 CARMA COLLOQUIUM
 Speaker: Prof. Florian Breuer, School of Mathematical and Physical Sciences, The University of Newcastle
 Title: The Parallel Worlds of Number Theory
 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 4:00 pm, Thu, 10^{th} May 2018
 Abstract:
There is an intriguing analogy between number fields and function fields. If we view classical Number Theory as the study of the ring of integers and its extensions, then function field arithmetic is the study of the ring of polynomials over a finite field and its extensions. According to this analogy, most constructions and phenomena in classical Number Theory, ranging from the elementary theorems of Euler, Fermat and Wilson, to the Riemann Hypothesis, Elliptic curves, class field theory and modular forms all have their function field analogues. I will give a panoramic tour of some of these constructions and highlight their similarities and differences to their classical counterparts.
This lecture should be accessible to advanced undergraduate students.
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