Andrew Granville

Andrew Granville is a British-Canadian mathematician renowned for his deep and influential contributions to number theory, particularly in analytic number theory and additive combinatorics. Born in 1962 in London, England, Granville has established himself as a leading figure in the mathematical community through his research on prime numbers, the distribution of primes, and Diophantine equations.

Educational Background

• Undergraduate Studies: Granville completed his bachelor's degree at the Trinity College, University of Cambridge.


• Doctoral Studies: He earned his Ph.D. in 1987 from Queen's University in Kingston, Ontario, Canada, under the supervision of Paulo Ribenboim, a prominent number theorist.

Academic Positions

• University of Georgia (1989–2002): After completing his doctorate, Granville joined the Department of Mathematics at the University of Georgia, where he progressed from assistant to full professor.


• Université de Montréal (2002–Present): He is currently a professor at the Université de Montréal in Montreal, Quebec, Canada. In this role, he continues to conduct research, teach, and mentor graduate students.


• 
  

  Visiting Positions: Granville has held visiting professorships and fellowships at several prestigious institutions worldwide, including:

  
  


• 
  

  Institute for Advanced Study (Princeton)

  
  


• École Polytechnique Fédérale de Lausanne (Switzerland)


• University of California, Berkeley

Research Contributions

Andrew Granville's research encompasses a wide range of topics within number theory. Some of his most notable contributions include:

1. Analytic Number Theory

Granville has made significant advances in understanding the distribution of prime numbers. His work often employs tools from complex analysis to tackle problems related to primes and zeta functions.

• Zeroes of L-Functions: He has studied the zero distributions of L-functions, which has implications for the Generalized Riemann Hypothesis.


• Siegel Zeroes: Granville has contributed to research on Siegel zeroes, which are hypothetical zeroes of L-functions that have profound implications for the distribution of prime numbers in arithmetic progressions.

2. The ABC Conjecture

Granville has worked extensively on the ABC conjecture, a central problem in number theory that explores the relationships between the prime factors of three positive integers ( a ), ( b ), and ( c ), satisfying ( a + b = c ). His research has shed light on the implications of the conjecture and its connections to other problems, such as:

• Diophantine Equations: Providing insights into solutions of equations where integer solutions are sought.


• Rational Points on Curves: Understanding the distribution of rational solutions on algebraic curves.

3. Additive Combinatorics

He has applied combinatorial techniques to number theory, exploring how sets of integers add together and the structure of sums and differences within these sets.

• Sumsets and Difference Sets: Investigating properties of sets formed by adding or subtracting elements of a given set.


• Erdős–Turán Conjecture: Contributing to problems related to the additive properties of integers.

4. Computational Number Theory

Granville has also engaged in computational aspects, utilizing algorithms and computational power to test conjectures and explore numerical examples that inform theoretical advancements.

Publications and Expository Work

In addition to research papers, Granville is known for his expository articles and efforts to make complex mathematical ideas accessible:

• "Prime Suspects: The Anatomy of Integers and Permutations": A graphic novel co-authored with Jennifer Granville and illustrated by Robert J. Lewis, blending mathematics with art to explore number theory concepts.


• Educational Articles: Writing pieces that explain advanced mathematical concepts to broader audiences, including students and educators.

Honors and Awards

Andrew Granville's contributions have been recognized through various prestigious awards and honors:

• Fellow of the Royal Society of Canada (1998): Elected for his outstanding contributions to mathematical sciences.


• Coxeter–James Prize (1995): Awarded by the Canadian Mathematical Society for his exceptional achievements in mathematical research.


• Jeffery–Williams Prize (2008): Another honor from the Canadian Mathematical Society, recognizing mathematicians who have made outstanding contributions to mathematical research.


• Invited Speaker at International Congress of Mathematicians (1994): A recognition of his prominence in the field, invited to speak at one of the most significant gatherings of mathematicians worldwide.

Mentorship and Influence

Granville has mentored numerous graduate students and postdoctoral researchers who have gone on to make their own contributions to mathematics. His teaching style emphasizes deep understanding and creative problem-solving.

Current Work

As of my knowledge cutoff in October 2023, Andrew Granville continues to be an active researcher and professor at the Université de Montréal. He collaborates with mathematicians globally, contributes to advancing number theory, and participates in conferences and seminars.

Summary: Andrew Granville is a distinguished mathematician whose work has significantly advanced our understanding of number theory. His research on primes, the ABC conjecture, and additive combinatorics has made a lasting impact on the field. Through his teaching, publications, and mentorship, he continues to inspire and shape the future of mathematics.