Megan Fairchild

Intro

Welcome to my personal webpage and thank you for visiting!

I just finished my fourth 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

Research

Available on the arXiv:
"The Non-Orientable 4-Genus of Non-Alternating 11 Crossing Knots" arXiv link
"Non-Orientable 4-Genus of Torus Knots" arXiv link

Masters Thesis:
"Using Knot Theory to Model and Analyze DNA Replication and Recombination"

Mentored Undergraduate Work:
"Non-Orientable 4-Genus of Torus Knots" (Spring 2024 - arXiv link above)
"Braids and Configuration Space" Fall 2023
"(1, 1)-Knots and Heegaard Floer Homology" Spring 2023

Invited Talks:
Math Colloquium (University of Nevada Reno): "Non-Orientable 4-genus of Knots"
AMS Sectional FSU: "Non-Orientable 4-genus of Knots"
Formal Topology Seminar (LSU): "Non-Orientable 4-genus of Knots"

Slides from previous talks:
Lightning Talk: Non-Orientable Surfaces in Knot Traces
20 min slide talk: Non-Orientable 4 Genus of Knots

Conferences Attended:
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 2024 - 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
Lead TA - Business Calculus
TA - Business Calculus

Graduate Instructional Assistant - Texas State University:
TA - Calculus II
TA - Pre-Calculus
Instructor - Intermediate Algebra

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 from the high school level, private tutored all undergraduate mathematics courses from 2012-current, and worked in the mathematics tutoring lab at Texas State.
Helping others learn and understand mathematics has always been a passion of mine. A fun fact, I have wanted to be a math teacher since I was in the third grade!

Service

Student Colloquium Committee (Officer) 2022-current

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

Directed Reading Program - LSU: Calculating a Knot Signature from its Seifert Surface

Notes I have made to help other graduate students:
Intro to HFK Homework
Introduction to Knot Concordance Notes

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 also climbed in Boulder, CO (Boulder Canyon and Clear Creek Canyon)

Elements

i = 0;

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

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