Talks

The main focus of these pedagogical talks will be on discussing the interplay between statistics and climate science as a two-way street. On one hand, thinking about the climate helps us understand many aspects of statistics, from the fundamental to conceptual to practical. On the other, statistical thinking is crucial and indispensable in studying climate. I will also emphasize that statistics plays an important role not just in climate studies, but more generally in understanding any complex system such as those from biological and social sciences as well. Another thread will be the discussion of interplay between uncertainty and dynamics, with an emphasis on the role of dynamical instabilities.

A brief tour of Chaos in 1-dimensional maps followed by a quick primer on Machine Learning. This will help researchers in Climate Science as there is an increasing use of AI/ML methods in this domain.

Climate networks can be used to forecast some important climate phenomena, such as the monsoon, the North Atlantic Oscillation, El Niño events and cyclones. A percolation framework is used to study the cluster structure properties which brings out the global structural changes in the climate network.

I present the recurrence analysis of temperature and relative humidity data from various locations spread over India, including the mountainous region, coastal region, and central and north eastern parts of India. This study reveals the spatiotemporal pattern underlying the climate dynamics and captures the variations in the complexity of the dynamics over the period 1948 to 2022. By reconstructing the dynamics from data, the recurrence pattern is studied using recurrence networks and the measures of the networks computed using a sliding window analysis on the data sets. This brings out the climate variability in different spatial locations and the heterogeneity across the locations chosen. The variations observed in dynamics can be correlated with reported shifts in the climate related to strong and moderate El Niño–Southern Oscillation events.

The failure to calculate the vacuum energy remains a central problem in theoretical physics. In my talk I present a new understanding of the cosmological constant problem, grounded in the insight that vacuum energy density can be expressed in terms of phase space volume. Introduction of a UV-IR regularization implies a relationship between the vacuum energy and entropy. Combining this insight with the holographic bound on entropy then yields a bound on the cosmological constant consistent with observations. It follows that the universe is large, and the cosmological constant is naturally small, because the universe is filled with a large number of degrees of freedom. The talk is based on our papers Phys.Rev.D 107 (2023) 12, 126016; e-Print: 2212.00901 [hep-th] and Int.J.Mod.Phys.D 32 (2023) 14, 2342004; e-Print: 2303.17495 [hep-th].

Observations of gravitational waves from binary black-hole mergers provide a unique testbed for General Relativity in the strong-field regime. To extract the most information, many gravitational-wave signals can be used in concert to place constraints on theories beyond General Relativity. Although these hierarchical inference methods have allowed for more informative tests, careful consideration is needed when working with astrophysical observations. Assumptions about the underlying astrophysical population and the detectability of possible deviations can influence hierarchical analyses, potentially biasing the results. In this talk, I will address these key assumptions and discuss their mitigation. Finally, I will demonstrate how we can leverage the astrophysical nature of gravitational-wave observations to our advantage to empirically bound the curvature dependence of extensions to General Relativity.

Chern-Simons theory is a topological quantum field theory which leads to link invariants, such as the Jones polynomial, through the expectation values of Wilson loops. The same link invariants also appear in a mathematical construction of Reshetikhin and Turaev which uses a trace on Yang-Baxter operators. Several algebraic structures are involved in these frameworks for computing link invariants, including the braid group, quantum algebras and centralizer algebras (such as the Temperley-Lieb algebra). In this talk, I will explain how the Askey-Wilson algebra, originally introduced in the context of orthogonal polynomials, can also be understood within the Chern-Simons theory and the Reshetikhin-Turaev link invariant construction.

Climate change is often related to the temporal variation of external driving forces, following a certain arbitrary trend. This poses difficulties to the analysis of complex dynamical systems under the impact of climate change, since all the analysis tools of nonlinear dynamics work only for autonomous systems or systems with periodic driving. To study the impact of climate change characterized by arbitrary time- dependence requires new methods to still use ideas of attractors, basins of attraction and bifurcations in the non-autonomous case. We discuss approaches which allow to study non-autonomous systems in the spirit of nonlinear dynamics: snapshot/pullback attractors, non-autonomous basins of attractions and bifurcations in non-autonomous systems like rate-induced transitions and basin boundary crossings. We use simple conceptual models of climate and ecosystem dynamics to illustrate these concepts.