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In the absence of local lifting obstructions, the global obstruction lies in a Tate{Shafarevich group that can be analyzed via Tate duality. But we want more, namely to preserve local properties of ...
We show that the asymptotic behavior of the partial sums of a sequence of positive numbers determine the local behavior of the Hilbert space of Dirichlet series defined using these as weights. This ex...
In this paper, local Tb theorems are studied both in the doubling and non-doubling situation. We prove a local Tb theorem for the class of upper doubling measures. With such general measures, scale i...
In this article, we develop a general method to obtain local limit theorems from distributional limit theorems. Our results use probabilistic arguments and yield explicit bounds on the quality of app...
For E/k an elliptic curve with CM by O, we determine a formula for (a generalization of) the arithmetic local constant of [4] at almost all primes of good reduction. We apply this formula to the CM c...
To any finite local embedding of Deligne--Mumford stacks $g: Y\to X$ we associate an \'etale, universally closed morphism $F_{Y/X}\to X$ such that for the complement $Y^2_X$ of the image of the diago...
Matrices of locally analytic functions in two variables correspond to the maximal Cohen-Macaulay modules over plane curve singularities and to the local determinantal representations.
Recently, there has been a wide interest in the study of aggregation equations and Patlak-Keller-Segel (PKS) models for chemotaxis with degenerate diffusion. The focus of this paper is the unification...
Let X be a Hilbert modular variety and V a non-trivial local system over X. In this paper we study Deligne-Saito’s mixed Hodge structure (MHS) on the cohomology groups Hk(X, V) using the method of Hig...
We consider the Dirichlet-to-Neumann map associated to the Schr\"odinger equation with a potential in a bounded Lipschitz domain in three or more dimensions. We show that the integral of the potentia...
For a reduced monomial ideal B in R=k[X_1,...,X_n], we write H^i_B(R) as the union of {Ext^i(R/B^[d],R)}_d, where {B^[d]}_d are the "Frobenius powers of B". We describe H^i_B(R)_p, for every p in Z^n...
We show that the frequent claim that the implied tree prices exotic options consistently with the market is untrue if the local volatilities are subject to change and the market is arbitrage-free. In...

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