Talks

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.

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.

Climate Change is one of the greatest challenges human beings will face in the 21st century. A large majority of the people do not think climate change is an urgent problem because the impact of climate change is not as dramatic as the COVID epidemic. The impact of climate change will, however, pose an existential threat to all mammals. In this lecture I will discuss the science of climate change. I will show the recent insight from the study of the natural climate change during the past million years indicates that the earth’s climate is not stable and has many tipping points. The ability of human being and other mammals to adapt to global warming beyond 2 degrees C is limited. The high impact but low-probability event like the slowing down of the Atlantic Meridional Ocean Circulation (AMOC) will alter the tropical climate dramatically.

The timing of monsoon season onset and withdrawal is of paramount importance to the population of the Indian subcontinent. Despite the rainy season occurring annually between June and September, the onset and withdrawal dates vary by up to a month from year to year, making accurate predictions a significant challenge.

However, a revolutionary approach has been developed those promises to transform our understanding of this phenomenon. By comprehending the core physical mechanisms involved in monsoon onset and withdrawal, spatial-temporal regularities have been discovered that can be used for forecasting. This approach fundamentally diverges from the traditional numerical weather and climate models by relying on the Nonlinear Dynamics and Nonlinear Phenomena in Statistical Physics.

This approach demonstrated successful results over a rigorous nine-year testing period, forecasting the onset date up to 40 days in advance and the withdrawal date up to 70 days in advance. It is also a...

The critical phenomena occur in the vicinity of the critical point. These phenomena are indicators of an impending critical transition. Earlier methods treated the critical phenomena as early warning signals. However, they do not show any example where early warning signals have been used to avert an impending transition. They have been used in models, experiments or retrospectively.

The talk will present a perspective on how to address this challenge. I will discuss important limitations that must be accepted to build the knowledge needed for better prediction. I will apply the theory of critical transitions to a prediction of the onset and withdrawal dates of the Indian summer monsoon.

The abruptness of the onset and end of the monsoon and its interannual variability within a month are key features of the phenomenon that make monsoon forecasting extremely challenging. I will describe the main principles of monsoon timing prediction and show the cases for central India. Special ...

Carl Sagan’s iconic question, "Who speaks for Earth?" from Cosmos invites us to reflect on whose voices are heard as we contemplate humanity's place in the universe. I will explore this question from the perspective of a queer mathematician, intertwining my personal journey with the broader experiences of LGBTQ+ scientists. Our diverse identities contribute to the richness of the scientific narrative, and by embracing our queerness, we ensure that the full spectrum of experiences is represented in the pursuit of knowledge. Drawing on Sagan’s legacy, I will argue that our voices, and our kindness to each other, are not just necessary but essential in shaping the future of science and our collective understanding of the world.