Twisted K-theory has many geometric applications. For example, Freed, Hopkins, and Teleman prove that the twisted K-theory of a compact Lie
group is closely related to representations of its loop group, and, in physics, twisted K-theory is supposed to measure certain field
strengths in string theory. My student Mehdi Khorami has given a new way to compute twisted K-theory and used it to explain the relationship to
twisted Spin^c bordism. I will explain his work in this talk.