Sushovan Majhi

Assistant Professor, George Washington University, D.C.

I am currently an assistant professor of Data Science at GWU.

Before that, I was a visiting assistant professor at GWU. Prior to GWU, I was a postdoc researcher and MIDS lecturer at the University of California, Berkeley.

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

Contact me at s.majhi@gwu.edu. 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

The theme of my research revolves around the mathematical foundations of data science. My research interests lie broadly in the following domains:

Applied Algebraic Topology
Topological Data Analysis (TDA)
Computational Geometry
Pattern and Shape Matching
Statistical Finance

To learn more about my research program, visit the research page.

Teaching

My teaching interests span a broad spectrum of fields—including foundations of data science, statistics, machine learning, computer science, topological data analysis. Here are some courses I have taught in recent years:

Introduction to statistics (undergraduate, Tulane University)
Statistics for data science (graduate, UC Berkeley)
Topological data analysis (graduate, NIT Sikkim, India)
Data mining (graduate, George Washington University)
Linear Algebra for Data Science (graduate, GWU)
- Course Website (the course websites are password protected. Please contact me for access)
Algorithm design for Data Science (graduate, GWU)
- Course Website (the course websites are password protected. Please contact me for access)

Find my teaching statement here.

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, Python, and R. 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.
[webapp]
[GitHub]

Invited Talks and Presentations

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 Reveal JS. Since then, I have been using it, customizing it, and relishing it. Although, I prefer to edit the source code for my slides in Quarto and output them in Reveal JS format.

List of my talks and presentations:

Oct 15, 2024

A Taste of Topological Data Analysis (TDA): Reconstruction of Shapes
Indian Institute of Technology, Mandi, India
Oct 7, 2024

A Taste of Topological Data Analysis (TDA): Reconstruction of Shapes
Vellore Institute of Technology, Chennai, India
Jun 14, 2024

Demystifying Latschev’s Theorem for Manifold Reconstruction
Symposium on Computational Geometry (SoCG), Athens, Greece

Abstract
Topological reconstruction of a manifold from a sample around it is a challenging computational problem, with varied applications in topological data analysis and manifold learning. Manifold structures appear frequently and naturally in many fields of science. Examples include Euclidean surfaces, phase spaces of dynamical systems, configuration spaces of robots, etc. Inferring the homotopy type of an unknown manifold from a set of finite (often noisy) observations constitutes the finite reconstruction problem. Latschev in his remarkable paper established the existence of a sufficiently small scale for the Vietoris–Rips complex of a dense sample to faithfully retain the topology of the manifold. The result is only qualitative, hence impractical for applications. We will discuss a recent development that provides the first quantitative result, along with a novel proof Latshev’s theorem.
Mar 28, 2024

Demystifying Latschev’s Theorem for Manifold Reconstruction
Montana State University

Abstract
Topological reconstruction of a manifold from a sample around it is a challenging computational problem, with varied applications in topological data analysis and manifold learning. Manifold structures appear frequently and naturally in many fields of science. Examples include Euclidean surfaces, phase spaces of dynamical systems, configuration spaces of robots, etc. Inferring the homotopy type of an unknown manifold from a set of finite (often noisy) observations constitutes the finite reconstruction problem. Latschev in his remarkable paper established the existence of a sufficiently small scale for the Vietoris–Rips complex of a dense sample to faithfully retain the topology of the manifold. The result is only qualitative, hence impractical for applications. We will discuss a recent development that provides the first quantitative result, along with a novel proof Latshev’s theorem.
Aug 23, 2023

Demystifying Latschev’s Theorem for Manifold Reconstruction
Applied Algebraic Topology Research Network (AATRN)
Links:

[YouTube]

[Slides]

Abstract
Topological reconstruction of a manifold from a sample around it is a challenging computational problem, with varied applications in topological data analysis and manifold learning. Manifold structures appear frequently and naturally in many fields of science. Examples include Euclidean surfaces, phase spaces of dynamical systems, configuration spaces of robots, etc. Inferring the homotopy type of an unknown manifold from a set of finite (often noisy) observations constitutes the finite reconstruction problem. Latschev in his remarkable paper established the existence of a sufficiently small scale for the Vietoris–Rips complex of a dense sample to faithfully retain the topology of the manifold. The result is only qualitative, hence impractical for applications. We will discuss a recent development that provides the first quantitative result, along with a novel proof Latshev’s theorem.
Aug 3, 2023

Graph Move’s Distance
The 34th Canadian Conference on Computational Geometry
Links:

[url]
Oct 15, 2022

Similarity Measures for Geometric Graphs
Fall Workshop on Computational Geometry, North Carolina State University
Links:

[url]
Jan 20, 2022

A Taste of Topological Data Analysis (TDA): Reconstruction of Shapes
ICFAI, Tripura
Links:

[url]

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.
Sep 30, 2021

A Taste of Topological Data Analysis (TDA): Reconstruction of Shapes
Hunter College, New York
Links:

[url]

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.
Jan 21, 2020

Shape Comparison and Gromov-Hausdorff Distance
Tulane University
Links:

[url]

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.
Aug 8, 2019

Shape Reconstruction
Tulane University
Links:

[url]

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.
Dec 3, 2016

Music, Machine, and Mathematics
Graduate Colloquium, Tulane University
Links:

[pdf]
Apr 16, 2016

Computational Complexity
Graduate Colloquium, Tulane University
Links:

[pdf]
Sep 8, 2015

The Mathematical Mechanic
Graduate Colloquium, Tulane University
Links:

[pdf]