‘Place-based’ pedagogies are a way to connect students and citizens with our local surroundings, enhance ecological awareness and drive environmental stewardship. In this talk I will describe a ‘River Curriculum’ being developed for school students by Jeevitnadi (Living River Foundation), a citizen-led nonprofit organization in Pune dedicated to reviving the rivers which are a lifeline of the city. https://www.imsc.res.in/outreach/lectures/2026.07.14_JR.png

In this talk, I will discuss the lower bound question for modular circuits, where each gate computes a Boolean function over the sum of its inputs based on the remainder with respect to some modulus. It is a long-standing conjecture that such circuits require large size to compute AND when their depth, and each modulus used in the gates, is restricted to a constant. We study a recently introduced framework of polynomial approximations, called torus polynomials, as a method to make progress on this conjecture. We show how some previous results in this direction, and techniques used for these results, are captured by our method. Finally, we propose an approach to make further progress based on this method. This is a joint work with Jayalal Sarma at CSE, IIT Madras. Speaker Bio: Vaibhav is a postdoctoral researcher at IMSc, Chennai. He completed his PhD from IIT Bombay under the supervision of Sundar Vishwanathan and Nutan Limaye.

Quantified Boolean formulas (QBFs) extend propositional logic by allowing variables to be universally or existentially quantified, naturally capturing two-player games between an existential and a universal player. While the satisfiability of a QBF asks whether the existential player has a winning strategy, the corresponding counting problem (#QBF) asks how many such winning strategies exist. This problem is significantly more challenging than the analogous #SAT problem for propositional formulas. This talk will present proof systems for #QBF, motivated by recent advances in the proof complexity of both QBF satisfiability and propositional model counting. It will begin with a simple baseline proof system for counting Skolem functions, and then examine systems based on the ∀-expansion rule of QBF proof systems. Both these approaches will be shown to have inherent structural limitations that give rise to lower bounds. To overcome these weaknesses, the talk will introduce Q-MICE, a new line-based proof system with sound inference rules for computing and certifying #QBF solutions, inspired by the MICE proof system for #SAT. Finally, the talk will highlight the strength of Q-MICE through several upper-bound results, including quantified versions of formulas that were previously known to be difficult for MICE. These results also separate Q-MICE from the naive #QBF proof systems. Beyond their theoretical significance, these proof systems provide a foundation for certifying and developing future #QBF solvers. This work is in collaboration with Leroy Chew, Vaibhav Krishan and Anil Shukla. It has been accepted for publication in SAT 2026. Speaker Bio: Sravanthi is a postdoctoral researcher at IMSc, Chennai. She completed her PhD from IIT Ropar under the supervision of Anil Shukla.

In algebraic complexity theory, one typically studies algebraic modelsto compute polynomials over fields. As a generalization, one can consider polynomials over semirings; in particular, we’ll focus on min-plus semirings. Polynomials over min-plus semirings are min-of-sums and so, these correspond to several minimization problems (e.g., Travelling Salesman problem). Many dynamic programming algorithms (e.g., Bellman-Held-Karp algorithm for TSP) can be viewed as circuits over min-plus semirings. In this talk, we’ll discuss about algebraic branching programs (which are weaker than circuits) over min-plus semirings. In particular, we’ll talk about ABPs of small width (which are well-studied over fields) over min-plus semirings; here, restricting the width means that only a few DP table entries are allowed to be updated in each round/phase of the algorithm. Finally, we’ll discuss an analogue of the class VNP (which, over fields, is defined as hypercube sums over small circuits) over min-plus semirings, its relationship with VP, and its equivalent definitions in terms of weaker (than circuits) models. This talk will be based on joint discussions with Balagopal Komarath and Jayalal Sarma. Speaker Bio: Harshil is a postdoctoral researcher at IIT Madras. He completed his PhD from IIT Gandhinagar under the supervision of Neeldhara Misra and Balagopal Komarath.

In the theory of projective modules over a commutative ring, a fundamental problem is the existence of a unimodular element. The problem is well understood when the rank of the projective module equals the dimension of the ring, but is much harder when the rank is smaller. It is typically studied via obstructions arising from $K$-theory, Chow(-Witt) groups, Grothendieck-Witt groups, and related invariants. Recent work of Asok, Bachmann, and Hopkins shows that in the corank $1$ case the Chern class in Chow groups gives the correct obstruction for smooth affine algebras over an algebraically closed field of characteristic $0$. In this talk, we consider the corank $1$ situation for an arbitrary ring of dimension $3$. We discuss a result of J. Fasel, where the vanishing of a certain Witt group defined via antisymmetric forms, together with a condition on some orbit space of unimodular elements, provides a positive answer to our question. We also see a few examples.