Seminars

TN Academy of Science Event

Consider any isolated region of the universe as our object of study. If we wish to predict the future of this region and postdict its past, we might expect that we will need to make observations everywhere in this region. However, recently, we have come to suspect a radical departure from this expectation. In this talk, I will provide an accessible introduction to the idea that all the information in any such region could be available to observers who are only on its boundary. Dynamical information about interactions occurring in the region is also seen to be encoded in the boundary correlators. We describe our progress towards making the computation of such correlators directly in position space tractable. We find that all correlators can be cast as if they were derived from the more symmetric conformal field theories. This representation provides a new approach to computing observables for non-gravitational processes too, such as those regularly probed in colliders. We are also led to a novel principle that organizes the usual approach to such computations via momentum space Feynman diagrams.

The study of exotic smooth structures on manifolds is a fundamental problem in differential topology. In particular, the classification of smooth structures on a given smooth manifold is closely related to the concordance inertia group, a subgroup of the group of homotopy spheres. In this talk, I will compute the concordance inertia group of the product of a closed, oriented, smooth 4-manifold with a k-sphere, where k ranges from 1 to 10, using the stable homotopy type of the 4-manifold and known computations of the stable homotopy groups of spheres. These results lead us to a classification, up to concordance, of all smooth manifolds that are homeomorphic to such products. As an application, I will present a complete diffeomorphism classification of smooth manifolds that are homeomorphic to the product of the complex projective plane with a standard sphere of dimension 4, 5, or 6.

Two-dimensional electron systems (2DESs) in a strong magnetic field host a rich variety of interacting ground states, including the celebrated fractional quantum Hall effect (FQHE), Wigner crystals (WC), and bubble and stripe phases. Since the discovery of the quantum Hall (QH) effect in GaAs-based 2DES nearly four decades ago, the field has remained an active area of research. Advances in the quality of GaAs heterostructures, along with the emergence of new platforms such as graphene heterostructures and ZnO-based 2DES, have further broadened the landscape of quantum Hall physics, unveiling novel correlated phases. This thesis presents a study of various interacting phases in the QH regime. Most of the prominent FQHE states of electrons in the lowest Landau level (LLL) are conveniently described in terms of non-interacting emergent topological particles known as composite fermions (CFs), with a few exceptions, such as the recently observed FQHE state at Landau level (LL) filling $4/13$ in graphene. Using the parton framework, which generalizes the CF theory, we propose a ground state wave function for the unconventional FQHE state at $4/13$ and compute its low-lying neutral excitations, unveiling the state’s microscopic structure. We further elucidate the topological properties of the state, including its elementary fractional charges and their Abelian braiding statistics, the number of chiral gapless edge modes, and the degeneracy of the ground state on a genus $g-$surface, among other characteristics. The energy gap to neutral excitations determines the stability of an FQHE state. Earlier calculations of neutral excitations based on the single-mode approximation (SMA) and the composite fermion exciton (CFE) approach suggested that for non-Laughlin primary Jain states at fillings $n/(2n{\pm}1)$ with $n{>}1$, the SMA gap does not provide an accurate description of neutral excitations at any wavelengths, unlike for Laughlin states where it is known to work for small to intermediate wave numbers. In contrast, recent numerical studies for small system sizes indicate that the long-wavelength SMA gap and CFE gap are approximately equal for these states. To resolve this apparent discrepancy, we compute the SMA gap on the sphere semi-analytically for large system sizes and demonstrate that it closely matches the CFE gap for non-Laughlin primary Jain states in the long-wavelength limit. In doing so, we derive a closed algebra of LLL-projected density operators on the sphere, analogous to the Girvin-MacDonald-Platzman algebra in planar geometry. Additionally, we revisit the earlier SMA gap calculations, identify the origin of the long-wavelength discrepancy, and propose a suitable modification to correct it. Graphene heterostructures provide a versatile platform for tuning the electronic band structure by varying the number of stacked graphene layers, which, in turn, modifies the LL eigenstate structure. The interaction energy of FQHE liquids and electron solids, such as WC and bubble phases, depends sensitively on the form of LL eigenstates, influencing their stability within a given LL. This motivates us to investigate the stability phase diagram of electron solid phases in several LLs of bilayer and trilayer graphene. Additionally, we study the competition between electron solids and Laughlin FQHE liquids to map out their relative stability in different LLs.

Deinococcus radiodurans R1 is the most radioresistant bacterium on earth, and can withstand high doses of ionizing radiation because of its efficient reactive oxygen species (ROS) management strategy. Recent scientific exploration have focused on understanding the ROS management mechanisms in D. radiodurnas. Notably, the absence of a well-curated genome-scale metabolic model (GEM) alongside a comprehensive map of the ROS metabolism constrains the systems-level exploration of the extreme radio-resistance exhibited by this bacterium. Our aim is to better understand the biochemical signatures of D. radiodurans R1, driving its extreme radio-resistance ability using genome-scale metabolic modelling. We have constructed the first genome-scale metabolic model (Dra_iPK792) for D. radiodurans with comprehensive information on ROS metabolism to obtain a systems-level understanding of the extreme radio-resistance exhibited by this bacterium.

In the first few microseconds after the Big Bang, the universe was filled with an extremely hot and dense phase of QCD matter known as the Quark-Gluon Plasma (QGP). This primordial state of matter is now recreated in heavy-ion collisions at RHIC and the LHC. When high-energy quarks or gluons—collectively known as partons—traverse the QGP, they interact with the medium before fragmenting into collimated sprays of hadrons, known as jets. The phenomenon of jet quenching, referring to the energy loss and modification of jets due to these interactions, is a key signature of QGP formation. Recent results from the STAR experiment provide new insights into jet-medium interactions in heavy-ion collisions. In this talk, I will highlight these observations, discuss their implications for our understanding of QCD under extreme conditions, and explore open questions and future directions related to jet quenching and the in-medium evolution of parton.

Cities are vibrant examples of complex systems, where infrastructure, mobility, communication, and contagion all emerge from decentralized human behavior. In this talk, I’ll show how a physics-based approach, rooted in network theory, scaling laws, and information theory, can reveal unifying principles behind the structure and dynamics of urban life. We’ll explore how social connectivity explains observed scaling laws in productivity and innovation, and how mobility patterns—measured through mobile phone and GPS data—can inform models of epidemic spread. I’ll introduce the Movement–Interaction–Return (MIR) model, which captures how local motion and interaction drive contagion dynamics, with direct applications to COVID-19 policy. Finally, I’ll discuss entropy-based measures of predictability and information flow in cities. Together, these ideas point to a broader understanding of how order and adaptability arise from movement and interaction in complex environments.

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.