Pre-Synopsis
Speaker: Ankita Dargad, IIT Bombay
Host: Niranjan Balachandran
Title: Games and Puzzles in Combinatorics: A Study of Wealth Nim, Partizan Subtraction, and Connected Ferry Covers
Time, day and date: 11:00:00 AM – 12:00:00 PM, Wednesday, April 29
Venue: Ramanujan Hall
Abstract: Combinatorial games and puzzles provide a rich framework for mathematical analysis, intertwining strategy, discrete mathematics, and computational complexity. This thesis investigates three distinct problems within this domain. First, we introduce and analyze the ``Robin Hood'' game, which models a territorial dispute in the Era of Pingala. Using Combinatorial Game Theory, we analyze its thermographs, temperatures, and mean values under varying rulesets. Second, we explore Partizan Subtraction games with Full and Truncated Support. We evaluate their canonical forms and atomic weights, establishing key structural properties of these subtraction games. Finally, we shift to Alcuin’s classical River Crossing Problem, generalized as the Ferry Cover problem. We show that the existing results on the Ferry cover problem extends to any hereditary property bank constraint. We then introduce a novel variant with connectivity constraints, departing from hereditary bank properties. We completely characterize ``boat-1'' graphs—where a single-capacity boat suffices to cross without violating connectivity—proving that a connected graph is boat-1 if and only if its block-cut tree is a path. We also provide a linear time algorithm to find minimum boat capacity required to transfer a tree under connectivity constraint.

Topology Seminar
Speaker: Lekha Das, IIT Bombay
Host: Rekha Santhanam
Title: N_infinty operads and indexing systems
Time, day and date: 12:00:00 PM – 1:00:00 PM, Wednesday, April 29
Venue: Room 113
Abstract: In this talk er will investigate the close connection between the category of N_infinity operads and the poset of indexing systems.