Inspiral Tests of Strong-field Gravity and Ringdown Tests of Quantum Black Holes

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The binary black hole merger events recently discovered by the LIGO and Virgo Collaboration offer us excellent testbeds for exploring extreme (strong and dynamical-field) gravity that was previously inaccessible. In this talk, I will first explain the current status of probing fundamental pillars of General Relativity using the inspiral part of the gravitational waveform. I will next describe how well one can constrain one type of quantum black holes, collapsed polymers, with the GW150914 ringdown. I will conclude with a list of important open problems.