Abstract
The study of the space of arcs on singular varieties dates back as far as pionner work of J. Nash who promoted the idea that singularities of algebraic varieties can be understood via the topology of its arc space. We also believe that many fundamental objects in the theory of representations of p-adic reductive groups as orbital integrals and characters should also be tied to singularities of certain arc spaces. We need a theory of perverse sheaves on arc and loop spaces, if we want to turn these believes into theorems or conjecture. A full fledged version of this theory is still under construction, and the speaker will explain some basic difficulties we encountered in this lecture.
About the speaker
Prof. Ngô Bảo Châu received his PhD in Mathematics from Paris-Sud University in 1997 and became the CNRS Fellow in Université Paris XIII afterwards. In 2004, he returned to Paris-Sud University as a Professor and moved to the Institute for Advanced Study, Princeton as a Long-term Member in 2007. In 2010, he joined The University of Chicago and is currently the Francis and Rose Yuen Distinguished Service Professor. Since 2011, he has also been the Scientific Director of the Vietnam Institute for Advanced Study in Mathematics.
Prof. Ngô has proved the Fundamental Lemma using some surprising methods. He was able to use geometric objects, called Hitchin fibrations, to solve this problem in pure mathematics. Not only did he prove this result, he provided a deeper understanding of this area of mathematics. For his proof of the Fundamental Lemma in the theory of automorphic forms, he was awarded the Fields Medal at the International Congress of Mathematicians in India in 2010.
Apart from the Fields Medal, Prof. Ngo received numerous awards, including the Oberwolfach Prize (2007); the Sophie Germain Prize by the French Academy of Sciences (2007); and the Clay Research Award by Clay Mathematics Institute (2004). He was also elected a Member of the American Academy of Arts and Sciences (2012) and a Fellow of the American Mathematics Society (2012).
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