Amish Mishra
Amish Mishra
Mathematics PhD candidate at Florida Atlantic University
CV | CV

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)

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

  1. Computation of Persistent Homology Using the Delaunay-Rips Complex: An efficient family of simplicial complexes for topological data analysis. (Talk)
    JMM (Virtual), April 2022
  2. Seeing Data: For Now We see Dimly, but Soon We Will See Shape to Shape. (Talk)
    3MT Thesis Competition 2022 FAU, April 2022
  3. Topological Data Analysis with Delaunay-Rips: Introducing an efficient method for TDA. (Talk)
    Florida Women in Mathematics Day 2022, February 2022
  4. The Delaunay-Rips Filtration. (Talk)
    Graduate Research Day at Florida Atlantic University, April 2021
  5. The Shape of Data: Inventing Efficient Methods for Topological Data Analysis. (Talk) 3MT Thesis Competition 2021 FAU, April 2021
  6. Numerical Range of Toeplitz Matrices over Finite Fields. (Poster)
    JMM (Baltimore, MD), January 2019
  7. Numerical Range of 3 × 3 Truncated Composition Operators. (Poster)
    Taylor University, October 2018
  8. Numerical Range of Toeplitz Matrices over Finite Fields. (Talk)
    Miami University Conference, September 2018
  9. Numerical Range of Toeplitz Matrices over Finite Fields. (Talk)
    2018 REU Conference (Indiana University), July 2018

Papers

  1. 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
  2. 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

  1. Math for Liberal Arts I. Florida Atlantic University, January 2022-May 2022.
  2. 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