Decomposition of elliptic multiple zeta values and iterated Eisenstein integrals

We describe a decomposition algorithm for elliptic multiple zeta values, which amounts to the construction of an injective map $\psi$ from the algebra of elliptic multiple zeta values to a space of iterated Eisenstein integrals. We give many examples of this decomposition, and conclude with a short discussion about the image of $\psi$. It turns out that the failure of surjectivity of $\psi$ is in some sense governed by period polynomials of modular forms.Comment: v2, minor change

Solvability and limit bicharacteristics

We shall study the solvability of pseudodifferential operators which are not of principal type. The operator will have real principal symbol and we shall consider the limits of bicharacteristics at the set where the principal symbol vanishes of at least second order. The convergence shall be as smooth curves, then the limit bicharacteristic is a smooth curve. We shall also need uniform bounds on the curvature of the characteristics at the bicharacteristics, but only along the tangents of a given Lagrangean manifold. This gives uniform bounds on the linearization of the normalized Hamilton flow on the tangent space of this manifold at the bicharacteristics. If the quotient of the imaginary part of the subprincipal symbol with the norm of the Hamilton vector field switches sign from $-$ to $+$ on the bicharacteristics and becomes unbounded as they converge to the limit, then the operator is not solvable at the limit bicharacteristic.Comment: Accepted for publication by Journal of Pseudo-Differential Operators and Application

Has Government Tax Policy in Greece Led to a Large Shadow Economy?

This capstone investigates the impact that tax policy has on the shadow economy in Greece. Greece has one of the largest shadow economies in the world and the largest in the European Union, with tax evasion being one of the main drivers. While previous research has provided measures of the shadow economy, none matches the shadow economy estimations with policies, laws, and agencies enacted by the government, specifically over the period in time of 1990-2012. This study contributes to the literature by connecting the policies implemented by the government with the size of the shadow economy in Greece, along with providing a new model based on prior versions of the currency-demand model. The study concludes by considering, a piece of cultural analysis to help explain why the people of Greece are so prone to evade taxes and enter the shadow economy. Research of Dr. Geert Hofstede’s work on cultural dimensions shows that Greeks have high levels of power-distance, collectivism, and uncertainty avoidance, all which can be used to explain why they are susceptible to keep evading taxes. Using an adaption of the currency demand model, the regression results show that the shadow economy increased with 1) an increase in the amount of people that are self-employed 2) decreases to the middle income tax rate 3) and with increases in the lowest income tax rate. These results suggest that the tax system needs a combination of stronger oversight and penalties because of the extremely high levels of uncertainty avoidance that Greeks possess. The results also show that revenue can be captured by raising the middle income tax rate, and that raising the tax rate on the lowest bracket will tend to force those people into the shadow economy. This study provides useful conclusions on the Greek shadow economy from both an economic perspective and a sociological perspectiv

Visualising Sha[2] in Abelian Surfaces

Given an elliptic curve E1 over a number field and an element s in its 2-Selmer group, we give two different ways to construct infinitely many Abelian surfaces A such that the homogeneous space representing s occurs as a fibre of A over another elliptic curve E2. We show that by comparing the 2-Selmer groups of E1, E2 and A, we can obtain information about Sha(E1/K)[2] and we give examples where we use this to obtain a sharp bound on the Mordell-Weil rank of an elliptic curve. As a tool, we give a precise description of the m-Selmer group of an Abelian surface A that is m-isogenous to a product of elliptic curves E1 x E2. One of the constructions can be applied iteratively to obtain information about Sha(E1/K)[2^n]. We give an example where we use this iterated application to exhibit an element of order 4 in Sha(E1/Q).Comment: 17 page

Unlocking Europe’s Piggy Bank Corporate Saving, Labor Power and Policies for Investment. Bertelsmann Stiftung Policy Paper 13 December 2019

European companies invest too little. Instead, firms increasingly retain profits and build up large savings which contributes to low growth, rising inequality and financial instability. Boosting private investment, therefore, has become main priority for the new Commission. Based on new empirical evidence this policy paper proposes a novel strategy to achieve this goal: strengthening the bargaining position of labor