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This experiment will make the most sensitive measurement ever of the shape of the electron. They are looking for a deviation from spherical that would indicate a difference in the laws of physics that govern matter and antimatter. This would show that the current theory of particle physics, the Standard Model is incomplete. Any deviation from roundness will be tiny, so, to measure the shape with sufficient accuracy they will have to build a machine that can look at the electrons in molecules with unprecedented accuracy.  

e-EDM is an experiment for the measurement of the electron electric dipole moment.   The electron EDM is a search for new physics beyond the Standard Model. The Standard Model predicts almost vanishingly small electron edms whereas many reasonable extensions predict measurably large values. This means any non-zero measurement of the electron edm would be clear evidence for physics beyond the Standard Model.  This very low-energy electron edm measurement probes physics at energy scales much higher than that reached at even the next generation of particle accelerator (of course, particle accelerators can probe a much wider range of high-energy physics). Low-energy particle edm measurements can be viewed as complementary to high-energy accelerator experiments.