I am fascinated by problems that require a blend of computational topology, geometry, and number theory. I have also been studying fractals which interesting geometrical objects that have been used in diverse applications such as cryptography, seismology, network optimization, and even weather forecasting. However, despite the wide range of applications and interest in fractals, the general theory of these objects is still in its infancy. My work on this research project has developed some theorems and conjectures in the field of combinatorics and has begun to shed some light on some areas of fractals, one-cell automata and dynamical systems … This need for optimization has become increasingly more important in today’s society from the perspective of both resource management as well as leveraging new opportunities. In terms of resource allocation, combinatoric optimization is being used to improve the efficiency of scheduling transportation (the traveling salesperson problem) to allocating scarce resources (such as militaryequipment or food distribution), through improving internet network traffic throughput, latency, and infrastructure costs. But the field has broader impact than just efficient resource allocation as it can more help in more efficiently processing large amounts of data. Increasingly, we are producing more information that we can efficiently sort through and understand, whether it is the 100k plus tweets per minute of the Presidential debates, the information gathered about global warming, or the data mining of consumer information.

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• Mathematics
• Optimization