Amish Mishra

amishra2019 [at] fau [dot] 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, Quantum Computing

Education

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

Ph.D. in Mathematics
Advisor: Dr. Francis Motta
CGPA: 3.8

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

Experience

Graduate Student Representative on Faculty Hiring Committee, Florida Atlantic University (2023)

Assessed faculty candidates for positions in data science and cryptology for university mathematics department
Collected and reported feedback from graduate students’ opinion of faculty candidates

Oak Ridge National Laboratory Summer Intern, Oak Ridge, TN (2022)

Funded by the NSF Mathematical Sciences Graduate Internship Program via ORISE
Researched Quantum Topological Data Analysis theories and techniques in the Computer Science and Mathematics Division
Developed quantum circuits for building simplicial complexes in Qiskit
Won 1st place in the 2022 Ignite Off! National competition

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
Demonstrated advantage of DR by training SVM model for sleep-wake classification based on heart rate data (code repo)

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

Topology, Data, and The Bridge Between (Talk)
Calvin University, March 2023
Topology, Data, and The Bridge Between (Talk)
Taylor University, March 2023
An Application of the Delaunay-Rips Complex to Sleep-Wake Classification Using Heart Rate Data (Talk)
Joint Mathematics Meetings 2023, January 2023
Efficient Topological Features for Machine Learning (Poster)
2022 SIAM Conference on Mathematics of Data Science, September 2022
Shaping Data with Quantum Computers (Talk)
2022 Ignite Off!, August 2022
Efficient Topological Features for Machine Learning (Poster)
Data-Driven Science and AI Conference FAU, May 2022
Computation of Persistent Homology Using the Delaunay-Rips Complex: An efficient family of simplicial complexes for topological data analysis. (Talk)
Joint Mathematics Meetings 2022, 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

Mishra, A., & Motta, F. C. (2023). Stability and Machine Learning Applications of Persistent Homology Using the Delaunay-Rips Complex. Front. Appl. Math. Stat. 9:1179301. doi: 10.3389/fams.2023.1179301. link.
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. link
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. link

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

Introductory Statistics x 2. Florida Atlantic University.
Math for Liberal Arts I x 1. Florida Atlantic University.
Methods of Calculus for the Life Sciences x 1. Florida Atlantic University.

Computing

Languages

English | Hindi | Spanish