Field of study: algebraic geometryAdvisor: Martin Olsson• Mastered 30 years of research on the mathematical theory of spherical varieties, and wrote a comprehensive and accessible introduction to the theory for others to learn from.• Designed a research agenda exploring possible solutions to new problems regarding spherical varieties and developed innovative tools and frameworks capable of producing nearly optimal solutions to new problems.• Analyzed the newfound solutions and quantified the extent to which they solved the original problems.• Shared my own research and discussed the research of colleagues in research seminars.• Worked primarily in a Linux terminal environment, producing LaTeX documents using vim and other command-line tools.

Terms: Fall 2016, Spring 2017, Summer 2019, Fall 2019, Summer 2021Courses taught: Calculus, Lower-division Linear Algebra, Real Analysis, Upper-division Linear Algebra• Taught 2 "discussion sections" with 20-25 students each, including teaching to supplement class lectures and providing hands-on practice with course material for fall and spring terms.• Designed and executed class lectures, homework assignments and exams while managing students’ grades as the primary instructor for summer terms.• Analyzed gaps in students’ understanding and found solutions through weekly office hours.• Successfully rated 0.5-1 standard deviations above average on student evaluations of instructor effectiveness in the math department.

• Co-managed a program that pairs undergraduates with grad students for one-on-one mentorship and independent reading of advanced material — assessed best fit for mentors and mentees, coached mentors, provided accurate information and applications on program website, and ensured accountability for all parties to meet program’s standards. • Managed program funding from a grant to host events and distribute learning resources for participants.• Wrote a web app to automate the workflow involved in processing applications, resulting in a 10-20% speedup on average.• Grew the program from 20-25 undergraduates per semester to 35-40 undergraduates per semester.• Expanded the program to the statistics, physics, and computer science departments, which led to the formation of an independent program in the physics department.

Terms: Fall 2016, Spring 2017, Fall 2017, Fall 2018, Spring 2019• Mentored undergraduate students interested in math and/or computer science.• Designed personalized, semester-long reading programs to guide individual students through advanced undergraduate material.• Coached students on effectively communicating what they learned through end-of-semester presentations.• Gained basic proficiency with machine learning in order to provide reading projects for computer science students.• Helped train neural networks written in Python to classify handwritten numbers from the MNIST dataset with over 97% accuracy.

Terms: Summer 2015 and Summer 2016Topic: symplectic geometry. Advisor: Jo Nelson.• Participated in lectures on background material to learn about a research-level mathematical problem.• Collaborated with a team of undergraduates to produce original research.• Created a prototype implementation of an algorithm in Haskell.• Improved performance by implementing the same algorithm in C++, resulting in a 10x increase in speed.• Used data gathered by the algorithm to determine the direction of research.• Successfully completed the research agenda by obtaining optimal solutions to the given problem, and used findings to write a paper.

Classes: topology and algebraic topology• Provided detailed feedback on problem sets to help students learn to write high-quality mathematical proofs.• Held weekly office hours to answer students' questions and facilitate learning.• Coordinated with professors' schedules in order to grade problem sets and hold office hours in a timely manner.

Topic: algebraic topology and knot theory. Advisor: Jennifer Hom.• Participated in lectures on background material to learn about a research-level mathematical problem.• Collaborated with a team of undergraduates to produce original research.• Created an improved version of a theorem by Ichihara and Temma and used it to solve a research problem for 4 new types of knots.• Showcased results at a national conference, 2015 Joint Mathematics Meeting Student Poster Session, and wrote a research paper on findings.

• Developed a prototype of an Android app for a social media startup using proficiency with Java.• Cross-functionally worked and collaborated with a UX designer and an iOS developer to provide a consistent and intuitive user interface across platforms.• Collaborated with a mentor to solve problems involving interfacing with the backend API.