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