Several Variables Pure Mathematics Not Elsewhere Classified Numerical And Computational Mathematics Not Elsewhere Classified Earth Sciences Not Elsewhere Classified Research interests q series identities Basic hypergeometric seriesTiling patterns arising from theory of quasicrystals, Dirichlet series analogues of q series, Dirichlet series and Riemann zeta functions, Theory of Partitions, Arithmetical functions and divisor functions, Visible Point Vector vpv identities includes lattice points in regionsOrdinary hypergeometric series, Number Theory in general including Diophantine equations, Voting Methodologies, Combinatorial objects in Enumerative Word problems, Schur functions, and the Google search algorithms. Researcher's projects I have two research monographs and quite a few number theory research papers as work in progress.

Structural change in times of increasing openness: In the process of estimating the dynamic effects of openness shocks on 26 EU countries, we develop a taxonomy of European economies that consists of core, periphery, financialized and Eastern European catch-up economies.

As these four country groups have responded in a distinct way to the openness shocks imposed by European integration, we argue that the latter should be seen as an evolutionary process that has given rise to different path-dependent developmental trajectories. These trajectories relate to the sectoral development of European economies and the evolution of their technological capabilities.

For a German blog post focused on the policy implications of our study see here. Pushing for convergence within Europe requires the implementation of several intertwined policy programs that we discuss further in this paper. Trade Networks and Economic Development In two closely related studies I investigate the structure of the World and European trade network Computational number theory research paper graph theoretic concepts and algorithms.

I characterize the evolution of the structure of these networks and ask whether the location of countries therein is not only a consequence, but also a determinant for their development trajectories.

I pay particular attention to the technological capabilities of the countries and the complexity of the products they are able to export. I find that poorer countries import the majority of complex products from richer countries, and export in exchange simple products to the more advanced economies.

This seems to be an important explanation for the lacking convergence among many countries in terms of prosperity and technological sophistication.

The Kaldor paradox revisited: We ask how price competitiveness and non-price competitiveness indicators are related to the evolution of export market shares. We also study the question of whether the determinants for export performance differ for more and less complex products.

Finally, we employ a quantile regression approach to identify differences between more and less developed countries in terms of the determinants for their export success. Economic complexity and income inequality Joint work with Svenja Flechtner The Economic Complexity Index has been found a good predictor for economic growth.

Yet the link between Economic Complexity and income inequality is less well understood.

We first review a number of potential mechanisms that could potentially link complexity and inequality. Then we use a dynamic panel approach to identify causal linkages between the two, which seem to be much more intricate than considered so far.

Measuring Economic Openness Joint work with Philipp Heimberger, Jakob Kapeller and Florian Springholz The impact of economic and financial openess has been of major interest in economics for quite a while.

Yet how openess should be measures is still an open issue. Here we surve existing measures for openess and study them using various statiscial measures. Thereby we identify various groups of openess measures that are similar to each other, but differ remarably to other types of openess measures.

This has important implications for the study of economic openess. We illustrate the practical importance of our findings by showing the fragility of several central results with respect to the choice of different openess measures.

Inequality and Social Mobility in Political Change: Exploring the dynamics of the Kuznets Curve [ Working paper ] According to the Kuznets hypothesis, inequality dynamics within countries follow a U-shaped trajectory: Acemoglu and Robinson offer an analytical infinit-horizon non-overlapping generations model to study the pattern from a political economic perspective.

We transform the analytical model into an agent-based version to provide a dynamic account of the Kuznets hypotheses and to study the importance of institutions governing social mobility for the shape and timing of the Kuznets curve.

Aspirations and social protest Joint work with Svenja Flechtner Together with Svenja Flechtner I build an ABM that models the decision of agents to participate in social protest or not.

We question the alleged link between social activism and social inequality. Research area 3 Philosophy of Economics: An epistemological framework for the validation and verification of computational models Published in: This is necessary if models are to be related to each other in a contructive manner: Getting the Best of Both Worlds?

Computational Economicsonline first The paper deals with the distinction between equation-based and agent-based models, and ways to fruitfully combine them. We apply to our ideas to a model by Acemoglu and Robinson on the Kuznets Curve. Journal of Contextual EconomicsVol.Massachusetts Institute of Technology Department of Mathematics.

For website help or updates, please email. The Development of Group Theory - MacTutor Math History Archives Linked essay describing the rise and progress of group theory from the 18th through the 19th centuries, with references (books/articles).

Integers: Electronic Journal of Combinatorial Number Theory International Journal of Algebra and Computation Journal of Inequalities in Pure and Applied Mathematics (Also check RGMIA research . Research Papers My research interests include: A Computational Introduction to Number Theory and Algebra (Version 2) A free ebook introducing basic concepts from computational number theory and algebra, including all the necessary mathematical background.

Progress in Computational Complexity Theory We brieď¬‚y survey a number of important recent achievements in Theoretical Computer Sci-ence (TCS), especially Computational Complexity Theory.

We will discuss the PCP Theorem, has been an open problem since the original paper on NP-completeness by Karp [33]. The purpose of this guide is to provide advice on how to develop and organize a research paper in the social sciences.

involving a greater number of subjects, and enhancing the generalization of the results; and information about theories of research [e.g., grounded theory].

The database covers both qualitative and quantitative research.

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Department of Mathematics and Statistics at UNC Greensboro