Cameron Franc

• 18. Eisenstein metrics.
• 17. The unbounded denominator conjecture for the noncongruence subgroups of index 7. Joint with Andrew Fiori.

• 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.

• 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).

Every year the McMaster Math and Stats Department takes part in the Putnam Mathematics Competition:

We will once again be participating, and you are invited to join us.

In 2022, Dr.'s Forman and Franc will hold weekly Tuesday evening practice sessions starting on Tuesday October 4, from 6-7pm, held in person in HH 207. All are welcome!

Any questions can be directed to Dr. Forman (formann@mcmaster.ca) or Dr. Franc (franc@math.mcmaster.ca). We hope to see many of you there!

• Concentrate on problems A1 and B1. They're often a little more manageable than other problems.



• Advice from Kedlaya-Poonen-Vakil: "The first lesson of the Putnam is: don't be intimidated. Some of the problems relate to complex mathematical ideas, but all can be solved using only the topics in a typical undergraduate mathematics curriculum, admittedly combined in clever ways. By working on these problems and afterwards studying their solutions, you will gain insight into beautiful aspects of mathematics beyond what you may have seen before. Be patient when working on a problem. Learning comes more from struggling with problems than from solving them. If after some time, you are still stuck on a problem, see if the hint will help, and sleep on it before giving up. Most students, when they first encounter Putnam problems, do not solve more than a few, if any at all, because they give up too quickly. Also keep in mind that problem-solving becomes easier with experience; it is not a function of cleverness alone.

  Be patient with the solutions as well. Mathematics is meant to be read slowly and carefully. If there are some steps in a solution that you do not follow, try discussing it with a knowledgeable friend or instructor. Most research mathematicians do the same when they are stuck (which is most of the time); the best mathematics research is almost never done in isolation, but rather in dialogue with other mathematicians, and in consultation of their publications. When you read the solutions, you will often find interesting side remarks and related problems to think about, as well as connections to other beautiful parts of mathematics, both elementary and advanced. Maybe you will create new problems that are not in this book. We hope that you follow up on the ideas that interest you most."

• Coming soon!