Sushovan Majhi

Postdoc Research Fellow, UC Berkeley

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I am currently a postdoc reseacher and MIDS lecturer at the School of Information, University of California, Berkeley.

Welcome to my homepage. The site showcases my research and software projects, ocassional tutorials, sporadic rants, and more.

As the odds of landing on my site at random are one in 1.9 billion (really!), you are probably looking for something, and Google just got too generous. Nonetheless, feel free to browse, find mistakes, and leave your valuable comments.

Find my CV here.

Education

  • Doctor of Philosophy in Mathematics
    Tulane University, New Orleans, USA
    2020
  • Master of Science in Mathematics
    Tata Institute of Fundamental Research, Bangalore, India
    2012
  • Bachelor of Science (Hons. in Mathematics)
    Ramakrishna Mission Vidyamandira, Calcutta University, India
    2009

Research

My research primarily revolves around the interface of mathematics and computer science. More specifically, my research is motivated by theoretical problems arising in topological data analysis (TDA), computational and applied topology, and computational geometry. I am also interested in solving real-life problems using tools from algebraic topology and geometry. My research interest also extends to applying TDA to other fields of science, like statistical finance and dynamical systems.

Research Interests:

  • Topological Data Analysis
  • Computational Topology
  • Applied Algebraic Topology
  • Computational Geometry
  • Pattern and Shape Matching
  • Statistical Finance

Publication

PhD Thesis

  • Title: Topological Methods in Shape Reconstruction and Comparison
    Link: Thesis
    2020

Preprints

  • 2022
    Distance Measures for Geometric Graphs
    Links: [arxiv] 
  • 2022
    Vietoris–Rips Complexes of Metric Spaces Near a Metric Graph.
    Submitted to: Journal of Applied and Computational Topology
    Links: [arxiv] 
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Journals

  • 2022
    On the Reconstruction of Geodesic Subspaces of $\pmb{\mathbb R^n}$.. International Journal of Computational Geometry and Applications
    With: Brittany Fasy, Rafal Komendaczyk, and Carola Wenk
    Links: [publisher]  [arxiv] 
  • 2022
    Approximating Gromov-Hausdorff Distance in Euclidean Space.. Computational Geometry: Theory and Applications (accepted)
    With: Jeffrey Vitter and Carola Wenk
    Links: [arxiv] 
  • 2021
    A Sentiment-Based Modeling and Analysis of Stock Price During the COVID-19: U- and Swoosh-Shaped Recovery.. Physica A: Statistical Mechanics and Its Applications 592: 126810, 2021 [https://doi.org/10.1016/j.physa.2021.126810.]
    With: Anish Rai, AjitMahata, Md Nurujjaman, and Kanish Debnath
    Links: [publisher]  [arxiv] 
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Proceedings of Conferences and Workshops

  • 2018
    Threshold-based graph reconstruction using discrete Morse theory. Fall Workshop on Computational Geometry, New York, NY, November 2018
    With: Brittany Terese Fasy and Carola Wenk
    Links: [arxiv] 
  • 2017
    Topological and Geometric Reconstruction of Metric Graphs in $\mathbb R^n$. Fall Workshop on Computational Geometry*, New York, NY, October 2017
    With: Brittany Terese Fasy, Rafal Komendaczyk, and Carola Wenk
    Links: [proceedings]  [arxiv] 
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Talks and Presentation

I had been a big fan of Beamer for quite some time. Who wouldn’t be when it comes to presenting slides full of math symbols? Although the math looked fancy and the audience was happy, the \(\LaTeX\)-based framework had also disappointed me quite often. I found the framework too restrictive to customize; my slides looked exactly like others’!

Features, that were lacking in Beamer during the time I broke up with it, were shining in RevealJS. Since then, I have been using it, customizing it, and relishing it.

List of my talks and presentations:

  • Aug 1, 2023
    A Taste of Topological Data Analysis (TDA): Reconstruction of Shapes
    ICFAI, Tripura
    Abstract: Topological data analysis (TDA) is a growing field of study that helps address data analysis questions. TDA is deemed a better alternative to traditional statistical approaches when the data inherit a topological and geometric structure. Most of the modern technologies at our service rely on 'geometric shapes' in some way or the other. Be it the Google Maps showing you the fastest route to your destination or the 3D printer on your desk creating an exact replica of a relic---shapes are being repeatedly sampled, reconstructed, and compared by intelligent machines. In this talk, we will catch a glimpse of how some of the famous topological concepts---like persistent homology, Vietoris-Rips and Cech complexes, Nerve Lemma, etc---lend themselves well to the reconstruction of shapes from a noisy sample.
    Links: [url] 
  • Sep 30, 2021
    A Taste of Topological Data Analysis (TDA): Reconstruction of Shapes
    Hunter College, New York
    Abstract: Topological data analysis (TDA) is a growing field of study that helps address data analysis questions. TDA is deemed a better alternative to traditional statistical approaches when the data inherit a topological and geometric structure. Most of the modern technologies at our service rely on 'geometric shapes' in some way or the other. Be it the Google Maps showing you the fastest route to your destination or the 3D printer on your desk creating an exact replica of a relic---shapes are being repeatedly sampled, reconstructed, and compared by intelligent machines. In this talk, we will catch a glimpse of how some of the famous topological concepts---like persistent homology, Vietoris-Rips and Cech complexes, Nerve Lemma, etc---lend themselves well to the reconstruction of shapes from a noisy sample.
    Links: [url] 
  • Aug 8, 2019
    Shape Reconstruction
    Tulane University
    Abstract: Most of the modern technologies at our service rely on 'shapes' in some way or other. Be it the Google Maps showing you the fastest route to your destination eluding a crash or the 3D printer on your desk creating an exact replica of a relic; shapes are being repeatedly sampled, reconstructed, and compared by intelligent machines. With the advent of modern sampling technologies, shape reconstruction and comparison techniques have matured profoundly over the last decade.
    Links: [url] 
  • Dec 3, 2016
    Music, Machine, and Mathematics
    Tulane University
    Links: [pdf] 
  • Sep 8, 2015
    The Mathematical Mechanic
    Graduate Colloquium, Tulane University
    Links: [pdf] 
  • Sep 1, 2021
    Shape Comparison and Gromov-Hausdorff Distance
    Tulane University
    Abstract: The Gromov-Hausdorff distance between any two metric spaces was first introduced by M. Gromov in the context of Riemannian manifolds. This distance measure has recently received an increasing attention from researchers in the field of topological data analysis. In applications, shapes are modeled as abstract metric spaces, and the Gromov-Hausdorff distance has been shown to provide a robust and natural framework for shape comparison. In this talk, we will introduce the notion and address the difficulties in computing the distance between two Euclidean point-clouds. In the light of our recent findings, we will also describe an O(n log n)-time approximation algorithm for Gromov-Hausdorff distance on the real line with an approximation factor of $5/4$.
    Links: [url] 
  • Apr 16, 2016
    Computational Complexity
    Graduate Colloquium, Tulane University
    Links: [pdf] 
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Software and Computing

I am a coding hobbyist. I enjoy solving online coding challenges. Although Java is my favorite programming language, I usually code in JavaScript and R. I develop softwares both for academia and industry. Some of them are listed here.

Shape Reconstruction

To complement my research, I implemented my topological reconstruction algorithm for planar metric graphs in this library. The library is written in JavaScript and made available to users as a web-app.

title: ShapeReconstruction
webapp
Github