## 2023 Student Research and Creative Activity Fair

#### Presentation Title

When does an analytic self-map of the open unit disc have a fixed point?

Mathematics

#### Other

Mathematics & Mechanical Engineering

Valentin Matache

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

COinS

Mar 24th, 10:30 AM Mar 24th, 11:45 AM

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.