Calabi-Yau geometry and string theory/F-theory

点击翻译按钮获取中文摘要

String theory incorporates all the amazing breakthroughs in fundamental physics from the 20th century, from Einstein's general theory of relativity, which describes the history and fate of our entire universe, to quantum mechanics, which explains the motion and interactions of sub-atomic particles. Correctly obtaining these broad features is not enough though; what physicists really want to know is what will happen at the next generation of particle colliders, most notably the Large Hadron Collider (LHC) at CERN. F-theory is the name given to a certain class of solutions of string theory, and has recently been shown to be capable of describing important features of particle physics. The challenge now is to find solutions to F-theory which can really describe our universe, gravity and all. To do this we are required to construct special 8-dimensional spaces called Calabi-Yau fourfolds . These are incredibly complicated but beautiful geometrical spaces which are also of considerable interest to mathematicians.The primary objective of this research is to construct solutions of F-theory on compact Calabi-Yau fourfolds, and use these to explain and make predictions about the physics we will soon observe at the LHC. It is also hoped that we will gain further insight into the mysterious and beautiful geometry of Calabi-Yau spaces.