Hui June Zhu (UCB)

Title: Newton polygons of L functions of exponential sums (Limiting behavior)

I will discuss a conjecture of Daqing Wan, proposed last year in this same seminar: Let d>2. Let A^d be the space of degree-d monic polynomials in one variable over the rationals Q, there exists a Zariski dense subset U in A^d such that for every f(x) in U the limit of Newton polygon of the exponential sum of f(x) mod p is equal to the Hodge polygon of the exponential sum of f(x) as p approaches infinity. I will explain this conjecture by giving explicit examples before sketching my proof of the conjecture.