A possible schedule is as follows; reality will certainly diverge from this.

Week 1. Definition of a lattice and its covolume. History and origins of the geometry of numbers. The problem of primes with missing digits. The shape of a lattice. Inner products, bases, quadratic forms, the Gaussian volume heuristic.
Week 2. The dual lattice. Minkowski minima. The general idea of a reduced basis. Minkowski’s theorems. Sublattices and projections.
Week 3. Lenstra–Lenstra–Lovász algorithm. Historical questions of interest in the geometry of numbers. More recent questions about lattice reduction.
Week 4. Counting points of bounded norm in a lattice: asymptotic and upper bounds. Primitive sublattices. Orthogonal sublattices. Covolume of orthogonal lattices.
Week 5. Manin’s conjecture. The equation $x_1y_1+\dots+x_ny_n=0$. Basic idea of Thunder’s proof. Assignment check-in deadline and lecture.
Week 6. Manin’s conjecture for $x_1y_1+\dots+x_ny_n=0$: completion of the proof. Review of course.
Week 7. Primes with missing digits: why geometry of numbers is relevant. Vaughan’s identity. The circle method. Statement of Maynard’s Proposition 9.3, Lemma 13.1, Proposition 13.3 and Proposition 13.4.
Week 8. Selected proofs from Maynard.
Week 9. Assignment final deadline.