Computational Algebra Seminar: Breuer -- Coefficients of modular polynomials

Speaker: Florian Breuer (Newcastle)
Title: Coefficients of modular polynomials
Time & Place: 15:00 - 16:00, Thursday 25 September, SMRI Seminar Room
Abstract: 
For every positive integer N there is a modular polynomial $\Phi_N(X,Y)$ with integer
coefficients which vanishes precisely at pairs $(j_1, j_2)$ of j-invariants of elliptic 
curves linked by a cyclic isogeny of degree N. These polynomials play an important role 
in cryptography and algorithmic number theory. 

I will give a student-friendly introduction to these polynomials and review what is 
known about the (rapid!) growth of their coefficients. Finally, I will present some new 
results showing that these coefficients are highly divisible by small primes.