University of New Hampshire
Mentor: Dr. Per Berglund
Del Pezzo Divisors, Calabi-Yau Manifolds and the Evolution of the Universe
We propose to study del Pezzo divisors and their realization in Calabi-Yau manifolds in order to address our fundamental description of the evolution of the universe. String theory, the leading candidate for a theory of quantum gravity, has great potential to provide insights into our fundamental understanding of nature. Developing an improved understanding of the models of the extra-dimensional space required by string theory is essential to increasing our knowledge about these phenomena. Most of these models are constructed by compactifying the ten-dimensional space of string theory on a Calabi-Yau manifold, resulting in the four-dimensional world we observe. One of the most promising avenues of finding string compactifications that fit real-world observations is by the use of Large Volume compactifications using so-called Swiss Cheese Calabi-Yau manifolds. Many Swiss Cheese Calabi-Yaus contain complex two-dimensional surfaces known as del Pezzo divisors. These hypersurfaces play a key role in string theory, but they have not been studied in a systematic fashion. Our goal is to analyze the del Pezzo divisors and their realizations in terms of Swiss Cheese Calabi-Yau manifolds systematically, to find new, interesting models of extra-dimensional space. These models will then be used to address issues in cosmology, in order to shed light on the central issues of dark matter, the accelerating expansion of the universe, and inflation.