When does an analytic self-map of the open unit disc have a fixed point?
Presenter Type
UNO Undergraduate Student
Major/Field of Study
Mathematics
Other
Mathematics & Mechanical Engineering
Advisor Information
Valentin Matache
Location
MBSC302 - U
Presentation Type
Oral Presentation
Start Date
24-3-2023 10:30 AM
End Date
24-3-2023 11:45 AM
Abstract
In mathematics, analytic functions are real or complex number-valued functions that may be expressed as an infinite sum of polynomials, called a power series. Given that analytic functions are expressible in such rudimentary terms, they are a fundamental object of study in pure mathematics, particularly in the field of geometric function theory, and applied mathematics, such as in the representation of solutions to partial differential equations. To study analytic functions in the abstract, rather than dealing with a single, particular analytic function, one deals with a space of analytic functions – an analytic function space. An example of an analytic function space is that of the space of analytic maps from the open unit disk in the complex plane into itself. In this project, we investigate when these analytic self-maps have a fixed point.
Scheduling
10:45 a.m.-Noon
When does an analytic self-map of the open unit disc have a fixed point?
MBSC302 - U
In mathematics, analytic functions are real or complex number-valued functions that may be expressed as an infinite sum of polynomials, called a power series. Given that analytic functions are expressible in such rudimentary terms, they are a fundamental object of study in pure mathematics, particularly in the field of geometric function theory, and applied mathematics, such as in the representation of solutions to partial differential equations. To study analytic functions in the abstract, rather than dealing with a single, particular analytic function, one deals with a space of analytic functions – an analytic function space. An example of an analytic function space is that of the space of analytic maps from the open unit disk in the complex plane into itself. In this project, we investigate when these analytic self-maps have a fixed point.