Email: kdemason [at] utexas.edu
Office: PMA 10.138
I am a second year graduate student at the University of Texas at Austin. Currently I am broadly interested in the calculus of variations, geometric analysis, Riemannian geometry, and convex analysis.
I graduated in 2020 from the University of Florida with a bachelors in mathematics and a minor in chemistry. My senior thesis contained a proof of the Gauss-Bonnet theorem for orientable 2-manifolds by computing variations of several geometric objects. You can view it here.
My CV can be found here. (Updated May 17 2022)
Over Summer 2020, I participated in UChicago's REU and worked with Dr. Robin Neumayer on topics in convex analysis. I was introduced to optimal mass transport, including the Monge and Kantorovich formulations, as well as some basic existence results of optimal plans. Afterwards, I learned how to apply mass transport theory to solve isoperimetric problems. We investigated a hypothesis I had involving the anisotropic perimeter in dimension n=2, and eventually proved it. Following this, I studied convex bodies and mixed volumes. Using this theory, I was able to give an alternative proof of the result. Finally, I gave a conjecture involving a way to compute the Minkowski sum of convex sets solely in terms of their support functions.
Over Summer 2019, I worked with Liam Mazurowski and Dr. Andre Neves as part of UChicago's 2019 REU. I learned about stable minimal surfaces, including the variational formulas, log-cutoff trick, and Sharp's compactness theorem. At the end, I gave a proof of a more basic compactness theorem using small curvature estimates.
From August 2018 to May 2020, I worked on several directed reading projects under the guidance of Dr. Luca Di Cerbo. I first learned basic differential geometry of curves and surfaces, then learned substantial Riemannian geometry. My senior thesis involved calculating variations of Christoffel symbols, components of the Riemann curvature tensor, and the volume element.
From January 2017 to May 2020, I worked in Dr. Alexander Angerhofer's physical chemistry lab. I analyzed the electronic structure of Oxalate Decarboxylase (OxDC) using an electron paramagnetic resonance (EPR) spectrometer. Learned to synthesize and purify protein. In studing OxDC, I used a process called redoxcycling to oxidize and reduce a central manganese; the changes in oxidation states can readily be measured using EPR. In addition, I spent a semester learning graduate-level EPR theory.
Under construction.
The following are several resources which may prove valuable to undergraduage and graduate students alike. I have uploaded various notes from directed reading courses/self study as well as many research/personal statements for applications. I hope you find these useful!
During Spring 2022 I took a course on Optimal Transportation at the Fields Institute by Robert McCann. Below you can find condensed notes focusing on entropic curvature dimension spaces and stability under Gromov-Hausdorff convergence. For a final project we had to read a paper and write exposition on it. I chose the 2014 paper by Figalli-Maggi-Pratelli proving stability for the anisotropic isoperimetric inequality via optimal transport. You can find my final report below too.
Entropic Curvature Dimension Spaces and Stability under Gromov-Hausdorff Convergence.
Optimal Transportation and Stability of the Anisotropic Perimeter.
These are expository notes written as a result of UChicago's REU program.
Optimal Mass Transport and the Isoperimetric Inequality.
Stable Minimal Surfaces.
I've compiled solutions for textbook problems (and other various homework problems) assigned in some courses while at UT Austin.
While studying for prelims at UT Austin, I worked many textbook problems and typed my solutions. I also typed up solutions for many past prelims. These are provided below, along with scans of my actual exams solutions.
When I was applying to grad school, I didn't get the chance to see anyone's personal statements. I think having some sort of guidance is essential, so I share the one I sent to UT here. Upon reflection, I think it helped to share my experiences and specifically what I learned from them. It also probably helped to list people I wanted to work with (and being genuine about it!) and researching available opportunities there that I could make use of.
The following website is good to keep track of which schools have sent out offers and for making connections. Do not read into it too much, it can be very toxic. Don't compare yourself to other students. Don't check it religiously.
The National Science Foundation Graduate Research Fellowship Program (NSF GRFP) provides graduate students with $34,000 over three years. Eligible students include undergraduates heading to grad school and first and second year graduate students. You can apply twice, once during undergrad and once during grad, so you might as well apply during undergrad! This gives you some experience with the process and what to look out for, and also allows you to practice writing proposals.
The NSF GRFP judges candidates based on two criteria, loosely defined as Intellectual Merit and Broader Impacts. These essentially amount to how promising of a researcher you are (past experience, internships, coursework, etc.) and how your research will impact society (diversity, health/knowledge benefits, etc.)
The NSF GRFP application consists 2-3 letters of rec of two statements: the personal and research statement. Both should address intellectual merit and broader impacts. More information on the application process and the judgement criteria can be found on the NSF GRP website below.
Here are some key points:
The following are my personal + research statements, as well as my ratings and comments. Feel free to read them to get a feel for how to write your own.
Sample NSF GRFP research statement.
Sample NSF GRFP personal statement.
Sample NSF GRFP ratings and comments.
Alex Lang has an amazing writeup of the NSF GRFP on his website. You can find it below.
Research Experiences for Undergraduates (REUs) provide exciting, informative opportunities to undergraduate students. For math majors, these take the form of collaborative research projects or directed self study programs.
Below is a presentation on REUs I gave to UF's University Math Society in 2019. It describes many of the possible REUs and the application process. I also share the programs I applied to and to which ones I was accepted.I encourage all undergraduates to apply to REUs -- epecially those of you coming from underrepresented groups! These are incredible opportunities and you are more than qualified to participate, I promise.
I have some personal opinions on specific REUs that I have heard from attendees. I will not post them here, but if you would like to hear them, email me.
The application process starts at this website where you'll find program listings. Most REUs have an application on this website, but some are on NSF's website. Generally speaking, you'll need a cover sheet (basic background info), transcript, letters of rec, and a personal statement. CVs are optional, but I'd reccommend them. You can find two personal statements below.
UChicago REU personal statement.
Lena Ji also has a good website on REUs, see below.
The Goldwater Scholarship is an opportunity for budding sophomore and junior year researchers to obtain funding. The scholarship provides $7500/yr until graduation. For anyone interested in pursuing research, this is certainly a good scholarship to apply to.
I will not post my application statements here. They are far too personal, but I will share them upon email request.