Title of the talk: Fair Resource Allocation via Fixed-Point Theorems and Graphs

Date , Time & Venue: Nov 21,2025 at 12 noon on Seminar Room, Dept. of Mathematics

Abstract: Allocation of resources is a frequently encountered problem in many settings, like house allocations, estate settlements, task assignments, course allocations, and border disputes. Questions of who gets what, specifically when the participating agents have individual preferences, are both practically pressing (spanning across areas like matchings, fair division, voting problems, among others) and theoretically rich (relying on techniques from mathematics, game theory, economics, and computer science).

In this talk, we will discuss various value-based (envy-freeness, equitability) and share-based (maximin-shares) fairness notions and present a comprehensive landscape of computing such desirable allocations. In particular, we will see a recent result (WINE 2025) that shows fairness and efficiency can be achieved simultaneously for allocating positively and negatively valued resources – advancing the understanding of a long-standing open question in discrete fair division. Our techniques rely on a novel application of fixed-point theorems combined with graph-theoretic and combinatorial arguments.

About the speaker: Dr. Aditi is currently a (Walmart) Post-Doctoral Fellow at the Indian Institute of Science, Bangalore, hosted by Prof. Siddharth Barman. Previously, she received her PhD from IIT Gandhinagar. Her research interests revolve around Computational Social Choice (Fair Division, Voting and Matching problems), Algorithmic Game Theory, Graph Theory, and Economics & Computation. She works on computationally 'hard' problems and finding some 'parameterized' or 'approximate' or a 'random' way around it.