Upcoming Talks

Title: Cut Locus, Injectivity Radius, and their Stability

Speaker:  Dr. Arita Bhowmick (Kerala School of Mathematics)

Venue: Ramanujan Hall, Department of Mathematics
Date and Time: 17 August 2026, (Monday) ,15:00 pm
Abstract:
Given a fixed point p on a Riemannian manifold (M, g), the cut locus Cut(p, g) is the collection of points q in M such that there exists a distance- minimizing geodesic from p to q, any extension of which fails to be distance- minimizing from p. In a sense, the nontrivial topology of the manifold is contained in the cut locus of a point: if one removes the cut locus, then what remains is diffeomorphic to an open ball of appropriate dimension. More generally, we shall define the cut locus of a submanifold N ⊂ M, and the distance between them is defined as the injectivity radius of N.
In the first part of the talk, we shall define the cut locus and some related concepts. We shall see examples to demonstrate the importance of studying the cut locus. Then, in the second part, we shall see how the injectivity radius behaves continuously if we perturb the metric. As a consequence, we shall get the Hausdorff stability of the cut locus as well. Once the technical definitions are over, the heart of the proofs are quite elementary.
Everyone is cordially welcome! There will be pictures.

Title: Recent Advances in AI-Assisted Mathematics: From Mathematical Discovery to AI Safety

Speaker:  Dr. Gautam Memana (incoming postdoc at Australian National University) 

Venue: Ramanujan Hall, Department of Mathematics
Date and Time: 18 August 2026, (Tuesday),15:00 pm
Abstract:
Recent progress in artificial intelligence has opened new avenues for mathematical discovery. I will survey several examples in which large language models, neural networks, and interpretable machine-learning methods have been used to discover proofs, conjectures, patterns, examples, and counterexamples. These include the discovery of hidden patterns in arithmetic data, the use of interpretable algorithms to turn numerical observations into theorems, and recent examples of large language models solving longstanding conjectures in mathematics. I will talk about some of my own experiments using neural networks to explore open combinatorial problems.
I will then turn the question around: rather than asking how AI can help us understand mathematics, what role can mathematics play in understanding AI? This leads naturally to questions of interpretability and AI safety. I will discuss some ways in which mathematicians can contribute to these problems, and briefly discuss some of my own work related to these questions. The broader theme is that mathematical ideas may help us better understand the behavior of increasingly capable AI systems, as well as the limitations of our current explanations of them.