't Hooft Defects, Monopole Bubbling, and SQM Localization
't Hooft defect are a good probe of non-perturbative phenomena in quantum field theories. In 4D N=2 supersymmetric gauge theories, we can exactly compute their expectation value using tools such as localization, spectral networks, and AGT techniques. From this we can learn about phenomena such as wall crossing of framed BPS states and monopole bubbling. However, the expectation value of 't Hooft defects computed using localization does not always match the result computed by other techniques. In this talk we will examine this flaw and discuss its physical interpretation and resolution.