# Curriculum Vitae

# Education

- Ph.D in Mathematics, The Ohio State University, 2022
- Thesis: Lattice Point Counting through Fractal Geometry and Stationary Phase for Surfaces with Vanishing Curvature
- Advisor: Krystal Taylor

- M.S. in Mathematics, The Ohio State University, 2017
- B.A. in “The Language of Mathematics”, New York University Gallatin School of Individualized Study, 2014

# Research Experience

**Asymmetric Cloning to Eavesdrop on BB84 Protocol:**(Mentor Alex Khan, April - August 2022)*QuForce Innovation Fellow,*- 1st Place Demo
- Worked with another mathematician and a physicist to determine the theoretical optimal strategy for asymmetric cloning on a quantum channel (minimizing disturbance while maximizing information gain).
- Compared theoretical expectation to the experimental results from implementation of asymmetric phase-covariant cloning on IonQ’s 11-qubit quantum computer (utilizing the Qiskit SDK).

(August - Present 2022)*Independent Researcher, Continuing QuForce Project*- Expanding our experimental investigation into the trade-off between information gain and detection when eavesdropping on quantum key distribution.
- Exploring the impact of noise on our base fidelity rates through implementation on IonQ using Native Gates directly.

**Ph.D. Thesis Project: Lattice Points Close to the Heisenberg Norm,**OSU (September 2017 - May 2022)- Worked with my advisor, Dr. Krystal Taylor, to answer questions at the intersection of harmonic analysis, number theory, and geometric measure theory.
- Adapted technique used by Iosevich and Taylor (2011) to count lattice points on and near smooth surfaces to instead count lattice points on and near surfaces with vanishing curvature.
- Removed the non-vanishing Gaussian curvature condition for similarly homogeneous objects defined by norms. The limitation lies in the decay of the Fourier transform of the surface measure.
- Leveraged the geometry of Heisenberg norm balls to attain results despite vanishing curvature. This work is generalizable to similar objects (those with less homogenous dilations along one axis).
- Utilized method to estimate the number of lattice points in and near the intersection of two surfaces (described by the same or different norms).

**Intern, Continuing Fall Project: Topological Data Analysis Applied to Football,**Mined XAI (December 2021 - January 2022)- Analyzed remaining play-types: engineered predictive features for punts to cluster into different strategies with UMAP and HDBSCAN. Clustered on the 1-skeleton of alpha complexes for initial kickoff positions.
- We expanded the SciPy Voronoi class to include points at infinity and compute Voronoi distance, then further extended this to an alpha complex class which constructs the 1-skeleton of an alpha complex.

**The Erdős Institute Boot Camp:**(September - December 2021)*Topological Data Analysis Applied to Football*- A Fall 2021 Top Project
- Collaborated with two mathematicians and a research scientist on the NFL Big Data Bowl 2022 Kaggle Challenge.
- Engineered predictive features by play-type to cluster into different strategies with UMAP and HDBSCAN.
- Applied predictive modeling to each cluster to create a new metric for special teams play.

(September - December 2020)*Predicting COVID Spread*- Partnered with physics Ph.D. student to study COVID-19 spread at the county level in the United States as of December 2020 utilizing Random Forest and Nearest Neighbors Predictors (implemented in Python).
- Compared responses to the pandemic across states by considering factors such as mask use, poverty levels, median age of the population, and population density in each county.

**Graduate Researcher at Autonomy Technology Research Center,**Wright State University (May - August 2018)- Collaborated with Dr. Trevor Bihl from Air Force Research Lab (AFRL) on an applied math problem in Detecting and Analyzing Anomalies with Topological Data Analysis.
- Improved community understanding of how topological data analysis (TDA) could be used for detecting and analyzing anomalies in large data sets—specifically those describing visual data.
- Compared the efficacy of analyzing the MNIST dataset through TDA to an analysis with diffusion maps by running topological models through the Ayasdi platform and applying diffusion maps in MATLAB.

**Elm Encryption/Decryption Program,**(January - May 2018)- Using the Elm programming language, developed a program to encrypt and decrypt messages in the ADFGVX cipher used by the Germans in World War I.
- Extended this program to implement the alterations to the cipher I developed in my undergraduate thesis.
- Inspired to use Elm and guided in learning to implement Elm code by Dr. Jim Carlson.

**Undergraduate Thesis Project: Linguistics and Mathematics in Cryptology,**NYU (January - April 2014)- Researched the effect on linguistic structures of various crypto-systems and techniques surveyed in previous study, The Evolution of Cryptology (listed below).
- Performed a comprehensive analysis–mathematical and linguistic–of both an original field cipher from World War I (the ADFGVX cipher) and my modified version.
- Focused on the mathematical representations of the ciphers’ attributes and their effects on the linguistic structure of the plaintext message as compared to the patterns and structures evident after encryption.
- Culminated in a 49-page analytical paper proposing meaningful alterations to the cipher, which were further supported by cryptanalytic techniques attempted against them and distinct differences in the patterns of original and encrypted messages.

- See CV PDF for more research and professional experience.

# Skills

*Data Analytics and Machine Learning:*Python (Pandas, NumPy, Scikit-learn, Matplotlib), Ayasdi (TDA).*Computer Languages:*Python, LaTeX, Java, basic Elm and Bash programming.*Tools/Platforms:*Jupyter Notebook, GitHub, Microsoft Office Suite, iWork, Zoom, Linux, Macs, and PCs.*Foreign Languages:*Functionally proficient in Spanish and Italian. Arabic (beginner), French (reading).*Public Speaking:*Twelve years of theatre performance and training, including Off-Broadway.

# Publications

*Asymmetric Cloning to Eavesdrop on BB84 Protocol*, with B. Pigott and H. Routray (in Preparation).*Lattice Point Counting through Fractal Geometry and Stationary Phase for Surfaces with Vanishing Curvature*(Dissertation).*Lattice Points Close to the Heisenberg Spheres*, with K. Taylor, OSU. La Matematica 2, 156–196 (2023). (arXiv).*A Tutorial on Topological Data Analysis for Big Data Analytics*, with T. Bihl, AFRL (Preprint).

# Conferences

- APS March Meeting Presentation: Asymmetric Cloning to Eavesdrop on BB84 Protocol (March 2023).
- miniMAGNTS Poster Presentation: Lattice Point Counting: From Gauss Circle Problem to Heisenberg Norms (August 2021).
- SIAM Annual Meeting, AWM Workshop Poster Presentation: Lattice Point Counting: From Gauss Circle Problem to Heisenberg Norms (July 2021).
- 3M RISE Symposium (June 2021).
- Hausdorff Trimester Program at The Hausdorff Center for Mathematics, Universität Bonn:
- Seminar Series: Harmonic Analysis From the Edge & Arithmetic Applications of Fourier Analysis (May-August 2021).
- The Polynomial Method, Summer School (June 2021).
- The Circle Method: Entering its Second Century, Summer School (June 2020–Postponed to May 2021).

- (Upcoming) Young Women in Geometric Analysis Presentation: Lattice Point Counting: From Gauss Circle Problem to Heisenberg Norms, The Hausdorff Center for Mathematics (April 2020–Postponed to 2021).
- IEEE NAECON Presentation: A Tutorial on Topological Data Analysis for Big Data Analytics (July 2019).
- First Midwest Graduate Student Conference: Geometry and Topology meet Data Analysis and Machine Learning Poster Presentation: Performing Topological Data Analysis through the Ayasdi Platform (June 2019).
- INFORMS Symposium Presentation: Big Data Analysis with Topological Data Analysis (October 2018).

# Service and leadership

**Project Mentor for The Erdős Institute Boot Camp**(October - December 2022)- Advising participants in four project groups on the data science lifecycle for their projects.
- Acting as a sounding-board for their ideas and general resource to help them succeed.

**SIAM, OSU Chapter Math Modeling Contest Judge**(November 2017, 2018, and 2019)- Graded undergraduate teams’ reports based on the merits of their mathematical models, analysis of their results, thoroughness of their conclusions, and the overall creativity and readability of their solutions.

**Association for Women in Mathematics, OSU Chapter***President*(Academic Year 2021 - 2022)- Created new chapter website with pages to highlight resources and opportunities for undergrads through post-docs.

*Vice President*(Academic Year 2020-2021)*Outreach Chair*(Academic Year 2019-2020)

**OSU Math Department Peer Mentor**(Academic Years 2016-2018 and 2019-2021)

# Research and Performance Awards

**Research Projects**- 1st Place: QuForce Demo Day (2022)
- Top Project: Erdős Institute Fall Boot Camp (2021)

**The Ohio State University**- Graduate Associate Performance Award (2021)
- Rhodus Graduate Fellowship (Autumn 2018 and 2019)
- Math Department Fellowship (2016)
- University Fellowship (2015)

**New York University**- Honors on Senior Thesis Project: Linguistics and Mathematics in Cryptology
- Founder’s Day Award
- Dean’s List
- National Merit Scholarship

# Teaching

**Teaching Assistant for The Erdős Institute Boot Camp**(May, September - December 2022)- Assisted students during group problem sessions, answering questions regarding technical and theoretical practices.
- Ensured groups progressed at a reasonable rate, providing hints as necessary.

**Teaching Associate at BAMM: Beyond the Classroom Summer Camp,**OSU (June 2021)- Evaluated middle and high school students’ submissions as they discovered the math behind magic tricks.
- Assisted students in Zoom help sessions and led afternoon discussions.

**Recitation Instructor, Tutor, and Grader,**OSU (August 2016 - May 2022)- Graded Intro Analysis I & II, Analysis Overview, honors and regular sections of Foundations of Higher Mathematics (proof writing course), and Linear Algebra.
- Contributed to creation of content for college pre-calculus Ximera textbook.
- Taught recitation sections of Calculus I.
- Tutored Calculus I & II, Calculus for Engineers, Business Calculus, and College Algebra.

**Tutoring Undergraduate Level**(September 2013 - May 2014)- Tutored college student in discrete mathematics, linear algebra, and programming (C++).
- Two to three days a week in three-hour sessions.

**Junior Faculty at HCSSiM, Hampshire College**(June - August 2012)- Taught algebraic topics such as modular arithmetic and basic group theory in first main course; taught lessons on fractals and random walks (eg., absorbing Markov chains) in chaos theory course.
- Taught two ``minis” (seven day, hour-long) on cryptology: pen and paper ciphers, then modern cryptology.
- Gave an hour-long, program-wide lecture on cracking the Enigma.
- Assisted students with assigned problems and course material during daily three-hour problem sessions.