New Trends in Analytic Number Theory

nt.number-theory
Start Date
2018-08-13 
End Date
2018-08-17 
Institution
University of Exeter 
City
Exeter 
Country
UK 
Meeting Type
summer school 
Homepage
https://www.lms.ac.uk/events/lms-cmi-research-schools 
Contact Name
 

Description

Analytic number theory is the branch of mathematics in which ideas and methods of real and complex analysis are brought to bear on problems about integer numbers. In particular, analytic techniques have led to major advances in number theory and helped to solve several important and difficult questions about integers. One of the crowning achievements of analytic number theory was the proof of the prime number theorem by using properties of the Riemann zeta function. In the last few years, analytic number theory has flourished and we have seen an upsurge of activity worldwide related to analytic number theory, prime number theory, and solutions to equations.

In this research school young researchers will learn key ideas and techniques of the field and about the most recent results and future directions of the field. It will benefit researchers having a background in number theory as well as those from parallel areas such as random matrix theory, Diophantine geometry and function field arithmetic. This research school will focus on three related topics and developments in analytic number theory:

  • (i) classical analytic number theory, prime number theory and its recent developments
  • (ii) Diophantine geometry and Hardy-Littlewood circle method
  • (iii) analytic number theory in the function field context

These are active research areas where techniques from analysis (real, complex and Fourier analysis) plays an important role in trying to solve questions about integer numbers. Six experts in analytic number theory and its applications will conduct three mini-courses. To complement the mini-courses, distinguished speakers with substantial reputations in prime number theory, elliptic curves, additive combinatorics and random matrix theory will give an overview and research lectures on recent advances in the field.

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