Seminars

The signal of a stochastic gravitational wave (GW) background has been sought for several decades and has just come within the observational reach through the pulsar timing array. While several sources of GW background have been analysed in the literature, the phenomenon of scalar-induced GW emerges as a simple and inevitable candidate. Scalar-induced GW are highly sensitive to primordial non-Gaussianity, such as three-point and four-point correlations of primordial scalar perturbations. In this talk, I shall discuss the unique signature of chirality imparted to scalar-induced GW by the parity-odd component of the four-point correlation, the trispectrum. The degree of chirality in GW allows us to impose an independent limit on the strength of the parity-odd trispectrum and compare against observational bounds. Our results motivate the treatment of chirality of GW and parity-odd trispectrum as complementary predictions of parity-violating theories. They further supplement our knowledge of primordial non-Gaussianity elicited from CMB and galaxy surveys.

Synopsis talk

In this talk, I will discuss the thermalization phenomena in closed as well as open quantum systems. Starting with the discussion of thermalization in non-integrable closed quantum systems, i.e., the eigenstate thermalization hypothesis (ETH), I will highlight the critical role entanglement plays in achieving it. Afterward, I will shift the discussion to open quantum systems (OQS), as environmental influence is ubiquitous. In the OQS paradigm, I will discuss about our study on thermalization through a more general process, called Quantum Homogenization. I will demonstrate how memory effects (non-Markovianity) of the dynamics affect thermalization, and present a qualitative comparison of the thermalization process for Markovian and non-Markovian dynamics. Finally, I will shed some light on the process of thermalization via post-Markovian dynamics, which is a generalization of Markovian dynamics incorporating the bath memory effects (hence, basically the ensuing dynamics is non-Markovian in nature). Join Zoom Meeting https://zoom.us/j/98206472628 Meeting ID: 982 0647 2628 Passcode: 560304

We formulate a two-sided Guionnet–Jones–Shlyakhtenko construction for a subfactor planar algebra $P$, producing two sequences of tracial, unital algebras that are trace-preservingly isomorphic. Their GNS completions yield a family $M^k$ for $k \geq 0$ of tracial von Neumann algebras. Specializing to the group planar algebra $P(G)$ of a finite group $G$ with $|G|=n>1$, we determine the algebras $M^1$ and $M^2$ using free probability cumulant computations and freeness. Both are interpolated free group factors: $M^1 \cong LF_{2n-1}$ and $M^2 \cong LF_{3-2/n}$. The argument relies on a two-sided trace, bounded left-regular representations, and free-product decompositions, and it identifies them without requiring a separate factoriality proof step.

This discussion will be in the context of the preprint of Harman and Wilson: https://arxiv.org/pdf/2507.14026

In abstract Hodge theory, Deligne’s delta splitting measures how far a mixed Hodge structure is from being real split. An allied notion, developed by S. Bloch, R.Hain et al., is that of a height for a special class of mixed Hodge structures called Biextensions. The notion of a Biextension is closely related to algebraic cycles homologous to zero. Given two such cycles in complimentary codimensions in an ambient smooth and projective variety, a certain cohomology group associated to the pair gives an example of a Biextension mixed Hodge structure. The height associated to such a Biextension is exactly same as the archimedean component of the height pairing of the two cycles developed by Bloch and Beilinson. In an ongoing project, the speaker along with J. I. Burgos Gil and G. Pearlstein has developed a theory of mixed Hodge structures and heights associated to Bloch’s higher cycles that generalizes the above study of Biextensions (see https://doi.org/10.1112/plms.12443 and arXiv:2410.17167 [math.AG], 2024). The purpose of this talk is to review the classical theory of Biextensions and explain the current work on its generalization.