On 19th April 2025, the Sci-Tech Spins Lecture Series was organised at IIT Delhi, of which, the lecture, titled "How to Cut a Cake Fairly", was delivered by Prof. Rohit Vaish of the Department of Computer Science and Engineering. The lecture was attended by 4 students of class 11, namely Preksha Yadav, Abhimanyu Singh, Annanya Deo, and Yash Pratap Singh, who were accompanied by their teacher, Ms Meenakshi.
The session focussed on the fascinating interplay between mathematics and real-world fairness problems, particularly highlighting scenarios such as rent division and cake cutting, problems that appear simple on the surface but are deeply complex when fairness is considered across multiple agents with differing preferences.
Prof. Vaish introduced several mathematical tools and theorems central to designing fair solutions to such problems. He delved into the cake cutting problem, where a divisible good (like a cake) must be shared among several individuals such that each person feels that he or she has received a fair share based on a subjective valuation. Similarly, the rent division problem addresses the fair allocation of rooms and corresponding rent among roommates. To address these challenges, Prof. Vaish explained the application of fundamental mathematical concepts such as Sperner’s Lemma, Brouwer’s Fixed Point Theorem, and Monk’s Theorem.
Overall, the experience was both intellectually stimulating and deeply enriching.
The emphasis on the real-world applicability of mathematical principles, particularly in designing algorithms for digital marketplaces, resource allocation, and social decision-making platforms, added immense value to the session. Prof. Vaish’s lucid explanations and interdisciplinary approach made the session a memorable one for students and faculty alike.
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