Mitchell Faulk
Scientist | Educator
About
Hello! And welcome to my personal page.
I’m a scientist and educator with a passion for uncovering patterns. My expertise includes project design and management, quantitative analysis and reasoning, and the communication and visualization of data. I thrive in devising simple, easy-to-understand frameworks for complex ideas. My colleagues would describe me as a driven creator whose products set the bar in organization and precision, and my students have praised my ability to communicate with enthusiasm and order—rekindling their own passions for analytical and rigorous thinking. Currently I'm seeking opportunities that will allow me to generate meaningful, lasting impact as part of a open, creative, collaborative team. Specific fields of interest include software, health, and data.
Projects
SET game simulator +
To simulate the card game SET® and study its statistics.
Executive summary ⮕ Blog posts ⮕ GitHub repository ⮕
Personal Blog
Blog website ⮕Embedding DM Stacks into GIT Quotient Stacks of Linear Representations
In July 2022 I gave a talk at Spec(Q-bar) on my recent work.
Abstract ⮕
Essay for Do Not Erase
I wrote an essay for photographer Jessica Wynne's book profiling scientists.
Author's webpage ⮕
NSF Graduate Research Fellowship
In 2015 I was awarded a Graduate Research Fellowship from the National Science Foundation.
Research proposal ⮕Teaching
Differential Geometry Notes
Lecture notes for a first-semester graduate-level course in (Mathematical) Differential Geometry, written as I attended a course by Melissa Liu, and subsequently edited by her afterwards.
PDF ⮕ TEX file ⮕
Real Analysis Course
Complete course materials for (Mathematical) Real Analysis, including self-contained lecture notes (96 pages), problem sets, and warm-up exercises.
Course webpage ⮕ Notes ⮕
Notre Dame Summer Research Experience
During the summers of 2013, 2014, and 2015, I orchestated a research experience for undergraduates at Notre Dame.
2015 Webpage ⮕Research
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Embedding Deligne-Mumford stacks into GIT quotient stacks of linear representations
2021 (with M. Liu)
Keywords: Algebraic Geometry, Deligne-Mumford stacks, GIT quotient stacks
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Some canonical metrics on Kähler orbifolds
2019 (PhD Thesis)
Keywords: Complex geometry, Kähler geometry, Canonical metrics, Orbifolds
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On Yau's Theorem for asymptotically conical orbifolds
2018
Keywords: Complex geometry, Kähler geometry, Orbifolds, Ricci curvature
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On Yau’s Theorem for effective orbifolds
2017
Keywords: Complex geometry, Kähler geometry, Orbifolds, Ricci curvature
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Exact results for perturbation to total positivity and to total nonsingularity
2014 (with M. Farber, C.R. Johnson, and E. Marzion)
Keywords: Linear algebra, C4-free graphs, Hadamard core, Matrix perturbation, Projective plane, Total positivity
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Equal entries in totally positive matrices
2014 (with M. Farber, C.R. Johnson, and E. Marzion)
Keywords: Linear Algebra, Totally positive matrices, Point-line incidences, Bruhat order of permutations, Outerplanar graphs
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2014 (Undergraduate Thesis)
Keywords: Vertex operator algebras, Non-commutative algebras, Representation theory, Conformal geometry