Number Theory

Number Theory is one of the oldest branches of modern mathematics. It is motivated by the study of properties of integers and solutions to equations in integers. Many of its problems can be stated easily, but often require sophisticated methods from a diverse spectrum of areas in order to study. Its modern formulations are wide reaching and have close ties to algebraic geometry, analysis, and group theory; together with computational aspects. Perhaps due to the fundamental and profound nature of the integers, Number Theory plays a special role in mathematics and applications: two of the Clay Millennium Prize Problems are in Number Theory, and many internet security protocols are based on number theoretic problems.

 

Number Theory is an active area of research for faculty at SFU, and together with faculty at UBC, we form one of the largest communities of Number Theory researchers in North America.

Current and Upcoming Events

Researchers

Faculty
Peter Borwein Classical analysis, number theory, and computation pborwein@cecm.sfu.ca
Nils Bruin Diophantine and arithmetic geometry nbruin@math.sfu.ca
Imin Chen Number theory and arithmetic geometry ichen@math.sfu.ca
Stephen Choi Analytic number theory kkchoi@math.sfu.ca
Ramsey theory and mathematics education vjungic@sfu.ca

Postdoctoral Fellows
 
Jens Bauch 2015 -
Colin Weir 2013 - 2015
Jonas Jankauskas 2012 - 2013
Paul Pollack 2011 - 2012
Charles Samuels 2009 - 2011
Katherine Stange 2009 - 2011
Sander Dahmen 2008 - 2010
Soroosh Yazdani 2010 - 2011
Ronald van Luijk 2006 - 2008
Chris Sinclair 2005 - 2007
Friedrich Littmann 2003 - 2005

Graduate Students
Navid Alaei  
Gleb Glebov    
Avinash Kulkarni    
Cho-Ho Lam    
Brett Nasserden    

Past Events

Graduate Program

A complete list of our graduate courses can be found here. Information about applying to our program can be found here. The following is a list of the courses relevant to studies in Number Theory.

Regular

MATH 724 Applications of Complex Analysis

MATH 725 Real Analysis

MATH 740 Galois Theory

MATH 741 Commutative Algebra and Algebraic Geometry

MATH 817 Groups and Rings

MATH 818 Algebra and Geometry

MATH 842 Algebraic Number Theory

MATH 843 Analytic and Diophantine Number Theory

Applications

MATH 447 Coding Theory

MACM 401 Introduction to Computer Algebra

MACM 442 Cryptography

Current Interest and Reading Courses

Theses and Projects

Navid Alaei Symmetric Differential Forms on the Barth Sextic Surface MSc Thesis 2015
Avinash Alexander Kulkarni On Jacobians of dimension 2g that decompose into Jacobians of dimension g MSc Thesis 2014
Patric Ryan McMahon Solvability of ternary equations of signature (3,3,2) MSc Thesis 2014
Himadri Ganguli On the correlation of completely multiplicative functions PhD Thesis 2013
Adrian Belshaw Strong Normality, Modular Normality, and Flat Polynomials: Applications of Probability in Number Theory and Analysis PhD Thesis 2013
James Ratcliffe Sums of rational functions MSc Thesis 2012
Steven Kieffer Computability in principle and in practice in algebraic number theory: Hensel to Zassenhaus MSc Thesis 2012
Eric Rinne Riemann Zero spacings and Montgomery's pair correlation conjecture MSc Thesis 2012
Alexander Molnar Fractional linear minimal models of rational functions MSc Thesis 2011
Kevin Doerksen On the arithmetic of genus 2 curves with (4,4)-split Jacobians PhD Thesis 2011
Michael Coons Some aspects of analytic number theory: parity,
transcendence, and multiplicative functions		 PhD Thesis 2009
Alan Meichsner The integer Chebyshev problem: computational explorations PhD Thesis 2009
Keshav Mukunda Pisot and salem numbers from polynomials of height one PhD Thesis 2007
Hesam Abbaspour Deligne-Lusztig character theory for general linear groups of rank 2 MSc Thesis 2007
Desmond Leung Small prime solutions to cubic Diophantine equations MSc Thesis 2006
Brett Hemenway On Recognizing Congruent Primes MSc Thesis 2006
Lisa Redekop Torsion Points of Low Order on Elliptic Curves and Drinfeld Modules MSc Thesis 2006
Idris Mercer Autocorrelation and flatness of height one polynomials PhD Thesis 2005
Adrian Belshaw On the normality of numbers MSc Thesis 2005
Pei Li On Montgomery's pair correlation conjecture to the zeros of the Riemann zeta function MSc Thesis 2005
Shabnam Akhtari On the Cyclotomic Polynomials with +1 or -1 Coefficients MSc Thesis 2004
Beth Powell Irreducible characters of GL_2(Z/p^2Z) MSc Thesis 2003

Undergraduates

Undergraduates interested in learning Number Theory can take MATH 342 Elementary Number Theory, which serves as a general introduction with minimal prerequisites. However, because research in Number Theory requires techniques from many areas, we encourage students interested in continuing in this area to take a broad spectrum of courses from our curriculum. For further guidance, please contact the Undergraduate Advisor.

 

Here is a sample of undergraduate research in Number Theory that has been done recently.

 

Richard Lei A Sieving Approach to S-Unit Equations NSERC USRA Report 2011
Robert Shih Plotting Plane Algebraic Curves Containing Singularities in Sage NSERC USRA Report 2010
Karin Arikushi Elliptic Curves with isomorphic 3-torsion over Q NSERC USRA Report 2005

 

For questions about this page, please contact: ichen@math.sfu.ca