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good afternoon itamp;#39;s my honor to share this afternoon session in number theory our first speaker is Fay Shang with the professor at MIT he received his PhD from Columbia in 2009 under the direction of Shifu Shang and after that he spent a year at Harvard as a postdoc before returning to Columbia and he would see the Ramanujan Prize in 2010 and more recently the new horizons and mathematics breakthrough prize and heamp;#39;s known for his work in the but Australia formula and the cross without contact affinity groups and today heamp;#39;ll talk about a relative trace formula approach to period cycles and heamp;#39;ll functions thanks for the introduction and itamp;#39;s a pleasure to speak here thanks to the organizers so this talk is going to be a report some recent progress between periods integral algebra cycles and their connection to L functions especially in the approach of relative trace formula so I will start with two motivating examples and the first example I want
