that people do their best work while they are still young, one of the startling aspects of Professor Friedlander's career is that he grows deeper and more prolific with age. In work done with Henryk Iwaniec, he proved that infinitely many prime numbers can be obtained as the sum of a square and fourth power. This work reached a large audience through wide media coverage of the receipt of the leading international award in number theory, the Cole Prize in Number Theory, by Professor Iwaniec. Professor Friedlander's collaboration with, and contribution to, the work of Professor Iwaniec is recognized in the citation for the Cole Prize, which states that "In particular, the prize is awarded for his paper (with J. Friedlander)", and quotes other joint work with Professor Friedlander. Professor Friedlander has published over 90 research papers, many in the most prestigious mathematical journals, and he sustains an extremely busy schedule of lectures at conferences, workshops, colloquia and external seminars, including a lecture at the International Congress of Mathematics, one of the most distinguished accolades in international mathematics.

Professor Friedlander has been a member of the University of Toronto since 1977 and has served the University very well through a record of civic commitment that included the Chairmanship of the Department of Mathematics. He holds a joint appointment in the Department of Physical Sciences in the University of Toronto at Scarborough and the Department of Mathematics in the Faculty of Arts and Science. In addition, Professor Friedlander has had several visiting appointments at Princeton and Berkeley. He is a dedicated teacher of undergraduates and supervisor of graduate students and postdoctoral fellows and has mentored young mathematicians of promise and accomplishments.

## Industry Applications (2)

### Education/Learning

### Research

## Research Interests (3)

### Analytic Number Theory

### Theory of Prime Numbers

### L-functions

## Accomplishments (5)

#### Fellow of the American Mathematical Society (professional)

The Fellows of the American Mathematical Society program recognizes members who have made outstanding contributions to the creation, exposition, advancement, communication, and utilization of mathematics.

#### Killam Fellowship (professional)

Awarded by the Canadian Council for the Arts.

#### CRM-Fields Prize (professional)

The prize recognizes exceptional achievement in the mathematical sciences.

#### Jeffery-Williams Prize (professional)

The prize recognizes mathematicians who have made outstanding contributions to mathematical research.

#### Fellow of the Royal Society of Canada (professional)

The fellowship of the RSC comprises distinguished men and women from all branches of learning who have made remarkable contributions in the arts, the humanities and the sciences, as well as in Canadian public life.

## Education (3)

#### Pennsylvania State University: Ph.D., Mathematics 1972

#### University of Toronto: B.Sc, Undergraduate Studies 1965

#### University of Waterloo: M.A., Graduate Studies 1966

## Links (1)

## Media Appearances (3)

#### Mathematician Renowned for Prime Number Theory Wins Shaw Prize

**Rutgers Today** online

2015-09-28

A Rutgers professor since 1987, Iwaniec is known for his work studying prime numbers, which are numbers that can be divided only by themselves or the number one to arrive at a whole number. While no formula can represent all prime numbers, Iwaniec and John Friedlander of the University of Toronto proved that an infinite number of primes can be generated by the formulaX2+Y4...

#### The Pursuit of Beauty

**The New Yorker** online

2015-02-02

Iwaniec and his friend, John Friedlander, a professor at the University of Toronto, read with increasing attention. “In these cases, you don’t read A to Z,” Iwaniec said. “You look first at where is the idea. There had been nothing written on the subject since 2005. The problem was too difficult to solve. As we read more and more, the chance that the work was correct was becoming really great. Maybe two days later, we started looking for completeness, for connections. A few days passed, we’re checking line by line. The job is no longer to say the work is fine. We are looking to see if the paper is truly correct.”...

#### Unknown Mathematician Proves Elusive Property of Prime Numbers

**Wired** online

2013-05-20

But the more researchers tried to overcome this obstacle, the thicker the hair seemed to become. During the late 1980s, three researchers — Enrico Bombieri, a Fields medalist at the Institute for Advanced Study in Princeton, John Friedlander of the University of Toronto, and Henryk Iwaniec of Rutgers University — had developed a way to tweak the definition of the level of distribution to bring the value of this adjusted parameter up to 4/7. After the GPY paper was circulated in 2005, researchers worked feverishly to incorporate this tweaked level of distribution into GPY’s sieving framework, but to no avail...

## Articles (5)

**Counting Primes in Arithmetic Progressions**

*Analytic Number Theory*F

2015 These notes represent an expanded version of a lecture delivered at the Urbana meeting of June 2014 in memory of Paul and Felice Bateman and of Heini Halberstam, and, in modified form, at the October 2014 workshop at the Royal Swedish Academy of ...

**Enumeration of certain varieties over a finite field**

*Proceedings of the American Mathematical Society*F

2014 Let {F}_q be a finite field of q elements. E. Howe has shown that there is a natural correspondence between the isogeny classes of two-dimensional ordinary abelian varieties over {F}_q which do not contain a principally polarized variety and pairs of positive integers...

**On Waring's problem: two squares and three biquadrates**

*Mathematika*F

2014 We investigate sums of mixed powers involving two squares and three biquadrates. In particular, subject to the truth of the Generalised Riemann Hypothesis and the Elliott–Halberstam conjecture, we show that all large natural numbers...

**Small representations by indefinite ternary quadratic forms**

*Number Theory and Related Fields*F

2013 We study nonhomogeneous Pythagorean triples, that is, solutions of the diophantine equation x^ 2+ y^ 2-z^ 2= D where D is fixed and non-zero. We are particularly concerned, for D large and positive, with counting the solutions having x, y, z, all small ...

**Cryptographic Applications**

*Cryptography and Computational Number Theory*F

2013 We outline some cryptographic applications of the recent results of the authors about small values of the Carmichael function and the period of the power generator of pseudorandom numbers. Namely, we show rigorously that almost all randomly selected ...