Position
Graduate Assistant, LSU
Emailjgarc86@lsu.eduOffice
363 Lockett Hall
CVWeb · PDF
Hello! I’m a PhD student at LSU studying mathematics. My research interests include topology and combinatorics, with a particular fondness for matroids.
I like getting involved in my community. I currently serve as secretary and webmaster of LSU’s AWM chapter, and as webmaster for LSU’s RTG. I also participate in the informal geometry and topology seminar and the DTC/informal combinatorics seminar.
I manage the department’s 3D print lab. More on that soon.
Lately
Working on a paper. Playing around with the websites I manage. Probably in my home office talking to my plants and reading.
Ph.D. Mathematics, Louisiana State University Advisor: Christin BibbyFall 2025–present
B.S. Mathematics, Louisiana State UniversityFall 2022–Spring 2025
Papers and Preprints
G. Agrahari, C. Bibby, S. Boros, H. Garcia, F. Heidercheidt, Z. Wang. On some structural properties of graphs with non-negative resistance curvature. arXiv:2607.13169 (2026). arXiv:2607.13169.
M. Fairchild, H. J. Garcia, J. Murphy, H. Percle. On the non-orientable 4-genus of torus knots with braid index 5 or 6.Journal of Knot Theory and Its Ramifications35 (2026), No. 7, 2650001. https://doi.org/10.1142/S021821652650001X.
Talks
Noncontractive Function Systems 6th TX-LA Mathematics Undergraduate ConferenceSpring 2023
On The “Kelly Sequence” 6th TX-LA Mathematics Undergraduate ConferenceSpring 2023
Teaching
MATH 1431, Business Calculus — Lab Leader/TA, LSU Sections 7, 11, 19Spring 2026
MATH 1431, Business Calculus — Lab Leader/TA, LSU Sections 7, 8, 9, 11, 25, 28Fall 2025
Per lab period, a student may earn 10 points total:
+7 points for attendance.
+3 points for correct solutions to end-of-class quizzes. Partial credit given.
A student may lose points for the following:
−0.5 points for tardiness (showing up after roll).
−1 point for use of a cell phone, increasing by 1 point per infraction.
Overview
The first 30–40 minutes of class will be devoted to reviewing concepts from the main lecture and homework. I encourage students to come with questions, specific or otherwise. Students who feel comfortable with the material may open Pearson to work on homework; collaboration and notes are permitted, so long as the volume of conversation is reasonable. Use of generative AI for homework is prohibited.
I enforce a strict no-phones policy. I expect all phones to be in bags, out of sight, and on silent. The required calculator for the course is affordable; graphing calculators and Desmos are also allowed.
Office Hours
Lockett 363, Monday, Wednesday, Thursday, and Friday 07:30–08:20; Tuesday 07:30–09:20.
Office hours do not require an appointment. I also hold hours by appointment, so email me if you cannot make a posted time. I welcome everyone, but prioritize students enrolled in the sections for which the hours are designated.
Absence
I excuse absences for the following reasons:
Email me day-of if you are sick, have an emergency, or there is hazardous weather. No note necessary.
Email me in advance if you have plans or appointments during class.
Email me a sick note or proof of valid excuse under LSU PS22.
If you miss class, it is your responsibility to inform me so you can make up missed content or quizzes. I offer retakes during office hours by appointment. In the first two cases above, retakes should be completed within 2 weeks of the absence; otherwise I deduct 30%. If you need more time, reach out to discuss.
I typically take roll within the first 5 minutes of class. It is always better to be tardy than absent.
MATH 1431: Business Calculus, Fall 2025
Time & Location
All sections meet in Library 232.
§7: Monday 14:30–15:20
§8: Tuesday 08:30–09:20
§9: Tuesday 09:30–10:20
§11: Tuesday 13:30–14:20
§25: Friday 10:30–11:20
§28: Friday 13:30–14:20
Grading
Per lab period, a student may earn 10 points total:
+9 points for attendance.
+1 point for correct solutions to end-of-class quizzes. Pass/fail; the questions are intentionally easy.
A student may lose points for the following:
−1 point for tardiness (showing up after roll).
−1 point for non-class-related use of a phone, increasing by 1 point per infraction.
Office Hours
Lockett 363, Tuesday 15:00–15:20 and Thursday 15:00–17:00.
Office hours do not require an appointment. I also hold hours by appointment; email me if you cannot make a posted time. I welcome everyone, but prioritize students enrolled in the sections for which the hours are designated.
Special office hours: December 11th, 08:00–12:00 (exam week).
Absence
I excuse absences for the following reasons:
Email me day-of if you are sick, have an emergency, or there is hazardous weather. No note necessary.
Email me in advance if you have plans or appointments during class.
Email me a sick note or proof of valid excuse under LSU PS22.
If you miss class, it is your responsibility to inform me so you can make up missed content or quizzes. I offer retakes during office hours by appointment. I typically take roll within the first 5 minutes of class; it is always better to be tardy than absent.
Comics
A selection of comics I have drawn. Subject matter varies. Clearly inspired by xkcd. All humor is derivative, but mine is especially so.
I like to take inspiration from the Catholic Church's calendar for my office hours.
The Mesozoic was far weirder than people give it credit for.
According to my partner, this is how mathematicians speak.
My friends should NOT give me access to their devices.
Sometimes we need the little things.
Correcting my friends' gender in-band since 2004!
These hydraulic press channels are getting out of hand!
Don't look at the file extension...
Blog
Occasional writing on math, my projects, and whatever else is on my mind. Available as an
RSS feed.
First, a confession. I corrected an issue where I accidentally pushed missing name information for a blog post. Hope that doesn't end up in anyone's feed...
I've not really been working on the 3D print lab as much due to travel in the summer. Kiri Cahill has been more than gracious in covering me in my absence and I'm told that things are going beautifully back home.
I have a new preprint out! On some structural properties of graphs with non-negative resistance curvature, as a coauthor my good friends Gyaneshwar Agrahari, Sean Boros, and Fernando Heidercheidt, a lovely and supportive mentor Zhiyu Wang, and my advisor Christin Bibby. Go check it out; it was really fun math to do, and I hope you'll think it's really fun math to read!
Lastly, I'm at Haverford this summer as a TA for an REU! It's been a lot of fun so far, and my group has been incredibly productive. I've taken more of a programming role on the project (I can't escape the stereotypes), and I expect that soon enough I'll put some visualizations and data up here for your viewing pleasure. I also have some awesome pictures and many fun stories; stay tuned for a future blog!
For now, I gotta get back to programming. I wonder how my slurm jobs are doing...
Disclaimer: This was written a month after the fact because I'm lazy/busy. Choose whichever word you think fits me best.
So, I'm not a number theorist. Shocking, I know. Regardless, I was invited by Fang-Ting Tu (a wonderful human being and, in her own words, the "cutest professor") to TA alongside Archisman Bhattacharjee for the number theory group at the 2026 Undergraduate FRC.
The reason I was asked: The book we were going through was The Topology of Numbers by Allen Hatcher. In my opinion, the book doesn't have a whole lot of topology in the first few chapters, but I found the content quite interesting regardless.
What made the program worthwhile, however, was the people. Big shout out to Nico, Greg, Jackie, Joseph, LJ, and Anthony.
They really were excellent at what they did and impressed me to no end. Sadly, I wasn't able to make their final presentation (had to catch a flight), but I'm told it went brilliantly.
Attached are some images of the group, posted with permission.
So, it's been a while since I posted and that's because I've been extremely busy. This blog will catalogue probably only one of those reasons.
Some of my friends will know that I'm not the greatest fan of travelling.
That in mind, it might seem a bit surprising that I'd attend a summer school in Italy.
In fact, this wasn't just to Italy; it was to the Alps! Not the fastest place to get to.
However, when I saw the offer... I just couldn't resist! The math looked too good.
I loved the trip! The people I got to meet, the math I got to learn, and the sights I got to see combined to a really enjoyable experience.
It was held in Dobbiaco, at the Gustav Mahler Cultural Center. My friends that enjoy classical music perked up when I told them the venue!
The first day, we went for a pretty long hike up a mountain. It was harder than I'd like to admit but hey, it set the scene for the school very well.
Out of everything that I enjoyed, meeting new friends was the best part of the experience. Being able to meet people from Italy, Greece, and Germany, an experience that's not always easy when you're camping out in the states, was delightful. More than that, the folks were delightful too, and they're a main reason I'd like to go back!
The one thing I'll complain a little bit about: There was too much cheese! I have a dairy allergy, so finding food to eat wasn't always easy.
I'm used to people liking cheese, but there was cheese with basically every meal. It was... impressive, in a way.
The last thing I'll share here are the pictures I was able to snag. The nature and venue were beyond beautiful and I'd leap at the opportunity to return.
Oh my GOODNESS the draft is finally live! The long-awaited rewrite of the LSU RTG website is finally up! Some new features:
The site has COLOR! Instead of a plain, white expanse, I leaned in to the blue and gold that the site originally used as highlights. I'm still not quite sure why the site was originally using blue instead of purple, but ce la vie.
Completely redesigned the people page to use dropdowns instead of just dumping all the people onto the page. Also, the python build script reads plaintext so it's super easy to add new people as needed!
Eliminated the activities page in favor of an expanded navigation bar.
Combined multiple, separate webpages into a single, tabbed page. This might change in the future for specific pages (workshops, DRP, etc), but was critical for the current site size to make navigation faster.
Changed the icon and decorations!
Actually, a bit of a story behind that last item…
The original torus design with folded paper didn't scan as well as I hoped. I couldn't figure out what I wanted. At one point, I even ended up browsing Escher's artwork. Hyperbolic tilings piqued my interest but the impossible Penrose triangle were just as appealing. I eventually was reminded of my love of knots and settled on a right-handed trefoil taken from a minimal grid diagram and rotated 90°.
But this is revealing a secret. See, that drawing is fairly notorious: Does it look like a trefoil on first glance? Because if you squint, it might look more like a figure 8. Both I and a friend got a tripped up at one point, but if you flip a few crossings, all's well. One of my professors even thought I had made a mistake while trying to draw the figure 8! While I'd love to say this was an intentional choice… it wasn't. I think it'll make a really fun trivia question some day.
I have a lot planned still! I'm going to revisit my custom build script (I'm on version 5) and add some of the custom code I have for writing calendars. Additionally, there's a lot the RTG has planned, so that content is forthcoming. In particular, one of my friends is going to be running a program next year and I'm really excited to work with her to design something custom with a home-cooked flair.
As you've noticed (presumably; you are on a new page, after all), I've updated this website considerably. This shouldn't come as a great shock to anyone. While I like the retro, deeply personal design I was using, it wasn't the most efficient to update. A clean design, prioritizing simplicity and modularity, was the solution.
There are, for now, two new sections. The blog section is, as you've been able to discover, a place for blogs and updates. I'm excited to write stories, information, and the occasional math blurb for all of the two-and-a-half people that'll read this.
The other new tab is the relevant links tab. It's probably the least special and it just lists the links that used to be scattered around the page. On desktop, the link isn't even shown and the sidebar takes care of showing the extra links.
However, there's more to come. I'll be organizing LSU's DTC seminar in the 2026-2027 academic year. Information on that will eventually have its own tab. I also may or may not be working on some fun and secret projects. Shh!
As a final note, I want to extend my heartfelt congratulations to all of my friends who successfully defended their theses this semester. I will particularly mention my friend Kiri Cahill. Her resilience, kindness, and Tikz ability are constant sources of inspiration and respect for me. Additionally, she managed the 3D print lab with me this past year. Her and her husband Kade have been beyond critical in getting the lab to where it is today.
