# Amish Mishra

amishra2019@fau.edu | amish-mishra.github.io

## Biography

Merging together creative problem-solving, team-building, and productivity, I endeavor to apply my mathematical and computing knowledge into advanced areas of research, industry, and academia. I have a background in rigorous coursework, presentations, and publications and am now a Mathematics PhD candidate making headway in Computational Topology research at Florida Atlantic University.

### Research Interests

Topological Data Analysis, Computational Topology, Data Science

## Education

**Florida Atlantic University**, Boca Raton, FL `(2019-December 2023)`

- Ph.D. in Mathematics
- Advisor: Dr. Francis Motta
- CGPA: 3.7

**Florida Atlantic University**, Boca Raton, FL `(2019-2021)`

- M.S. in Applied Mathematics and Statistics
- CGPA: 3.7

**Taylor University**, Upland, IN `(2015-2019)`

- B.S. in Mathematics and Computer Science
- CGPA: 3.7

**Metro Delhi International School**, New Delhi, India `(2011-2015)`

- High School Diploma
- CGPA: 3.9

## Experience

**Computational Topology Researcher**, Florida Atlantic University `(2020-Present)`

- Designed and implemented in Python a new filtration we named The Delaunay-Rips (DR) filtration
- Mathematically characterized stability of Persistence Diagrams generated by DR
- Tested runtime and utility of DR in Machine Learning classification tasks on synthetic datasets via Persistence Images (current work)

**President of SIAM Student Chapter**, Florida Atlantic University `(2021-Present)`

- Organized meetings and planned SIAM events for students to connect with industry workers and researchers

**Mathematics Tutor**, Florida Atlantic University `(2019-Present)`

- Tutored students in a variety of subjects from Math for Liberal Arts, Statistics, and Calculus to Real Analysis, Linear Algebra, and Complex Analysis

**Analysis of Algorithms Project**, Florida Atlantic University `(2021)`

- Coded dynamic programming and brute force approach to solving the matrix-chain multiplication problem
- Documented theoretical and empircal runtime comparisons of the two algorithms

**MyOpenMath Problem Coder**, Florida Atlantic University `(2020)`

- Programmed randomly-generated problems and step-by-step solutions for algebra problems in myOpenMath

**Student System Administrator**, Taylor University `(2018-2019)`

- Wrote a bash script to push files onto multiple external drives upon connecting drives
- Produced a batch script to connect multiple CSE CUPS printers to lab machines across the department
- Researched issues and solutions to deploying CSE OS image via FOG

**RT Logic Project Team Member**, Taylor University `(2018)`

- Designed and implemented innovative algorithms for use in a next generation satellite communications architecture
- Developed software in Pycharm (IntelliJ’s IDE) and Linux environment
- Presented research in RT Logic’s facility in Colorado

**Undergraduate Mathematics Researcher**, Taylor University `(2018)`

- Characterized the numerical range of various matrices over Complex Field and Finite Fields
- Wrote Matlab and Mathematica code to aid in exploration of numerical range for our choice of matrices

**Information Technology Student Staff**, Taylor University `(2015-2018)`

- Trained other technicians with hardware and software
- Researched solutions to systemic computer errors and workflow improvement
- Re-built laptops and desktops with university Windows images

## Presentations

*Computation of Persistent Homology Using the Delaunay-Rips Complex: An efficient family of simplicial complexes for topological data analysis.*(Talk)

JMM (Virtual), April 2022*Seeing Data: For Now We see Dimly, but Soon We Will See Shape to Shape.*(Talk)

3MT Thesis Competition 2022 FAU, April 2022*Topological Data Analysis with Delaunay-Rips: Introducing an efficient method for TDA.*(Talk)

Florida Women in Mathematics Day 2022, February 2022*The Delaunay-Rips Filtration.*(Talk)

Graduate Research Day at Florida Atlantic University, April 2021*The Shape of Data: Inventing Efficient Methods for Topological Data Analysis.*(Talk) 3MT Thesis Competition 2021 FAU, April 2021*Numerical Range of Toeplitz Matrices over Finite Fields.*(Poster)

JMM (Baltimore, MD), January 2019*Numerical Range of 3 × 3 Truncated Composition Operators.*(Poster)

Taylor University, October 2018*Numerical Range of Toeplitz Matrices over Finite Fields.*(Talk)

Miami University Conference, September 2018*Numerical Range of Toeplitz Matrices over Finite Fields.*(Talk)

2018 REU Conference (Indiana University), July 2018

## Papers

- Guillaume, M.,
**Mishra, A.**, Thompson, D.*Numerical Range of Toeplitz Matrices over Finite Fields.*ACMS 22nd Biennial Conference Proceeding, vol. 22, 2020, pp. 151-158. https://acmsonline.org/wp-content/uploads/2020/06/proceedings-2019.pdf - Guillaume, M. &
**Mishra, A.***Numerical Range of 3 × 3 Truncated Composition Operators.*Ball State Undergraduate Mathematics Exchange, vol. 13, no. 1, 2019, pp. 36-48. https://digitalresearch.bsu.edu/mathexchange/volume-13/

## Coursework

### Mathematics

- Abstract Algebra
- Advanced Statistics
- Calculus I, II, III
- Complex Analysis
- Computational Topology
- Dynamical Systems
- Functional Analysis
- General Topology
- Linear Algebra
- Mathematical Modeling
- Numerical Analysis
- Operations Research
- Ordinary Differential Equations
- Partial Differential Equations
- Real Analysis

### Computer Science

- Analysis of Algorithms
- Data Structures and Algorithms
- Introduction to Computer Systems
- Introduction to Data Science
- Machine Learning
- Multi-Tier Web Application Development

### Physics

- University Physics I, II
- Modern Physics

## Teaching

- Math for Liberal Arts I. Florida Atlantic University, January 2022-May 2022.
- Methods of Calculus for the Life Sciences. Florida Atlantic University, August 2021-December 2021.

## Computing

Python | Matlab | Mathematica | Octave | R | RStudio | JupyterLab | IntelliJ IDE | Pycharm IDE | CSS | HTML | Java | GitLab | GitHub | Latex | Markdown | Bash | Linux

## Languages

English | Hindi | Spanish