The Unified Vectors, a team of 8 Cheenta students, secured a spot in the Top 20 during the Team Round and earned a Distinguished Honorable Mention in the overall competition, placing them in the top 25% of participants.

The Stanford Math Tournament is a prestigious online event featuring four rigorous rounds: Power Round, Team Round, Individual Round, and Guts Round. Participants from around the world compete in these challenging rounds that test their mathematical skills in various areas like algebra, geometry, combinatorics, and calculus.

The Unified Vectors dedicated a month to preparation, utilizing mock tests and strategic planning to fine-tune their skills.

We congratulate Krishiv Mohan, Raghav Mukhija, Dakkshitaa Agarwal, Reyaansh Agrawal, Saket Manikantan, Sudarshan Manikantan, Vihaan Shah and Aryan Dixit for their hard work and determination.

The research was presented by Aditya Punatar, a 10th grader, and Himansu Takur, who is pursuing a degree in Electronics and Telecommunication Engineering. Both students collaborated on this project during the summer of 2024.

Their work focuses on the use of the Upper Half Plane Model and hyperbolic geometry to improve the forecasting of stock prices. Traditional forecasting models like LSTM and GARCH often struggle with capturing market volatility and sharp transitions. The proposed hyperbolic model addresses these limitations by analyzing stock price trajectories through turning angles and hyperbolic distances, offering a more nuanced understanding of market dynamics.

The research was built upon established models like ARMA (AutoRegressive Moving Average) and LSTM (Long Short-Term Memory) networks, with the key innovation being the integration of the hyperbolic model. This new approach enhanced the models' ability to handle nonlinear relationships in stock data, which traditional models had difficulty capturing. Through this research, they demonstrated how combining machine learning with advanced geometric methods could significantly improve forecasting accuracy.

The students tested their models using historical stock price data from Yahoo Finance, and the hyperbolic model outperformed both ARMA and LSTM in predicting market behavior, with a notable decrease in the root mean square error for key stock prices like Apple and Google.

This event showcased the journeys of two exceptional students, Nandagovind and Arjun, as they prepare for their undergraduate studies. Nandagovind, whose profile is heavily based on his achievements in Olympiads, has received conditional offers from prestigious universities like Oxford and Warwick. He specifically chose Oxford due to its unique Mathematics and Computer Science program, which aligns with his future research aspirations. Nandagovind has also been involved in various student-run organizations and internships, which added significant value to his profile. However, he acknowledges the challenge of funding his education and is considering a loan to finance his studies in the UK.

Arjun, a standout in the math Olympiad community, secured an unconditional offer and a full scholarship from Trinity College, Cambridge. His achievements include representing India at the International Mathematics Olympiad (IMO) and winning multiple medals over the years. Arjun highlighted how his passion for mathematics led him to focus on Olympiads, and despite initially planning to give the JEE exams, he ultimately decided to pursue math Olympiad-related opportunities. His experience emphasizes the importance of focusing on what truly excites you, as well as the benefits of having backup colleges when applying to top-tier institutions.

Both students shared insights into their preparation, with Nandagovind focusing on Olympiad competitions, research projects, and student organizations, while Arjun emphasized the significance of participating in math Olympiads. They also discussed the challenges of managing the funding for their studies abroad. The session provided valuable lessons for aspiring students, showcasing how dedication, strategic planning, and passion for a subject can lead to success in top universities worldwide.

Jayaditya Gupta, a Class 10 student from Mumbai, India, has prepared an inspiring presentation on Euler’s Characteristic and Herz’s Investigations in Group Theory. Jayaditya was part of the Hyperbolic Geometry Group during the summer program, and his talk beautifully bridged the worlds of geometry and algebra.

In her presentation, Jayaditya began with the elegant Euler characteristic formula for surfaces of different genus, guiding the audience through detailed proofs using intuitive visual models like the double torus. From there, he transitioned into the fascinating world of group diagrams, using examples like the symmetric group S3S_3S3​ to demonstrate how group relations are represented geometrically.

The highlight of his talk was the detailed discussion on Herz’s investigations, where he examined how group diagrams evolve on hyperbolic surfaces and how the number of group elements relates to the genus of the surface. He concluded by connecting these ideas to the word problem in group theory, emphasizing how geometric tools can help solve abstract algebraic challenges.

In this event, Grade 9 students Adwaita and Siddharth presented an insightful session on projective geometry and its application in 3D reconstruction. Their project focused on using projective geometry concepts, including homogeneous coordinates, epipolar geometry, and cross ratios, to achieve 3D reconstruction through depth estimation.

The session began with an introduction to projective geometry, explaining its role in fields like computer vision and 3D modeling. Adwaita and Siddharth demonstrated how depth estimation is achieved using perspective projections, camera calibration, and triangulation. They showcased their work by reconstructing landmarks like the Eiffel Tower and India Gate, using 2D images to create accurate depth maps and 3D models.

The students also highlighted the broader applications of their approach, including cultural heritage preservation, urban modeling, and virtual reality, where accurate 3D models are essential.

The event concluded with a Q&A session, where the students discussed their methodology and the potential for future advancements in 3D reconstruction. Adwaita and Siddharth's presentation demonstrated a strong understanding of complex geometric concepts, inspiring the audience with the future possibilities of projective geometry in technology and modeling.

This event featured three exceptional students—Arjun, Angad, and Inaya—who shared their journeys to prestigious universities like Harvard, Purdue, and Stanford. Arjun discussed his focus on mathematics, Olympiads, and research in number theory, which contributed to his Harvard application. Angad highlighted his unique background as a national-level athlete and his involvement in volunteer tutoring and research. Inaya spoke about her work in floating solar, research projects, and achievements in Olympiads and F1 in Schools, which helped her secure a spot at Stanford. The session   provided valuable insights into managing academics, extracurriculars, and university applications, offering inspiration for aspiring students.