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Regular version of the site
2018/2019

Research Seminar "Arithmetic Dynamics"

Type: Optional course (faculty)
When: 2 module
Instructors: Vladlen Timorin
Language: English

Course Syllabus

Abstract

These lectures are aimed at presenting some aspects of the dynamics of polynomials in one variable with coefficients in a number field. We shall discuss two deep conjectures that have been proved to be very influential in the development of this field: the uniform boundedness conjecture by Silverman, and the dynamical Andre–Oort conjecture Baker and DeMarco. It will be the opportunity to present various tools coming from arithmetic geometry or from complex dynamics that are used to approach these challenging problems
Learning Objectives

Learning Objectives

  • The seminar is intended to introduce the subject area to the students, and to offer them an opportunity to prepare and give a talk
Expected Learning Outcomes

Expected Learning Outcomes

  • improvement of presentation skills and preparation for participation in research projects in the subject area
Course Contents

Course Contents

  • The uniform boundedness conjecture
  • Fatou/Julia theory for complex polynomials
  • Canonical heights for complex polynomials
  • Non-archimedean polynomial dynamics
  • The dynamical Andre–Oort conjecture
  • Equidistribution of points of small height
Assessment Elements

Assessment Elements

  • non-blocking Tasks
  • non-blocking Exam
Interim Assessment

Interim Assessment

  • Interim assessment (2 module)
    0.7 * Exam + 0.3 * Tasks
Bibliography

Bibliography

Recommended Core Bibliography

  • Charles Favre, & Mattias Jonsson. (2002). The valuative tree. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsbas&AN=edsbas.BBA459D6

Recommended Additional Bibliography

  • Favre, C., Kiwi, J., & Trucco, E. (2011). A non-archimedean Montel’s theorem. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsbas&AN=edsbas.6B1FBFAB