Michael M. Schein

What Graduate Students (and the Rest of Us) Can Learn from Lesson Study.

Lesson study is a professional-development process in which teachers collaboratively plan, execute, observe, and discuss lessons in the classroom. Lesson study can be implemented in a college environment to develop and improve the teaching skills of both new and experienced faculty. Focusing on a single lesson allows the lesson study participants to conduct an in-depth investigation of teaching and learning issues and can produce a lively exchange of ideas about teaching and learning among faculty, graduate students, and undergraduate students in a nonevaluative setting.

Weights of Galois representations associated to Hilbert modular forms

Abstract Let F be a totally real field, p ≧ 3 a rational prime unramified in F, and a place of F over p. Let be a two-dimensional mod p Galois representation which is assumed to be modular of some weight and whose restriction to a decomposition subgroup at is irreducible. We specify a set of weights, determined by the restriction of ρ to inertia at , which contains all the modular weights for ρ. This proves part of a conjecture of Diamond, Buzzard, and Jarvis, which provides an analogue of Serres epsilon conjecture for Hilbert modular forms mod p.

Normal zeta functions of the Heisenberg groups over number rings I: the unramified case

Let

Bolza Quaternion Order and Asymptotics of Systoles Along Congruence Subgroups

K

Weights in Serre’s conjecture for Hilbert modular forms: The ramified case

be a number field with ring of integers

Normal zeta functions of the Heisenberg groups over number rings II — the non-split case

\mathcal{O}_K

An irreducibility criterion for supersingular representations of ₂() for totally ramified extensions of ℚ_{}

. We compute explicitly the local factors of the normal zeta functions of the Heisenberg groups

On the universal supersingular mod p representations of GL2(F)

H(\mathcal{O}_K)

On modular weights of Galois representations

that are indexed by rational primes which are unramified in

On the flat cohomology of binary norm forms

K