Sushovan Majhi
Talks & Presentations
Invited lectures, conference talks, and seminars 15 talks listed
  • Mar 6, 2025

    Topological Stability
    Spring Topology and Dynamics, Christopher Newport University
    Links:

    [url] 

  • Jan 9, 2025

    Predicting the Onset and Withdrawal of the Indian Monsoon using Persistent Homology
    Joint Mathematics Meetings, Seattle
    Links:

    [url] 

    Abstract A monsoon is a wind system that seasonally reverses its direction, accompanied by corresponding changes in precipitation. The Indian monsoon is the most prominent monsoon system, primarily affecting India’s rainy season and its surrounding lands and water bodies. Every year, the onset and withdrawal of this monsoon happens sometime in May-June and September-October, respectively. Since monsoons are very complex systems governed by various weather factors with random noise, the yearly variability in the dates is significant. Despite the best efforts by the India Meteorological Department (IMD) and the South Asia Climate Outlook Forum (SCOF), forecasting the exact dates of onset and withdrawal, even within a week, is still an elusive problem in climate science. The onset and withdrawal days can be attributed to sudden changes of regime (transition to and from chaos) in the weather. During such a transition to chaos, topological signatures such as the Persistence Diagram of the system change drastically within a short period. The dynamics of the Indian monsoon depend on many weather factors such as rainfall, temperature differential, wind speed, etc. A good starting point for analyzing the weather dynamics is to use Takens’ embedding on the monsoon index to reconstruct the phase space. Then, we detect the transition to chaos using topological data analysis (TDA) by tracking the history of the death and birth of -dimensional topological features. Recently, TDA has proven successful in detecting chaos and approximating bifurcation diagrams for known dynamical systems, like the Lorenz system. In this talk, we use the historical data (1948-2015) of the Indian monsoon index to Develop an early warning system for the onset and withdrawal of the Indian monsoon. In addition to giving specific onset and withdrawal dates, the proposed warning system also produces statically significant confidence bands (widows of dates) to predict transitions for a given level of significance.
  • Nov 17, 2024

    Lower Bounding the Gromov–Hausdorff Distance
    Tulane University, New Orleans

  • Nov 14, 2024

    Lower Bounding the Gromov–Hausdorff Distance
    Fall Workshop on Computation Geometry, Tufts University

  • 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] 

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