16-10-2026
Speaker: Harshita Agarwal
Abstract: Neural networks are usually trained using only examples. But often we also know a simple mathematical rule the answer should follow — even when we don't have much data to work with. This talk introduces Physics-Informed Neural Networks (PINNs): a simple way to teach a network to respect such a rule, using nothing more than ideas we already know — the chain rule and gradient descent. We'll build the idea step by step, from how a basic network learns, to how it can check a rule exactly, and finally see it all come together on one simple example. No physics or PDE background is needed; the talk stays friendly and non-technical throughout, explained through pictures and one running example rather than long derivations.
Time: 4:00 PM–5:00 PM
Venue: Hybrid (Ramanujan hall and Google meet)
09-10-2026
Speaker: Ankita Dargad
Abstract: The classical Ferry Cover problem asks for the minimum boat capacity needed to transport all vertices of a graph across a river such that no edge remains on either bank at any time - a requirement that the banks induce stable (independent) sets. We study a natural generalization in which the banks must satisfy an arbitrary graph property. For hereditary properties such as acyclicity or planarity, we show that the structural characterization of small-boat and large-boat graphs established by Csorba, Hurkens, and Woeginger extends directly.
We then turn to the connected-bank variant, where the property of interest - connectedness - is not hereditary: both banks must induce connected subgraphs throughout the transfer. We provide a complete characterization of graphs that can be transferred with a boat of size one (boat-1 graphs): a connected graph is boat-1 if and only if its block-cut tree is a path. This characterization yields a linear-time recognition algorithm. As a consequence, we show that every biconnected graph is boat-1, since such graphs admit an st-numbering. We also develop an efficient algorithm for determining the boat number of trees. Our work opens new directions for river-crossing problems under non-hereditary bank constraints.
Time: 4:30 PM–5:30 PM
Venue: Hybrid (Ramanujan hall and Google meet)
24-09-2026
Speaker: Samit Pandit
Abstract: To be added.
Time: 5:15 PM–6:00 PM
Venue: Hybrid (Ramanujan hall and Google meet)
11-09-2026
Speaker: Omkar Ramdas
Abstract: You might have heard about the Colored hats guessing game where 'n' players, each wearing a randomly assigned black or white hat, must attempt to guess their own hat color without communicating. A simple strategy easily yields a 50% success rate, so the real question is "Can we improve this success rate significantly?". We will demonstrate how to improve these odds for a large, fixed 'n' by translating the game into a structural problem on the Boolean hypercube $\{0,1\}^n$. We will then use some basic probabilistic methods to get better strategy which will "almost" surely make you win. If time permits, we will see its connections with Hamming codes.
Time: 3:30 PM–4:30 PM
Venue: Hybrid (Ramanujan hall and Google meet)
04-09-2026
Speaker: Madhav Varshney
Abstract: We analyze two-player competitive edge-coloring games played on a complete graph, examining the core theoretical principles governing these graph games. We frame bounds using diagonal Ramsey numbers and apply the Erdős–Selfridge potential argument directly to the edge set of the graph to derive the asymptotic winning thresholds.
Time: 5:15 PM–6:15 PM
Venue: 215
21-08-2026
Speaker: Aditya Dwivedi
Abstract: Magic squares have been studied by thinkers for centuries, often appearing in classical texts across cultures, such as the Lo Shu square, Buduh square, or the bhadra chaturashra. The problem of counting magic squares was also pursued by many thinkers over centuries, often leading to calculations in specific cases (see Al-Ashabb et al., Mandadi et al., Mattingly et al., Dvivedi et al.).
But what happens when we move beyond these specific historical constructions and ask a generalised question: exactly how many n x n magic squares exist for a given line sum r?
This talk explores the surprising bridge between this ancient combinatorial problem and modern commutative algebra. After reviewing the elementary 1 x 1 and 2 x 2 matrices, we will introduce the celebrated Anand-Dumir-Gupta conjectures. Using the Birkhoff-von Neumann theorem, we will construct a specific subring generated by permutation matrices. By analysing the Hilbert series of this ring, we arrive at the elegant final result: the number of n x n magic squares is simply a polynomial in the line sum r.
Time: 3:30 PM–4:30 PM
Venue: Ramanujan Hall
14-08-2026
Speaker: Aditya Khambete
Abstract: Most of you are already familiar with the Strong Law of Large Numbers. But have you ever wondered about how to prove it? The Strong Law of Large Numbers is a fundamental result in probability theory, asserting that normalized partial sums converge almost surely to the expected value. In this talk, I present Etemadi's elementary proof for identically distributed, pairwise independent random variables with finite first moment. The talk would be accessible to anyone who has completed a probability course.
Time: 5:15 PM–6:00 PM
Venue: 114
05-08-2026
Speaker: Ankita Parashar
Abstract: Symmetry appears everywhere in mathematics, from the rotations of a square and a sphere to the hidden structures behind Fourier analysis and number theory. Representation theory provides a powerful language to study these symmetries by translating groups into matrices and linear transformations. In this talk, we will explore how simple geometric symmetries lead to the idea of representations, and their surprising connections to Fourier series and modular forms, which are key objects in the two subjects: Fourier Analysis and Number theory.
Time: 5:30 PM–6:30 PM
Venue: Ramanujan Hall