Tyler Kelly

Mirror quintics and Shioda maps

Abstract: In this talk, we will introduce the idea of Mirror symmetry, and explicitly compute a Mirror quintic utilizing an automorphism class of a quintic. We will then work to show that we can relate mirror quintics through using an old trick newly called the Shioda map. We will look at these maps to find that we can utilize them towards our advantage in looking at properties induced by them on Calabi-Yau threefolds. This gives rise to the opportunity to look at the Picard-Fuchs equations of each Calabi-Yau threefold, and we can start to relate these equations using a correspondence. There is an interesting result that lets us not have to worry about computing Picard-Fuchs equations explicitly for all cases anymore.