Let K be a number field. For which primes p does there exist an elliptic curve
admitting a K-rational p-isogeny? Although we have an answer to this question over the rationals, extending this to other number fields is a fundamental open problem…
Postnikov constructed a cellular decomposition of the totally nonnegative Grassmannians. The poset of cells can be described (in particular) via Grassmann necklaces. We study certain quiver Grassmannians for the cyclic quiver admitting a cellular decom…
Each metric graph has canonically associated to it a polarized real torus called its tropical Jacobian. A fundamental real-valued invariant associated to each polarized real torus is its tropical moment. We give an explicit and efficiently computable f…
The classical Loewner’s theorem states that operator monotone functions on real intervals are described by holomorphic functions on the upper half-plane. We characterize local order isomorphisms on operator domains by biholomorphic automorphisms of t…
We prove that it is consistent that Club Stationary Reflection and the Special Aronszajn Tree Property simultaneously hold on
, thereby contributing to the study of the tension between compactness and incompactness in set theory. The poset which…
We construct a new type of planar Euler flows with localized vorticity. Let
,
, be m arbitrarily fixed constants. For any given nondegenerate critical point
of the Kirchhoff–Routh function defined on
corresponding to
, we c…
For a Galois extension
with
and
, we determine the
-module structure of
. Although there are an infinite number of (pairwise nonisomorphic) indecomposable
-modules, our decomposition includes at most nine indecomposabl…
We develop tools for constructing rigid analytic trivializations for Drinfeld modules as infinite products of Frobenius twists of matrices, from which we recover the rigid analytic trivialization given by Pellarin in terms of Anderson generating func…