I only watched one: Bo'az Klartag and Oded Regev, Quantum one-way communication can be exponentially stronger than classical communication. It presents a classical lower bound for a promise problem from linear algebra which the authors call Vector in Subspace Problem. Their lower bound is based on a very interesting geometric argument on the n-dimensional sphere. This result implies an exponential gap between one-way quantum and classical communication complexity.
Others that I would like to watch (which are related to my own interests) are:
- Tsuyoshi Ito, Hirotada Kobayashi and John Watrous, Quantum interactive proofs with weak error bounds.
- Loïck Magnin, Martin Roetteler and Jérémie Roland, On the additive and multiplicative adversary methods.
- Jianxin Chen, Xie Chen, Runyao Duan, Zhengfeng Ji, Zhaohui Wei and Bei Zeng, On the solution space of quantum 2-SAT problems.
- Andrew Childs and Robin Kothari, Quantum query complexity of minor-closed graph properties.