Priyanka Magar-Sawant
Mathematician at Raphe mPhibr | PhD, IIT Bombay
"Applying the analytical rigor of Pure Mathematics to solve complex challenges in Aeronautics."
Mathematician at Raphe mPhibr | PhD, IIT Bombay
"Applying the analytical rigor of Pure Mathematics to solve complex challenges in Aeronautics."
I am a Mathematician at Raphe mPhibr Pvt. Ltd., where I bridge the gap between theoretical research and industrial application. I hold a PhD in Mathematics from IIT Bombay with postdoctoral experience at IIT Madras. My academic background in the classification of smooth structures in manifolds provides a unique lens for solving high-dimensional problems in technology.
Currently, my work focuses on mathematical modeling and log data analysis to enhance autonomous UAV systems. Transitioning from pure mathematics to Aeronautics has allowed me to applying rigorous analytical methods to fast-paced, real-world sectors. I am dedicated to apply my background in topology to develop functional, high-impact solutions for autonomous systems.
Raphe mPhibr, Noida
Aerospace & Defense R&D: Specializing in UAV geometries and Log Data Analysis.
IIT Madras, Chennai
Conducted advanced mathematical research in topological complexity and its application in robotics.
IIT Bombay, Mumbai
Assisted in advanced courses including Calculus, Linear Algebra, and Differential Equations.
IIT Bombay
Thesis: Smooth structures on PL-manifolds of dimensions between 8 and 10.
S.P. Pune University, Pune
S.P. College, Pune
Outside of my core work, I enjoy discussing the role of mathematics in industry. I occasionally connect with academic institutions to share my experiences regarding career transitions, helping students and researchers navigate professional paths beyond traditional academia.
Department of Mathematics, IIT Jodhpur, Rajasthan
Presented a session for M.Sc., M.Tech., and PhD students on "Career Coordinates," mapping core mathematical subjects like Topology, Graph Theory, and Differential Equations to roles in Aeronautics, Finance, and AI.
Exploring how mathematical research translates into professional roles is a journey many of us share. I've found that having access to the right mentorship and career guidance makes this transition feel much more natural.
For those looking into internships or professional growth, these two platforms are excellent places to start:
A community helping researchers find high-impact industrial roles through seminars and career-building bootcamps.
A dedicated space for mentorship and guidance, helping students navigate professional next steps after university.
Transitioning from specialized academic research into an industrial role is not a departure from your training; it is an evolution of how you apply it. The core strength of a mathematician—analytical rigor and structured thinking—is precisely what is required to solve the high-dimensional, complex challenges found in modern technology.
Below is a mapping of mathematical tools to industrial domains, followed by a curated library of foundational and advanced resources aimed at bridging the gap between theory and impact.
Applying Differential Equations and Manifold Theory to model autonomous flight paths and stabilize UAV geometries in complex physical environments.
Drawing on Stochastic Calculus, Probability Theory, and Time-Series analysis to navigate financial markets and risk assessment.
Leveraging Linear Algebra, Optimization, and Measure Theory to design robust neural architectures and predictive industrial models.
Using Number Theory, Combinatorics, and Graph Theory to secure global digital infrastructure and develop quantum-resistant protocols.
The versatility of mathematical frameworks allows for diverse career paths across nearly every technical sector. To illustrate the transition from theory to application, I have curated a few representative roadmaps showing how specific sections of the toolkit align with certain high-impact industrial domains.
Focus on Section III (Dynamics) and Section V (The Toolkit). This path bridges the transition from abstract manifold theory to physical hardware modeling.
Prioritize Section IV (Stochastic Modeling) and Section I (Foundations) for mastering the analytical rigor required for uncertainty modeling.
Concentrate on Section II (Statistical Learning) and computational translation in Section V for neural architectures.
Focusing on the logic of linear maps. The foundation for AI architectures and signal processing.
RefresherEssential for high-dimensional analysis and classifying complex manifold structures.
Ghrist's NotesBridge between DEs and Machine Learning. Discover governing laws from industrial log data.
Expert ReferenceThe core of modern machine learning and solving optimization problems over loss landscapes.
Boyd's BookBy 3Blue1Brown. Visualizing what derivatives represent in physical spring-mass systems.
Watch SeriesA theory-focused introduction to ML respecting mathematical depth.
Watch LecturesHigh-standard guide to modeling techniques based on the ISL text.
View MaterialsStarting point for visualizing and solving real-world physical configurations.
ReferenceSteve Brunton’s series on stabilizing systems—essential for robotics and aeronautics.
Watch SeriesRigorous introduction to Ito's Lemma and Black-Scholes for financial transitions.
Technical BriefMastering Git, the shell, and technical tools omitted in standard math tracks.
Learn ToolsOpen-source algorithms. See how geometry creates autonomous flight paths.
Explore Repo