Sam Mundy

I am a postdoc UCSB. Previously I was at Princeton, and before that, I was a graduate student at Columbia. My advisor was Eric Urban.

My email address is mundy "at" ucsb "dot" edu.

For an introduction to some of my research, here is a video of a talk I gave in the Princeton/IAS Number Theory Seminar in March of 2023.

Some papers

Degeneration of monodromy in the theory of Eisenstein congruences for classical groups. This paper gives a new Hecke-theoretic method to control the growth of monodromy in p-adic families of automorphic Galois representations for unitary groups and quasisplit classical groups.

A vanishing theorem for residual Eisenstein cohomology. This paper provides a general setup under which maximal parabolic residual Eisenstein classes vanish above middle degree but not below.

Automorphic cohomology, Arthur's conjectures and applications to G₂. To appear in American Journal of Mathematics.

On the Bernstein--Zelevinsky classification and epsilon factors in families. This paper introduces and studies a notion of family of smooth admissible representations of p-adic GL_n, and under mild hypotheses, proves the coherence of epsilon factors for such families, as well as for arbitrary products and functorial lifts of such.

Eisenstein series for G₂ and the symmetric cube Bloch--Kato conjecture. This paper does what my thesis below does, but under less restrictions (in particular the level 1 hypothesis of my thesis is removed here). In the appendix, I also expand the discussion of Arthur's conjectures for G₂ relative to what is said in my thesis.

Eisenstein series for G₂ and the symmetric cube Bloch--Kato conjecture. This is my Ph.D. thesis, which essentially contains the paper below. Besides what is described below, in this thesis I p-adically deform a certain Eisenstein series for G₂ in a generically cuspidal family, and I use the Galois representations attached to cuspidal members of this family to construct a certain nontrivial class in the Selmer group of the symmetric cube of the Galois representation attached to a cuspidal eigenform of level 1.

Multiplicity of Eisenstein series in cohomology and applications to GSp₄ and G₂. In this paper I locate every instance of certain Eisenstein series in the cohomology of GSp₄ and G₂ and prove that my list is exhaustive. This is a first step in my thesis.