Abstract: Round Surgery Diagrams for 3-manifolds.

In this talk, we introduce round surgery diagrams in S^3 as a natural analogue of Dehn surgery diagrams for constructing 3-manifolds. We establish a precise correspondence between a natural class of round surgery diagrams and Dehn surgery diagrams in S^3. Consequently, every closed connected oriented 3-manifold can be obtained by round surgery on a framed link in S^3, recovering Asimov’s result. Different round surgery presentations can yield the same 3-manifold. We define four local moves on round surgery diagrams and prove that any two diagrams presenting the same 3-manifold are related by a finite sequence of these moves, yielding a Kirby Calculus for round surgery. As an application, we show that 3-manifolds obtained by round 1-surgery on two-component fibred links in S3 admit taut foliations, hence carry tight contact structures. This is a joint work with Dr. Prerak Deep and part of his doctoral thesis.

About the speaker: Dr. Dheeraj Kulkarni is an assistant professor of mathematics at IISER Bhopal. He received his Ph. D. in 2012 from IISc Bengaluru under the supervision of Professor Siddhartha Gadgil. His research interests are in Geometry and Topology, and in particular Contact and Symplectic Topology.

More about him: https://sites.google.com/iiserb.ac.in/dheerajkulkarni

Abstract: The routes to chaos and the global bifurcations leading to chaotic behavior are two fascinating areas of research in nonlinear dynamics.
Chaotic dynamics are observed in a wide range of mathematical models across various disciplines of science and engineering. In recent years, the structural sensitivity of models with respect to their bifurcation structures leading to chaos has received increasing attention. The main objective of this talk is to discuss the structural sensitivity of the bifurcation structure associated with the classical Hastings–Powell model and the global bifurcations that give rise to chaotic regimes in the modified Lorenz system. A systematic bifurcation analysis, incorporating both local and global bifurcations, provides deeper insights into the routes to chaos and the nature of transient dynamics. The techniques discussed here can also be applied to problems arising in other areas of science and technology.

About the speaker: Dr. Malay Banerjee is a Professor in the Department of Mathematics and Statistics at IIT Kanpur, where he has served since April 2008. His research interests include: Mathematical Ecology, Nonlinear Dynamics, Mathematical Epidemiology, Spatio-temporal Pattern Formation. Dr. Banerjee earned his Ph.D. in Applied Mathematics from the University of Calcutta in 2005.

Abstract: Life is full of complex, evolving systems — from markets to environmental systems. Using tools from mathematics, statistics, physics, and AI, scientists can unravel patterns hidden within large datasets. This talk would offer a glimpse into how we decode real-world complexity using data science.

About the speaker: Dr. Anirban Chakraborti is a Professor at Jawaharlal Nehru University and a Fellow of the World Academy of Sciences (FTWAS). He is a founding member of the Centre for Complexity Economics, Applied Spirituality and Public Policy at O. P. Jindal Global University, and an International Member of the Centro Internacional de Ciencias AC. His work focuses on complexity science, econophysics, and computational approaches to social and economic systems.

More about him and his group: http://www.jnu.ac.in/Faculty/anirban/index.html