Geospatial Analysis
by Ajay Gundlapalli & Nikhil Alam

Advanced Geometric Techniques
by Raghav Mukhija & Arnav Tayal

Epidemiological Modelling
by Shreyas Vivek & Raghav Pai

SWARM Intelligence
by Ayaan Maredia, Tarunesh Sathish & Akshaj Nadimpalli

Elliptic Curve Cryptography
by Souradip Das & Vethathiriyan

Hybrid CNN Models
by Ahan Bhowmik & Aniruddh Modi

Optimization of Urban Accessibility
by Prisha Shrimali

Advancement of  Sarcasm Detection
by Bala Harini Ramesh & Avyay Kodali

Research Seminar: Elliptic Curve Cryptography

Presenters: Vethathiriyan (Singapore, Grade 9), Souradip Das (India, Grade 11)

Abstract: This paper delves into the critical role of elliptic curves in advancing the field of public-key cryptography, with a particular focus on Elliptic Curve Cryptography (ECC) and its comparative efficiency against the Rivest-Shamir-Adleman (RSA) algorithm. Starting with an exploration of the group law on elliptic curves, the paper establishes the mathematical foundations that enable ECC to provide robust security mechanisms. The core of the analysis compares ECC and RSA, emphasizing the significant benefits of ECC in terms of computational overhead and key size efficiency.

Research Seminar: Optimization of Robotic Surgery using Geometry & Deep Learning

Presenters: Raghav Mukhija (India, Grade 9) & Arnav Tayal (India, Grade 10)

Abstract: Robotic surgery is a promising method to improve surgical outcomes. The field of robotic surgery is poised for remarkable transformations driven by advances in machine learning (ML) and artificial intelligence (AI). This research aims to integrate advanced geometric techniques and deep learning to address the challenges associated with robotic-assisted surgeries. This paper outlines the methodology for optimizing surgical procedures by leveraging metric spaces for accurate anatomical measurements, group theory for optimal robotic motion planning, and data augmentation techniques for improving machine learning models used in surgical planning and intraoperative guidance. The main goal of this research is to enhance the precision and safety of robotic-Assisted Surgery (AAS). The main objective of this study is to improve the surgical outcomes by integrating advanced geometric technique and deep learning. This research will contribute to the development of more reliable and effective robotic systems, paving the way for continued advancements in surgical technology.

Research Seminar: Epidemiological Modelling and Outbreak Prediction using Hyperbolic Geometry

Presenters: Raghav Pai (India, Grade 11) & Shreyas Vivek (UAE, Grade 11)

Abstract: This paper introduces a novel approach to modeling disease transmission using hyperbolic geometry, specifically the Poincaré disk model. Traditional models like Susceptible-Infected-Recovered (SIR) assume homogeneous populations, which oversimplifies real-world interactions. By incorporating hyperbolic distance, the Poincaré disk model captures spatial clustering and irregular social interactions, offering a more realistic framework for studying epidemics. Simulations of the first wave of COVID-19 in India were performed using both the Poincaré disk and SIR models. Results show that the Poincaré disk model better captures localized transmission patterns and spatial dynamics, providing deeper insights into how diseases spread through structured populations. This approach highlights the importance of accounting for social network structures in epidemic modeling, offering valuable guidance for targeted public health interventions such as localized lockdowns and vaccination strategies. Our findings demonstrate the advantages of hyperbolic geometry in epidemiological modeling, with potential applications for improving future outbreak predictions and interventions.

Research Seminar: Optimising Urban Accessibility: Constructing a 15-Minute City Using a Steiner Tree

Presenter: Prisha Shrimali (USA, Grade 10)

Abstract: This study presents a novel approach to constructing 15-minute cities (15-MCs) by utilizing graph-theoretical techniques, with a particular emphasis on the Steiner tree problem and its polynomial-time approximation. The aim is to optimize urban layouts by minimizing travel distances between essential services - such as pharmacies, post offices, and supermarkets—within pedestrian networks. By modeling these networks as weighted graphs, where nodes represent key amenities and edges reflect travel times, the Steiner tree framework is employed to minimize total distance while maintaining connectivity. This mathematical formulation significantly reduces computational complexity by focusing on service dis tribution rather than residential zones. Additionally, metric geometry is applied to measure distances within real-world urban topographies, providing a more accurate assessment of accessibility. The integration of these mathematical constructs not only enhances the efficiency of urban planning but also contributes to the creation of resilient, sustainable cities in response to the growing challenges of urbanization.

Research Seminar: Evaluation of Hybrid CNN Models for Binary Brain MRI Classification

Presenters: Ahan bhowmick (USA, Grade 9), Aniruddh Maheshwari (USA, Grade 9)

Abstract: This study presents a novel hybrid approach for brain tumor detection using magnetic resonance imaging (MRI) scans from The Cancer Imaging Archive (TCIA) . The proposed model combines feature extraction techniques like Histogram of Oriented Gradients (HOG) and Local Binary patterns (LBP) with a deep learning methodology (Convolutional Neural Network (CNN) based on ResNet50). This multimodal architecture processes traditional texture and edge features with deep learning representations, leveraging both handcrafted and learned features to enhance classification performance. Employing a 5-fold cross-validation strategy on 5,264 images, the model achieved exceptional performance with the average results across all folds being: validation accuracy (0.9967), precision (0.9999), recall (0.9945), and an F1 score of (0.9969), showcasing superiority over other models. Notably, our approach demonstrated consistent performance across training and validation sets, mitigating common overfitting issues observed in other models. Comparative analysis against established architectures such as VGG16, ResNet50, and a regular CNN showed that our model outperforms these alternatives in classification accuracy and robustness. This research contributes to medical image analysis by demonstrating the potential of hybrid models to revolutionize the field of brain tumor diagnosis Brain tumor detection , Feature extraction, CNN, Data augmentation.

Research Seminar: Applications of Projective Geometry in 3D Reconstruction

Presenters: Siddharth Garimella (USA, Grade 9), Adwita Kumar (Ghana, Grade 9)

Abstract: Projective geometry provides a powerful mathematical framework for modeling and understanding transformations and projections, offering significant applications across various domains, including computer vision, graphics, and 3D modeling. This work focuses on utilizing projective geometry principles to achieve 3D reconstruction through depth estimation, leveraging concepts such as homogeneous coordinates, epipolar geometry, and cross-ratios. By transforming two-dimensional images into accurate three-dimensional models, our approach demonstrates the effectiveness of projective transformations for capturing complex structures and geometries. The results, exemplified by the 3D reconstructions of the Eiffel Tower and India Gate, validate the robustness and precision of our method in real-world scenarios. Depth maps were successfully generated and used to build detailed 3D models, showcasing the model's capability to translate intricate features from 2D projections into cohesive three-dimensional representations. These findings highlight the potential for future research to further enhance depth estimation accuracy and explore applications in fields such as augmented reality, robotics, and cultural heritage preservation, thereby solidifying the relevance of projective geometry in advancing 3D reconstruction technologies.

Research Seminar: Boosting Financial Econometrics via Machine Learning

Presenters: Himanshu Thakur (India, Grade 12), Aaditya Punatar (India, Grade 10)

Abstract: Financial econometrics has traditionally relied on robust statistical models like GARCH and VAR for market analysis, risk assessment, and economic forecasting. While these models provide foundational insights into market dynamics, they often struggle with the nonlinear complexities of modern financial data. The emergence of machine learning (ML) offers transformative capabilities in financial econometrics, enhancing predictive accuracy by leveraging vast datasets, capturing intricate patterns, and providing timely forecasts. This research aims to bridge existing gaps by integrating traditional econometric approaches with advanced ML algorithms, including Random Forests, Neural Networks, and Long ShortTerm Memory (LSTM) networks. Employing a comprehensive methodology that combines supervised and unsupervised learning, feature engineering guided by economic theory, and dimensionality reduction techniques like PCA and LASSO, we strive to improve market prediction, model interpretability, and robustness. By comparing the predictive performance of ML models against conventional methods, we seek to demonstrate the enhanced capabilities ML brings to financial forecasting and risk assessment, with broader implications for market stability and economic growth.

Advanced students apply for research projects. It helps them learn more, improve their CV and gives them an edge in university applications.