In this talk, we will discuss a systematic approach to gravitational waves generated by localized sources in de Sitter spacetime, starting from quadrupolar radiation and moving toward a general multipolar framework. We will first review the geometry of de Sitter spacetime and explain how it modifies the standard flat-space description of radiation. Next, we will discuss de Sitter Teukolsky waves and demonstrate their relation, through explicit gauge transformations, to other quadrupolar solutions in the literature. We will explain how a consistent truncation of the source multipole expansion can be performed while preserving stress-tensor conservation and the generalized harmonic gauge conditions, alongside its asymptotic Bondi description. Going beyond the quadrupole, we will describe the construction of the source-generated metric through octupolar order, including its electric and magnetic ($\ell=3$) sectors. Finally, we will present recent work extending this construction to arbitrary multipole order using an exact map to an auxiliary flat-space problem. The resulting framework provides a systematic starting point for studying gravitational radiation and its observables at arbitrary multipole order in an accelerating background.

Neutrino Astronomy started with the observation of Solar neutrinos and then the Supernova neutrinos. Establishing that neutrinos are massive through the observation of neutrino oscillations led to neutrino physics becoming an integral part of astrophysics. The kilometer-cubed size detector IceCube has taken the astrophysical role of neutrinos  further by detecting extremely high energy neutrinos from extra galactic sources. This has also led to the concept of Multi-Messenger astronomy. In this talk, I will describe some of the highlights of IceCube results and how we hope to learn more about the universe from these results.

A classical theorem of Kronecker states that the Mahler measure, $M(P) = 1$ for any monic, irreducible polynomial with integer coefficients if and only if $P$ is a $n$-th cyclotomic polynomial for some natural number $n$. If a monic irreducible polynomial $P(x)\in \mathbb{Z}[x]$ with $P(0) e 0$ which is not a cyclotomic polynomial, then $M(P) > 1$. In 1933, D. H. Lehmer posed the following problem. Does there exist a positive constant $c$ such that $M(P) \geq 1+c$ for all monic, polynomial $P$ with $P(0) e 0$ and integer coefficients? Recently, we proved the following results. Let $\mathcal{P}$ be the collection of all monic, irreducible non-cyclotomic polynomials $P$ of degree $d\geq 1$ with integer coefficients and $P(0) e 0$. For a given prime $p$, we partition $\mathcal{P} = \bigcup_{R\geq 0} \mathcal{P}_{p,R}$. Then for a fixed $R\geq 0$, we prove Lehmer's Problem for all primes $p$. Also, for any fixed prime $p$ and $d$ large enough, we proved a quantitative uniform lower bound for the Lehmer's Problem by varying $R\leq d/\log d$. We also note that Lehmer's problem is equivalent to prove a uniform lower bound by varying $R\leq d-1$ and for any fixed prime $p$. In this talk, we discuss the proof of a case when $R = 1$. This is a joint work with Piyush Kumar Jha.

******************* Zoom Link to Join: https://zoom.us/j/9071552168?omn=91327579187 Meeting ID: 907 155 2168 Passcode: 813471 ******************* The world we live in is composed of chemicals, which can have either beneficial or harmful effects on human health. Beyond chemical exposures, physical environmental factors, such as ultraviolet (UV) radiation, can also influence human health. Among the beneficial chemicals are plant secondary metabolites, which often serve as defence mechanisms in plants, and can have therapeutic applications. In contrast, endocrine-disrupting chemicals (EDCs), which are present in many everyday products, can interfere with normal endocrine function. Against this background, my thesis addresses two objectives: (a) to characterise the natural product chemical space and investigate its therapeutic relevance, and (b) to characterise biological responses to environmental exposures and investigate chemical-target activity relationships. To address the first objective, we curated the chemical profiles of essential oils from aromatic Indian medicinal plants, along with extensive metadata, and made the data available through the sCentInDB database (https://cb.imsc.res.in/scentindb/). We analysed the structural and scaffold diversity of the chemical space using chemical similarity networks and cyclic systems retrieval curves. Our analyses showed that sCentInDB exhibits a level of chemical diversity comparable to that of other aroma-related databases. This resource can support research relevant to the conservation of aromatic medicinal plants, the establishment of quality standards for essential oils, and applications in the perfumery, flavouring, and pharmaceutical industries. We further explored how integrating traditional medicinal knowledge with phytochemical information could facilitate the investigation of therapeutic applications. To this end, we updated IMPPAT, a database of Indian medicinal plants, their phytochemicals, and their therapeutic uses at the plant-part level, to build IMPPAT 3.0. The updated database incorporates information on single herbal drugs (SHDs) and polyherbal formulations (PHFs) used in Ayurveda. The compiled data is accessible via https://cb.imsc.res.in/imppat/. Also, the data is used to develop a knowledge graph, IMPPAT-KG. Lastly, we demonstrated the utility of IMPPAT 3.0 through a network medicine analysis of SHDs indicated for rheumatoid arthritis. To address the second objective, we first curated information on the differential expression of biomolecules, including genes, proteins, metabolites, and microRNAs (miRNAs), in response to UV radiation. This information is available through the UVREK database (https://cb.imsc.res.in/uvrek/). We performed enrichment analyses to identify the biological processes, molecular functions, and pathways associated with UV responses. This FAIR-compliant database provides a resource for investigating the molecular responses to UV exposure and identifying candidate biomarkers that may contribute to risk stratification and the detection of UV-associated disorders. We then shifted our focus from physical to chemical exposures by investigating the structure-activity relationships of environmental chemicals which can bind to multiple endocrine receptors. Data from the ToxCast project are widely used to develop computational models for predicting the biological activities and potential toxicity of environmental chemicals. We investigated activity cliffs in these data, which are structurally similar chemicals that exhibit substantial differences in activity. We also identified instances in which multitarget activity cliffs corresponded to matched molecular pairs (MMPs). Structural classification of these cliffs provided insights into the chemical features associated with changes in receptor activity. Altogether, my thesis characterises two aspects of chemical space relevant to human health: the therapeutic potential of natural products and the biological effects of environmental stressors. By developing curated FAIR-complaint databases and applying computational and network-based analyses, this work contributes resources and methods for exploring the therapeutic relevance of natural products and understanding biological responses to physical and chemical environmental exposures.