Search
Now showing items 1-10 of 16
The stabilization of the Frobenius-Hecke traces on the intersection cohomology of orthogonal Shimura varieties
(2017-05-13)
The orthogonal Shimura varieties are associated to special orthogonal groups over Q of signature (n, 2) at infinity. In this work we prove a version of Morel’s formula for the Frobenius-Hecke traces on the intersection ...
Judging Gerrymandering: Improving Methods for Measuring Partisan Distortion and Its Component Parts
(2017-07-14)
This paper improves upon the existing mathematical methods for measuring partisan distortion and evaluating partisan gerrymandering in plurality-won, single-member district electoral systems. The measures and models presented ...
Nilpotence and Descent in Stable Homotopy Theory
(2017-04-18)
We study various applications of the ideas of descent and nilpotence to stable homotopy theory. In particular, we give a descent-theoretic calculation of the Picard group of topological modular forms and we prove a partial ...
Mechanics of Glacier Hydrology
(2017-08-31)
Liquid water exists throughout the glacier system. At the surface of glaciers and ice sheets, liquid water is produced when the seasonal surface energy forcing warms the ice above its melting temperature. This meltwater ...
Toward Computing Extremal Quasiconformal Maps via Discrete Harmonic Measured Foliations
(2017-02-07)
Conformal maps, which preserve angles, are widely used in computer graphics for applications such as parameterization. However, conformal maps are usually unavailable between multiply-connected domains or when extra ...
Settling Debts Efficiently: Zero-Sum Set Packing
(2017-07-14)
A common situation that arises in real life is the need to use peer-to-peer payment methods such as Venmo or Paypal to solve debts among a group of friends. Rather than sending each other money after every incurred expense, ...
High-SNR Capacity of AWGN Channels With Generic Alphabet Constraints
(2017-01-26)
We present a generalized notion of entropy taken with respect to a measure in a coordinate-independent manner and prove several novel entropy convergence theorems. A particular focus is entropy of random variables on smooth ...
The p-curvature conjecture and monodromy about simple closed loops
(2017-04-27)
The Grothendieck-Katz p-curvature curvature conjecture is an analogue of the Hasse Principle for differential equations. It states that a set of arithmetic differential equations on a variety has finite monodromy if its ...
Symmetric Powers and the Equivariant Dual Steenrod Algebra
(2017-05-09)
The structure of the Steenrod algebra of stable mod p cohomology operations and its dual A_* was worked out completely by Milnor - for every prime p, A_* is a graded-commutative Hopf algebra. However, much of this structure ...
Mod-P Isogeny Classes on Shimura Varieties With Parahoric Level Structure
(2017-05-11)
We study the special fiber of the integral models for Shimura varieties of Hodge type with parahoric level structure constructed by Kisin and Pappas in \cite{KP}. We show that when the group is residually split, the points ...