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Caltech/UCLA Joint Analysis Seminar

Friday, February 9, 2018
4:30pm to 5:30pm
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Downs 103
Factorising X^n
Jonathan Hickman, Department of Mathematics, University of Chicago,
How many ways can the polynomial X^n be factorised as a product of linear factors? Well, of course, the answer depends on the ring... In this talk I will describe joint work with Jim Wright investigating certain exponential sum estimates over rings of integers modulo N. This theory serves as a discrete analogue of the (euclidean) Fourier restriction problem, a central question in contemporary harmonic analysis. In particular, as part of this study, the question of counting the number of factorisations of polynomials over such rings naturally arises. I will describe how these number-theoretic considerations can themselves be approached via methods from harmonic analysis.
For more information, please contact Mathematics Department by phone at 626-395-4335 or by email at [email protected].