Cameron Franc

Name	Cameron Franc
Location	Hamilton, Ontario
Office	TBD
Hours	By appointment
Email	franc at math dot mcmaster dot ca

I'm an Assistant Professor at McMaster University. My research is in number theory, with an emphasis on modular forms and L-functions. Recently I've also started thinking about vertex operator algebras and their relationship with modular forms and number theory.

Previously I was an assistant prof at the University of Saskaktchewan, a postdoc at the University of Michigan and UCSC, a grad student at McGill, and an undergrad at Queen's.

Download CV (updated 10/2020)

Submitted papers	17. The unbounded denominator conjecture for the noncongruence subgroups of index 7. Joint with Andrew Fiori.
Accepted and Published papers and notes	16. Densities of bounded primes for hypergeometric series. Joint with Brandon Gill, Jason Goertzen, Jarrod Pas and Frakie Tu. Research in Number Theory, 2020. 15. Classification of some vertex operator algebras of rank 3. Accepted for publication in Algebra and Number Theory. Joint with Geoff Mason. 14. Constructions of vector-valued modular forms of rank four and level one. International Journal of Number Theory. Joint with Geoff Mason. 13. Nonabelian Hodge theory and vector valued modular forms. Contemporary Mathematics. Joint with Steve Rayan. 12. Vector valued modular forms and decompositions of vector bundles. CMS Bulletin. 11. On unbounded denominators and hypergeometric series. Journal of Number Theory. Joint with Terry Gannon and Geoff Mason. 10. Vector bundles and modular forms for Fuchsian groups of genus zero. Communications in Number Theory and Physics. Joint with Luca Candelori. 9. Generating weights for the Weil representation attached to an even order cyclic quadratic module. Journal of Number Theory. Joint with Luca Candelori and Gene Kopp. 8. On the structure of modules of vector valued modular forms. Ramanujan Journal. Joint with Geoff Mason 7. Vector valued modular forms and the modular orbifold of elliptic curves. International Journal of Number Theory, 2016. Joint with Luca Candelori. 6. Three-dimensional imprimitive representations of the modular group and their associated modular forms. Journal of Number Theory, 2015. Joint with Geoff Mason. 5. Hypergeometric series, modular linear differential equations, and vector-valued modular forms. The Ramanujan Journal, 2015. Joint with Geoff Mason. 4. Fourier-coefficients of vector-valued modular forms of dimension 2. The Canadian Mathematical Bulletin, 2015. Joint with Geoff Mason. 3. Computing fundamental domains for the Bruhat-Tits tree for GL2(Qp). LMS Journal of Computation and Mathematics, 2014. Joint with Marc Masdeu. 2. Nearly rigid analytic modular forms and their values at CM points. Ph.D. thesis, McGill University, 2011. Advised by Henri Darmon. 1. On a generalisation of Artin's conjecture. Pure and Applied Math. Quarterly, 2008. Joint with Ram Murty.
Other	Slides from my talk at the AMS sectional meeting held at Loyola University, October 2015. Slides from my talk at a workshop in honour of Noriko Yui (LSU April 2015). Slides from my talk at the recent Automorphic Forms Workshop (UofM March 2015). Scan of Katz's article on Crystalline cohomology, Dieudonne modules and jacobi sums. Translation of Boutot-Carayol (note: this is from my time as a grad student and it's full of typos).

Past courses	Class field theory (Math 286), UCSC, Spring 2014 Complex analysis (Math 103a), UCSC, Spring 2014 Algebraic Geometry II (Math 223b), UCSC, Winter 2013 Algebra (Math 111a), UCSC, Fall 2012 Complex analysis (Math 103a), UCSC, Winter 2012 Linear algebra and geometry (Math 133), McGill University, Fall 2008
Other	Handout from a talk on the Skolem-Mahler-Lech theorem for undergraduates. Slides from a talk on Math and Music for undergraduates. Slides from a talk on special values of the Riemann zeta function for undergraduates.