Talks

This lecture journeys through my multidisciplinary art practice grounded in the language of mathematics, mythology and metaphysics. From sacred geometries inspired by temple architecture to recursive drawings based on chess algorithms, my work seeks to bridge the material and the infinite. Influenced by constructs such as the golden ratio, Fibonacci sequences, Penrose tilings, and knight’s tours, my sculptures and drawings embody systems of order that reveal poetic possibilities. This talk will also explore how myth, memory, and cultural frameworks from South India—such as Kolams and cosmological diagrams—become vehicles for visualizing the vast, often hidden structures that underpin reality.
 

Counting the number of divisors of an integer is an interesting question that can be approached in multiple ways. We will explore this question and the multiple streams of thoughts and techniques that originate from it.

In this talk, we will explore the transformative role of artificial intelligence (AI) in modern banking. Since the release of ChatGPT in November 2022, AI technology has seen a rapid evolution. This rapid development has led to a surge in interest and adoption across various sectors. The presentation will explore the mathematical foundations and AI techniques that drive innovative solutions in the banking sector. We will look at how AI-powered solutions have reduced scams and frauds, the application of generative AI in enhancing customer messaging and accelerated decision making.

Optimal foraging theory provides a rich set of predictions for where, what, and how animals should forage in the natural world. These predictions are anchored on maximizing calorie intake while minimizing time and energy costs. However, food is more than calories, and animals should, in fact, be seeking specific protein and carbohydrate intakes to meet (darwinian) fitness goals. In this talk, I will go from classic optimal foraging theory to the nutritional geometry approach to illustrate how wild animals meet nutritional targets. Using our work with insectivorous and herbivorous lizards, I will share how foraging in the wild can be an impressive mathematical task.

‘Luck’ has always been seen as a vague and difficult-to-quantify aspect of sport. Commentators and players often talk about it, but in imprecise terms, putting an approximate ‘gut-feel’ value to its cost to the opposing team. (‘The dropped catch of Virat Kohli cost England at least 30 runs’)

In a collaboration with IIT-Madras, a small team at ESPNcricinfo worked on this aspect as part of a suite of new, in-depth metrics which would help understand better the nuances of T20 cricket. Luck Index attempted to define these specific ‘lucky events’ along with the team that benefited, and then work out the value of that event based on putting together an alternative narrative of what would have transpired in that team innings without that ‘lucky event’.

Luck Index was part of a set of three metrics developed by ESPNcricinfo along with IIT-Madras, the other two metrics being the Forecaster and Smart Stats. The Forecaster is a predictive tool which forecasters team score and win percentages for each team based on the current match situation, while Smart Stats gives impact values to each batting and bowling performance based on detailed match context inputs. These metrics have helped in a better and more nuanced understanding of T20 cricket.

Ordered structures that tile the plane in an aperiodic fashion - thus lacking translational symmetry - have long been considered in the mathematical literature. A general method for the construction of quasicrystals is known as *cut-and-project* ($\mathsf{CNP}$ for short), where an irrational slice "cuts" a higher-dimensional space endowed with a lattice and suitably chosen lattice points are further "projected down" onto the subspace to form the vertices of the quasicrystal. However, most of the known examples of $\mathsf{CNP}$ quasi-tilings are Euclidean. In this talk, after presenting the main ingredients of the Euclidean prescription, we will extend it to Lorentzian spacetimes and develop Lorentzian $\mathsf{CNP}$. This will allow us to discuss the first ever examples of Lorentzian quasicrystals, one in $(1+1)$- and another in $(1+3)$-dimensional spacetime. Finally, we will argue why the latter construction might be relevant for *our Lorentzian spacetime*. In particular, we shall appreciate how the picture of a quasi-crystalline spacetime could provide a potentially new string-compactification scheme that can naturally accommodate for the hierarchy problem and the smallness of our cosmological constant. Lastly, we will comment on its relevance to quantum geometry and quantum gravity; first, as a conformal Lorentzian structure of no intrinsic scale, and second through the connection of quasicrystals to quantum error-correcting codes.

Modern quantum simulations methods often use a fictitious imaginary time introduced by Feynman to exactly transform static quantum problems to dynamic imaginary time classical ones [1]. In addition to imaginary time simulation methods such as centroid molecular dynamics and path integral Monte Carlo, one can apply this quantum-classical isomorphism to self-consistent field theory (SCFT). An advantage of the field-theoretic perspective is that it can be exactly transformed into quantum density functional theory (DFT), meaning that the theorems of DFT (Hohenberg-Kohn and Mermin theorems) prove an equivalence between classical imaginary time SCFT dynamics and static quantum results [2]. Since imaginary time is assigned the same properties as regular time, one can replace the imaginary time in the SCFT equations with real time (a Wick rotation), which gives the equations of time-dependent DFT. The time-dependent DFT theorem (Runge-Gross theorem) then proves that one obtains all results of standard quantum mechanics from this imaginary time classical starting point. These results make it very tempting to consider treating imaginary time as an element of reality. This quantum reconstruction from imaginary time will be discussed, including a speculative look at treating imaginary time in the context of special relativity, with a preliminary comparison to the deformed special relativity of Magueijo and Smolin. [1] D. M. Ceperely, Reviews of Modern Physics 67, 279 (1995) [2] R. B. Thompson, Journal of Chemical Physics 150, 204109 (2019) [3] J. Magueijo and L. Smolin, Physical Review D 67, 044017 (2003)