Let $X$ be a complex toric variety equipped with the action of an algebraic torus $T$, and let $G$ be a complex linear algebraic group. We classify all $T$-equivariant principal $G$-bundles $\mathcal{E}$ over $X$ and the morphisms between them. When $G$ is connected and reductive, we characterize the equivariant automorphism group $\text{Aut}_T(\mathcal{E} )$ of $\mathcal{E}$ as the intersection of certain parabolic subgroups of $G$ that arise naturally from the $T$-action on $\mathcal{E}$. We then give a criterion for the equivariant reduction of the structure group of $\mathcal{E}$ to a Levi subgroup of $G$ in terms of $\text{Aut}_T(\mathcal{E} )$. We use it to prove a principal bundle analogue of Kaneyama's theorem on equivariant splitting of torus equivariant vector bundles of small rank over a projective space. When $X$ is projective and $G$ is connected and reductive, we show that the notions of stability and equivariant stability are equivalent for any $T$-equivariant principal $G$-bundle over $X$.

Jyoti Dasgupta Bivas Khan Indranil Biswas Arijit Dey Mainak Poddar

Realization of noncentrosymmetric magnetic Weyl metals is expected to exhibit anomalous transport properties stemming from the interplay of unusual bulk electronic topology and magnetism. Here, we present spin-valve-like magnetoresistance at room temperature in ferrimagneticWeyl metal Mn$_2$PdSn that crystallizes in the inverse Heusler structure. Anomalous magnetoresistance display dominant asymmetric component attributed to domain wall electron scattering, indicative of spin-valve-like behavior. Ab initio calculations confirm the topologically non-trivial nature of the band structure, with three pairs of Weyl nodes proximate to the Fermi level, providing deeper insights into the observed intrinsic Berry curvature mediated substantial anomalous Hall conductivity. Our results underscore the inverse Heusler compounds as promising platform to realize magnetic Weyl metals/semimetals and leverage emergent transport properties for electronic functionalities.

Arnab Bhattacharya Mohammad Rezwan Habib Afsar Ahmed Biswarup Satpati Samik DuttaGupta Indra Dasgupta Indranil Das

Ti/Al multilayer thin films with precise thickness have been deposited using a combination of dc and rf magnetron sputtering techniques. Cross-sectional transmission electron microscopy (TEM) revealed unmixed fifteen parallel and alternate layers of Ti and Al with sharp interfaces, each measuring 27 nm and 15 nm in thickness, respectively. The Ti layer was composed of hcp and fcc phases while the Al layer was fcc. Both x-ray diffraction (XRD) and selected area electron diffraction (SAED) analysis confirmed the identity of these phases. Detection of fcc-Ti in as-deposited the Ti/Al multilayer thin film by XRD established that the fcc-Ti phase is not an artifact of TEM sample preparation, as have been envisaged by some of the previous researchers. The fcc-Ti phase appeared when dual rf guns were used for Ti deposition and the diffraction peak intensity corresponding to fcc phase increased when the gun power was raised. A modified equation of state based thermodynamic analysis confirmed that the formation of hcp phase as opposed to the thermodynamically stable fcc phase of pure Ti is due to crystallite size reduction and not impurity driven.

Ramaseshan Rajagopalan Arup Dasgupta Ramachandran Divakar Sitaram Dash Nithya Ravindran Saroja Saibaba Ashok Kumar Tyagi Supriya Bera Indranil Manna

In a recently developed microscopic mean field theory, we have shown that the dynamics of a system, when described only in terms of its pair structure, can predict the correct dynamical transition temperature. Further, the theory predicted the difference in dynamics of two systems (the Lennard-Jones and the WCA) despite them having quite similar structures. This is in contrast to the Schweizer-Saltzman (SS) formalism which predicted the dynamics of these two systems to be similar. The two theories although similar in spirit have certain differences. Here we present a comparative study of these two formalisms to find the origin of the difference in their predictive power. We show that not only the dynamics in the potential energy surface, as described by our earlier study, but also that in the free energy surface, like in the SS theory, can predict the correct dynamical transition temperature. Even an approximate one component version of our theory, similar to the system used in the SS theory, can predict the transition temperature reasonably well. According to our analysis, the absence of the Vineyard approximation in the SS formalism led it to predict similar dynamics for the two systems. Interestingly, we show here that despite the above mentioned shortcomings the SS theory can actually predict the correct transition temperatures. Thus microscopic mean field theories of this class which express dynamics in terms of the pair structure of the liquid while being unable to predict the actual dynamics of the system are successful in predicting the correct dynamical transition temperature.

Indranil Saha Manoj Kumar Nandi Chandan Dasgupta Sarika Maitra Bhattacharyya

The space of Hodge cycles of the general Prym variety is proved to be generated by its Neron-Severi group.

Indranil Biswas Kapil H. Paranjape

We investigate the analog of holomorphic vector bundles in the context of Sasakian manifolds.

Indranil Biswas Georg Schumacher

The aim here is to continue the investigation in \cite{AB} of Jacobians of a Klein surface and also to correct an error in \cite{AB}.

Pablo Arés-Gastesi Indranil Biswas

The paper deals with the reformulation of quantum uncertainty relation involving position and momentum of a particle on the basis of the Kerridge measure of inaccuracy and the Fisher information.

Indranil Chakrabarty

In ``Ramified G-bundles as parabolic bundles'' (J. Ramanujan Math. Soc. (2003) Vol. 18) with Balaji and Nagaraj we introduced the ramified principal bundles. The aim here is to define the Higgs bundles in the ramified context.

Indranil Biswas

The stratified vector bundles on a smooth variety defined over an algebraically closed field $k$ form a neutral Tannakian category over $k$. We investigate the affine group--scheme corresponding to this neutral Tannakian category.

Indranil Biswas