Intro

Currently, I am a senior mathematics major at Reed College. In May 2019, I graduated with the highest honors from Frenship High School as an AP Scholar and earned 30 hours from ASU. By the end of my sophomore year of Reed College, I have earned the Commendation for Excellence in Scholarship by the Administration Committee of Reed College twice. In summer 2020 I was a participant of the altREU at PSU under PI Christof Teuscher, working with Bhavana Panchumarthi under Art Duval of UTEP on the Abelian Sandpile Model.

In the summer of 2021, I participated in the REU at the University of Michigan under Jennifer Kenkel, Janet Page, and Daniel Smolkin. We explored the asymptotic behavior of differential powers of ideals, specifically relating simple D-modules to the differential closure of ideals. Currently, you can find our REU paper here, and our pre-print is here. Finally, in 2022, I spent the summer working under Karim Adiprasito on combinatorial Hodge Theory. Our draft will soon be on the arXiv.

My CV is here.

Research

In the summer of 2022, I participated in an REU at the Hebrew University, where I worked under Karim Adiprasito, funded by his ERC Consolidator grant. We studied the Hopf Conjecture initially, but then we discovered a generalization and simplification of Karim's proof of the g-conjecture. Specifically, our approach involves embedding the simplicial complex into the moment curve. Our draft will soon be on the arXiv.

In the summer of 2021, I participated in an REU at the University of Michigan, where I worked under Jennifer Kenkel, Janet Page, and Daniel Smolkin funded by Karen Smith’s NSF grant DMS-1801697. We studied the differential power operation on ideals. We began with a focus on monomial ideals in characteristic 0 and found a class of ideals whose differential powers are eventually principal. We also studied the containment problem between ordinary and differential powers of ideals in analogy to earlier work comparing ordinary and symbolic powers of ideals. We further defined a possible closure operation on ideals, called differential closure, in analogy with integral and tight closure. We showed that this closure operation agrees with taking the radical of an ideal if and only if the ambient ring is a simple D-module. Our pre-print is here.

In the summer of 2020, I participated in an REU at PSU by PI Christof Teuscher. The REU is called an altREU because Christof created it considering the COVID-19 Pandemic. Christof recognized that many would lose the opportunity to research during the summer, with his own NSF REU site being canceled. I had been working with Art Duval of UTEP on the Abelian Sandpile Model applied to DDoS mitigation. Our final writeup can be found here.

In the summer of 2019, I worked under Andrew Whitbeck within the Experimental High-Energy Particle department at TTU, working toward developing the LDMX project. Lab work included SketchUp design, data collection from oscilloscopes, scintillators, and PMTs, data science with Python, and electrical circuit design and modification. My final writeup can be found here.

Courses

In the Fall of 2022, I am taking Math 470 with Dave Perkinson looking to prove the log-concavity of Kazhdan-Lusztig Polynomials on representable matroids. I am also taking History 389 on Latin American Labour History and German 110: Introductory German. In the Spring, I will continue my thesis and take Geometric Topology I, II at Portland State, Math 382: Algorithms and Data Structures, and Math 387: Computation and Complexity.

In my junior year, I took Math 321, 341, 412, 442, and 481 (Measure Theory, Discrete Geometry, Galois Theory, Algebraic Topology, and Independent Study on the Combinatoric of Coxeter Groups, respectively). In the Spring, I enrolled in the virtual (due to COVID and Russian War) Math in Moscow and took Introduction to Homological and Commutative Algebra and Algebraic Geometry. Finally, I also took an anthropology course on South Asia and a creative writing course on personal essays.

In my sophomore year, I took Physics 201(Oscillations and Waves), Math 113, 202, 311, 332, 342, 372 (Discrete Structures, Vector Calculus, Complex Analysis, Abstract Algebra, Topology and Categories, and Algebraic Combinatorics respectively), and Philosophy 202 (Introduction to Metaphysics).

In my first year, I took Physics 101, 102 (General Physics I and II), Math 112, 201 (Introduction to Analysis and Linear Algebra), Philosophy 201 (Logic), and Humanities 110 (Introduction to the Humanities). I took the last two Credit/No Credit because of the COVID-19 Pandemic.

In Fall 2020, I also participated in the remote BSM program for non-credit, where I took Math 310: Real Functions and Measures.

In Fall 2020, I worked as a grader for Math 111. In Spring 2021, I worked as a course assistant for Math 113 and a drop-in tutor. In Fall 2021, I worked as a grader for Math 111 and Math 202, as well as being a drop-in tutor. In Spring 2022, I was a drop-in tutor and a grader for Math 332. Currently, in Fall 2022, I am a drop-in tutor and a grader for Math 372. I currently tutor for Physics 101,102, and Math 112, 113, 201, 202, 311, 321, 332, and 342.

Contact

Email: mostephen@reed.edu

Phone: +1(806)-778-9403

Address: 3203 SE Woodstock Blvd MS 1085, Portland, OR 97202

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