Thesis defense
Speaker: Mr. Umesh Shankar, IIT Bombay
Host: Krishnan Sivasubramanian 
Title: Polynomials arising in permutation enumeration
Time, day and date: 4:00:00 PM – 5:00:00 PM, Tuesday, December 09
Venue: Room 113
Abstract: -

Mathematics Colloquium
Speaker: Akshaa Vatwani, IIT Gandhinagar
Host: Keshav Aggarwal
Title: Multiplicative functions in arithmetic progressions
Time, day and date: 4:00:00 PM – 5:00:00 PM, Wednesday, December 10
Venue: Ramanujan Hall
Abstract: Given an arithmetic function $f:\mathbb N \to \mathbb C$, it is of interest to study whether it is uniformly distributed in residue classes. A well-known example is the Bombieri Vinogradov theorem, which establishes that the primes are equidistributed in arithmetic progressions on average with a level of distribution $1/2$.
In this talk, we discuss a mean-value estimate for trilinear forms involving arbitrary sequences over arithmetic progressions, excluding the contribution of exceptional characters. We prove upper bounds in terms of the $L^{2}$-norms of the corresponding sequences.
As an application, we obtain a Bombieri-Vinogradov type theorem for a broad class of multiplicative functions supported on smooth numbers. In particular, we show that these functions are equidistributed in arithmetic progressions on average over moduli $q \le x^{3/5-\varepsilon}$, if they satisfy a Siegel-Walfisz criterion. This is joint work with Aditi Savalia and Arindam Roy.

Numerical Analysis Seminar
Speaker: Dr Mark Flegg, Monash University
Host: Neela Nataraj
Title: Advancing Scalable Particle-Based Reaction-Diffusion (PBRD) for the Whole-Cell Era.
Time, day and date: 4:00:00 PM – 5:00:00 PM, Thursday, December 11
Venue: Ramanujan Hall
Abstract: Whole-cell modelling (WCM) is a grand challenge for 21st-century science, demanding an interdisciplinary approach to create predictive tools that bridge the gap from fundamental molecular structures to the emergent behaviours of life. While a spatially- resolved model of a minimal cell has recently been proposed, its scalability to more complex cells remain a major hurdle. The most formidable computational bottleneck of these multi- physics, modular, WCMs lies in simulating stochastic reaction-diffusion processes. Reaction- Diffusion Master Equation (RDME) methods, for example the Spatial Gillespie Algorithm, are the most widely used approach but are fundamentally constrained by their reliance on discrete spatial domains. In contrast, Particle-Based Reaction-Diffusion (PBRD) simulations, while offering high spatial resolution and molecular-level stochasticity, have been historically overlooked in favour of RDME methods because the more significant scalability limitations of PBRD methods have typically been considered an insurmountable barrier to advancing WCMs.
This talk will shed light on this scientific blind spot by introducing recent breakthroughs in PBRD methodologies that directly address and overcome its traditional scalability limitations. By exploring the mathematical foundations for how PBRD can efficiently simulate the molecular scale kinetics of increasingly complex cell types, this work pushes the boundaries of what is computationally feasible and paves the way for the next generation of whole-cell simulations.

In this talk, I will introduce several statistical and mathematical models for monitoring the emergence and spread of antimalarial drug resistance. Results will be presented from a geostatistical model that have generated spatio-temporal predictions of resistance based on prevalence data. These data are available only at discrete study locations and times. In this way, I will explain how the model output provides new insight into the spread of drug resistance and unveils new information that existing techniques cannot provide.  I will then discuss how the results of these models have been used to update public health policy, showing how mathematics can help to inform strategies against malaria.