On Zariski’s Cancellation Problem (Zariski 1949; Gupta 2014) - Weekend Classics

Welcome to Revise and Resubmit and today’s special episode, Weekend Classics. Mathematics is often seen as the language of the universe, and within this vast field lies a problem posed in 1949 by the legendary algebraic geometer, Oscar Zariski. This problem, known as Zariski’s Cancellation Problem, is a cornerstone of algebraic geometry, and in 2014, it met its match in the brilliant mind of Dr. Neena Gupta. Today, we’ll dive into her groundbreaking work published in the journal Advances in Mathematics—an article that reshaped how we understand geometric dimensions and algebraic structures. Dr. Gupta is no ordinary mathematician. Hailing from Bethune College and the Indian Statistical Institute, her journey has been marked by brilliance and perseverance. While pursuing her Ph.D., she became captivated by the Zariski Cancellation Problem, dedicating herself to unraveling its mysteries. And unravel she did—earning accolades like the Shanti Swarup Bhatnagar Prize and the prestigious Ramanujan Prize. Her work is a testament to the power of curiosity and determination. But here’s the puzzle we’ll explore today: What does it mean to cancel dimensions in geometry, and why does this problem remain open in characteristic zero? How does Dr. Gupta’s solution in positive characteristic shift the paradigm of algebraic geometry? A heartfelt thank you to Dr. Neena Gupta and Elsevier for this masterpiece of mathematical insight. Don’t forget to subscribe to Revise and Resubmit on Spotify, check out our YouTube channel Weekend Researcher, and join us on Amazon Prime Music and Apple Podcast. Stay curious, and let’s continue the journey of discovery! Reference Gupta, N. (2014). On Zariski’s Cancellation Problem in positive characteristic. Advances in Mathematics, 264, 296–307. https://doi.org/10.1016/j.aim.2014.07.012 Gupta, N. (2015). A survey on Zariski cancellation problem. Indian Journal of Pure and Applied Mathematics, 46(6), 865–877. https://doi.org/10.1007/s13226-015-0154-3 Infosys Prize 2024 Link: https://www.infosysprize.org/laureates/2024/neena-gupta.html 2025 AWM-AMS Emmy Noether Lecturer https://awm-math.org/wp-content/uploads/2024/02/PR-Noether-2025.pdf Youtube channel link ⁠https://www.youtube.com/@weekendresearcher⁠