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## Line Arrangements in P2(C) and Their Finite Covers

*Paula Tretkoff*

### in Complex Ball Quotients and Line Arrangements in the Projective Plane (MN-51)

- Published in print:
- 2016
- Published Online:
- October 2017
- ISBN:
- 9780691144771
- eISBN:
- 9781400881253
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691144771.003.0006
- Subject:
- Mathematics, Geometry / Topology

This chapter discusses the free 2-ball quotients arising as finite covers of the projective plane branched along line arrangements. It first considers a surface X obtained by blowing up the singular ... More

## Cryptographic Primitives

*Andreas Bolfing*

### in Cryptographic Primitives in Blockchain Technology: A mathematical introduction

- Published in print:
- 2020
- Published Online:
- October 2020
- ISBN:
- 9780198862840
- eISBN:
- 9780191895463
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198862840.003.0003
- Subject:
- Mathematics, Computational Mathematics / Optimization, Logic / Computer Science / Mathematical Philosophy

This chapter provides a very detailed introduction to cryptography. It first explains the cryptographic basics and introduces the concept of public-key encryption which is based on one-way and ... More

## Torsion of Elliptic Curves and Unlikely Intersections

*Fedor Bogomolov, Hang Fu, and Yuri Tschinkel*

### in Geometry and Physics: Volume I: A Festschrift in honour of Nigel Hitchin

- Published in print:
- 2018
- Published Online:
- December 2018
- ISBN:
- 9780198802013
- eISBN:
- 9780191840500
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198802013.003.0002
- Subject:
- Mathematics, Geometry / Topology

This chapter studies effective versions of unlikely intersections of images of torsion points of elliptic curves on the projective line.

## Public-Key Encryption

*Keith M. Martin*

### in Everyday Cryptography: Fundamental Principles and Applications

- Published in print:
- 2017
- Published Online:
- July 2017
- ISBN:
- 9780198788003
- eISBN:
- 9780191829956
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198788003.003.0005
- Subject:
- Mathematics, Computational Mathematics / Optimization, Logic / Computer Science / Mathematical Philosophy

In this chapter, we introduce public-key encryption. We first consider the motivation behind the concept of public-key cryptography and introduce the hard problems on which popular public-key ... More

## The simple pendulum

*S. G. Rajeev*

### in Advanced Mechanics: From Euler's Determinism to Arnold's Chaos

- Published in print:
- 2013
- Published Online:
- December 2013
- ISBN:
- 9780199670857
- eISBN:
- 9780191775154
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199670857.003.0003
- Subject:
- Physics, Atomic, Laser, and Optical Physics

The simple pendulum is a simple mechanical system with a surprising depth. It can be solved in terms of Jacobi elliptic functions. A simple physical argument shows that these functions are doubly ... More

## Period Domains and Period Mappings

*James Carlson*

*Eduardo Cattani, Fouad El Zein, Phillip A. Griffiths, and Lê Dũng Tráng (eds)*

### in Hodge Theory (MN-49)

- Published in print:
- 2014
- Published Online:
- October 2017
- ISBN:
- 9780691161341
- eISBN:
- 9781400851478
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691161341.003.0004
- Subject:
- Mathematics, Geometry / Topology

This chapter seeks to develop a working understanding of the notions of period domain and period mapping, as well as familiarity with basic examples thereof. It first reviews the notion of a ... More

## How to Explain Number Theory at a Dinner Party

*Michael Harris*

### in Mathematics without Apologies: Portrait of a Problematic Vocation

- Published in print:
- 2017
- Published Online:
- May 2018
- ISBN:
- 9780691175836
- eISBN:
- 9781400885527
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691175836.003.0015
- Subject:
- Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter continues the discussion began in Chapter α. It presents the fourth and final part of author's response to the question, “What is it you do in number theory, anyway?” Here he deals with ... More

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