Optimal Transport 
Speaker: Sooraj AP, IIT Bombay
Host: Harsha Hutridurga
Title: Topics in Optimal Transportation
Time, day and date: 11:00:00 AM – 12:00:00 PM, Monday, April 27
Venue: Ramanujan Hall
Abstract: -

IPDF Extension Talk
Speaker: Chandan Bhaumik, IIT Bombay
Host: Manoj K Keshari
Title: Symplectic modules over certain subrings of a polynomial ring
Time, day and date: 4:00:00 PM – 5:00:00 PM, Monday, April 27
Venue: Ramanujan Hall
Abstract: In this talk, I will discuss the cancellation and splitting problems of symplectic modules over two families of subrings of a polynomial ring: the geometric subring and the graded subring.

Schur-Weyl duality
Speaker: Sulakhana Chowdhury, IIT Bombay
Host: Shripad Garge
Title: -
Time, day and date: 5:00:00 PM – 6:00:00 PM, Monday, April 27
Venue: Room 105
Abstract: -

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.

Talk
Speaker: Aditya Dwivedi, IIT Bombay
Host: Rekha Santhanam
Title: A généralisation of the HKR theorem for simplicial vector spaces.
Time, day and date: 11:00:00 AM – 12:00:00 PM, Friday, May 01
Venue: Room 215
Abstract: Hochschild homology, introduced by Hochschild in 1945 remains an important invariant of associative algebras. The theory of Associative algebras has connections to sevelars areas in commutative algebra, algebraic geometry and algebraic topology. In their 1962 paper, Hochschild, Konstant and Rosenberg proved a landmark result in this area which is now known as the HKR-theorem. Several generalisations have been done of the HKR theorem to highlight connections with the de Dham complex, Andre Quillen homology and cyclic homology.

In this talk, we present the work of Pirashvilli(2000) proving a version of HKR theorem for simplicial k vector spaces. The proof defined stable homotopy groups of such objects and the classical HKR theorem follows from the general case.