Megan Fairchild

Intro

Welcome to my personal webpage and thank you for visiting!

I just started my 5th and final year of the doctoral program in mathematics at LSU being co-advised by Oliver Dasbach and Shea Vela-Vick. I plan to graduate in May 2025. My career goal is to stay in academia, hopefully continuing research and teaching mathematics at the university level.

Education:
MS in Mathematics, May 2022, Louisiana State University, Baton Rouge, LA
MS in Mathematics, December 2018, Texas State University, San Marcos, TX
BS in Mathematics, May 2016, Texas State University, San Marcos, TX
Minor in Computer Science

Research

Publications and Preprints

• The Non-Orientable 4-Genus of Non-Alternating 11 Crossing Knots
  Set to appear in the Journal of Knot Theory and its Ramifications.
  arXiv link
• Non-Orientable Surfaces in Knot Traces PDF available upon request
• Whitehead Doubles and Non-Orientable Surfaces arXiv link
• Non-Orientable 4-Genus of Torus Knots arXiv link

Masters Thesis

Using Knot Theory to Model and Analyze DNA Replication and Recombination Link

Mentored Undergraduate Research

Listed on the service tab, or click here

Invited Talks

• Joint Mathematics Meetings at Seattle, WA: Non-Orientable Surfaces in Knot Traces
• Math Colloquium (University of Nevada Reno): Non-Orientable 4-genus of Knots
• Texas State University Topology Seminar: Non-Orientable Surfaces Bounded by Knots and the Knot Trace
• AMS Sectional at University of Kansas: Talk Title: TBD
• AMS Sectional University of Albany: Non-Orientable Surfaces Bounded by Knots and the Knot Trace
• Topology Students Workshop at Vanderbilt: Non-Orientable Surfaces in Knot Traces
• AMS Sectional FSU: Non-Orientable 4-genus of Knots
• Geometry and Topology Seminar (LSU): Non-Orientable 4 Genus of 11 Crossing Non-Alternating Knots

Slides from previous talks

20 min slide talk: Non-Orientable Surfaces Bounded by Knots and the Knot Trace
Lightning Talk: Non-Orientable Surfaces in Knot Traces
20 min slide talk: Non-Orientable 4 Genus of Knots

Conferences Attended

• upcoming: Nebraska Conference for Undergraduate Women in Mathematics 2025
• upcoming: Joint Mathematics Meetings at Seattle, WA 2025
  Talk Title: Non-Orientable Surfaces in Knot Traces
• upcoming: AMS Sectional at University of Kansas 2025
  Talk Title: TBD
• AMS Sectional University at Albany 2024
  Talk Title: Non-Orientable Surfaces Bounded by Knots and the Knot Trace
• ICERM Braids Reunion Workshop 2024 - Brown University
• Topology Students Workshop 2024 - Vanderbilt University
  Talk Title: Non-Orientable 4-Genus of Knots
• Topology Summer School & Conference 2024 - University of Georgia
  Lightning Talk: Non-Orientable Surfaces in Knot Traces
• AMS Sectional 2024 - Florida State University
  Talk Title: Non-Orientable 4-Genus of Knots
• Texas Geometry and Topology 2023 - Rice University
• SEC Topology 2023 - University of Alabama
• Topology Conference 2023 - University of Georgia

Course Projects

Brunnian Braids and Their Relation to Homotopy Groups of Spheres. Spring 2022.
The Betti Numbers of the Data Set of the Work of Bob Ross. Fall 2018
Analyzing Betti Numbers of Range Image Patches. Fall 2018.
Analyzing Betti Numbers of the Zodiac Constellations. Fall 2018.
The History of the Alexander Horned Sphere. Spring 2017.
The History of i , the Imaginary Number. Spring 2017.
The Eccentricity of Directed Graphs. Fall 2012.

Teaching

Lecturer - Texas State University

Co-Coordinator of Math 1316 (Contemporary Mathematics) Teaching Forum
Instructor - Contemporary Mathematics
Instructor - Co-Enroll Intermediate and College Algebra
Instructor - Co-Enroll Elementary Algebra and Contemporary Mathematics

Graduate Instructional Assistant - Louisiana State University

Instructor - Calculus I
Lead TA - Business Calculus
TA - Business Calculus

Graduate Instructional Assistant - Texas State University

Instructor - Intermediate Algebra
TA - Calculus II
TA - Pre-Calculus

Undergraduate Instructional Assistant - Texas State University

TA - Pre-Calculus

Tutoring

I have been tutoring mathematics since I was in high school, where I was also a classroom assistant. I have tutored math at the high school level, private tutored everything from graduate topology to college algebra, and worked in the mathematics tutoring lab at Texas State.
Helping others learn and understand mathematics has always been a passion of mine.

What do you want to be when you grow up?

A fun fact, I am chasing my childhood dream. I have wanted to be a math teacher since I was in the third grade! The dream has grown and evolved, but I have always loved mathematics.

Service

Ambassador for LSU Math

Nominated to represent LSU Math and be a mentor for undergraduate women in mathematics at the 27th annual Nebraska Conference for Undergraduate Women in Mathematics

Mentor for Undergraduate Research

Topological Data Analysis - Fall 2024
Homological Algebra - Fall 2024
Intro to 3-Manifolds and Heegaard Diagrams - Fall 2024
Intro to Heegaard Floer Homology - Summer 2024
Non-Orientable 4 Genus of Torus Knots: arXiv link - Spring 2024
Seifert Surfaces and Knot Signatures - Spring 2024
Braids and Configuration Space - Fall 2023
(1, 1)-Knots and Heegaard Floer Homology - Spring 2023 and Fall 2022.

Curriculum Development

Co-Coordinator of Contemporary Mathematics, Texas State University
Re-structured syllabus, created course material currently being used.

Mentor for young graduate students

• I developed a website about the general exam study materials and preparation guide to help younger graduate students. The goal was for previous graduate students to share their experience and offer guidance in their specific field on what to study, foundational knowledge, and commonly asked questions. We also have an advice colomn where older graduate students submitted advice (generic, motivational, or subject specific) to the younger generation. Link: Preparing for the General Exam
• Mental Health Ally: panelist for 'Surviving Graduate School.' On the list of People to talk to about mental health issues, course issues, or really any issue in general.
• Topology Help: assist first year graduate students with studying for their qualifying exams, study help to all graduate students in topology, Rolfsen reviews held in my office, active recruiter for the VIR course.

Student Colloquium Committee

Officer: 2022-current
Website management for LSU Student Colloquium Committee website, calendar management, flyer creation/design

Organizer

Informal Topology and Geometry Seminar (LSU)
Graduate Students in 4 Dimensions and Less Seminar (LSU)

GEAUX Math LSU (new graduate student orientation)

T-shirt designer (see below for some of my designs)
Topology talk: "Brunnian Braids and Their Relation to Homotopy Groups of Spheres."
Qualifying Exam Preparation (Topology): introductory talk

Notes I have made to help other graduate students

Intro to HFK Homework
Introduction to Knot Concordance Notes
Introduction to Topological Spaces and Homology

University Participation

Department of Mathematics T-Shirt Design Winner (2018)

Three Minute Thesis 3MT
People's Choice Award (2018)

Math in the Picture - Texas State University: (winner 2017, 2018)
2017: Making Mandalas with Sine and Cosine Functions
2018: The Ammonite - Golden Ratio in Nature

Extra

Please enjoy the photo of my dog, Lucy.

I am an intermediate Spanish speaker. My goal is to one day be fluent!

I am originally from Austin, TX. I grew up on Lake Travis and love swimming and water sports.

Rock climbing

The main background photo is the Austrian Alps from when I visited Innsbruck in January 2024
Both rock climbing photos of me were taken in Little Cottonwood Canyon in Utah
I learned to climb at the greenbelt in Austin. I have climbed at Boulder Canyon in Boulder, CO, Clear Creek Canyon in Golden, CO, the Uintas mountain range in Utah, both Big and Little Cottonwood canyons in Salt Lake City, the greenbelt in Austin, and bouldered in bull creek and McKinney Falls (both in Austin).
In Baton Rouge, I suppose I could climb trees? Though I mainly pull on the plastic rocks at my local rock gym.

Elements

i = 0;

while (!deck.isInOrder()) {
    print 'Iteration ' + i;
    deck.shuffle();
    i++;
}

print 'It took ' + i + ' iterations to sort the deck.';