Pathogen-host interactions are pivotal in the initiation and progression of infectious diseases. Understanding the mechanisms by which pathogens modulate the host immune system, particularly the innate immune response, which remains underexplored in several contexts, is essential for developing effective disease control strategies. A fundamental component of innate immunity is the recognition of pathogen-associated molecular patterns (PAMPs) by pattern recognition receptors (PRRs), which, although initially identified on immune cells, are now known to be ubiquitously expressed across various cell types. PAMPs are evolutionarily conserved molecular motifs present in diverse pathogens, including bacteria, viruses, fungi, and parasites, but absent in host tissues. Examples of common PAMPs include lipopolysaccharides, flagellin, peptidoglycan, and viral nucleic acids. These are specifically recognised by PRRs such as Toll-like receptors (TLRs), NOD-like receptors (NLRs), RIG-I-like receptors (RLRs), and C-type lectin receptors (CLRs). PAMP recognition triggers signalling cascades that activate inflammatory responses, cytokine production, antigen presentation, and the subsequent priming of adaptive immunity. Despite this defence mechanism, many pathogens, both in livestock and humans, have evolved strategies to evade or manipulate host immunity. For example, Mycobacterium bovis inhibits phagolysosome fusion in macrophages and downregulates interferon-gamma responses, facilitating chronic infection, while Bovine herpesvirus disrupts cytokine signalling to establish latency. These immune evasion strategies, especially notable in intracellular pathogens, reflect a continuous evolutionary arms race between host defence and pathogen survival. Our research investigates this dynamic interface using two models: (1) the host-specific response to Peste des petits ruminants virus (PPRV), where sheep and goats are susceptible but cattle and buffaloes exhibit mild subclinical infections with seroconversion; and (2) Bovine Tropical Theileriosis caused by Theileria annulata, which transforms bovine immune cells and promotes a pro-inflammatory and proliferative environment. Through comparative analysis and secretome profiling, we have explored the identification of novel molecules that have potential application in disease control as well as potential therapeutic applications in bovine mastitis

The story began when Marina was doing a STARIS undergraduate research internship with Peter. We were studying transitive but imprimitive permutation groups through their invariant equivalence relations, and were looking at the case where the equivalence relations commute; in our shared office, Rosemary overheard our conversation, and said, “Statisticians know about those things; we call them orthogonal block structures”. An orthogonal block structure is a lattice of commuting uniform equivalence relations. These are combinatorial objects which may have trivial automorphism group. We will discuss the history of how they arose in experimental design. A better behaved special case occurs when the lattice is distributive; these are called poset block structures. They always have a large automorphism group, a generalised wreath product of symmetric groups, described by a poset with a set attached at each of its points. Our main results are a proof that a group preserving a poset block structure is contained in a generalised wreath product of permutation groups defined from the action (an extension of the Krasner–Kaloujnine theorem), and that a generalised wreath product over a poset is the intersection of the iterated wreath products of the same groups over all linear extensions of the poset.

My lecture will focus on a very classical subject: Can a non-trivial solution to a PDE vanish with all its derivatives at a point? I will start with a brief historic overview. ThenI will talk about a new sharp estimate of the order of vanishing of solutions to parabolic equations with variable coefficients. I will then show that an application of such an estimate for real-analytic leading coefficients leads to a novel parabolic Donnelly-Fefferman type nodal set estimate. This is based on joint work with Vedansh Arya and Nicola Garofalo.

The IMSc Foundation Series 2025 in Theoretical Physics is a week-long academic initiative organized by the Outreach Team at the Institute of Mathematical Sciences (IMSc), Chennai. The program is scheduled from 23rd to 27th June 2025 and will offer three intensive short-term courses at the MSc Physics level tailored for early-stage physics students from Chennai and nearby regions. The courses will be delivered by renowned academicians from IMSc Chennai, aiming to bridge the gap between coursework and research. Through these engaging lectures, participants will gain insights into the Master's level topics from a research perspective. Our goal is to inspire the next generation of physicists and encourage them to pursue careers in academic research.

The IMSc Foundation Series 2025 in Theoretical Physics is a week-long academic initiative organized by the Outreach Team at the Institute of Mathematical Sciences (IMSc), Chennai. The program is scheduled from 23rd to 27th June 2025 and will offer three intensive short-term courses at the MSc Physics level tailored for early-stage physics students from Chennai and nearby regions. The courses will be delivered by renowned academicians from IMSc Chennai, aiming to bridge the gap between coursework and research. Through these engaging lectures, participants will gain insights into the Master's level topics from a research perspective. Our goal is to inspire the next generation of physicists and encourage them to pursue careers in academic research.