Abstract: Random processes with strong memory arise naturally in various disciplines including physics, economics, biology, geology, etc. Memory can be multifaceted and can arise due to interactions of more than one underlying phenomena. Many of these processes exhibit superdiffusive growth due to the effect of memory. A class of one-dimensional, discrete-time such models called “random walk with m memory channels” was introduced and discussed in a recent paper on statistical physics by Saha (2022). In these models, the information of m independently chosen steps from the walker’s entire history is needed to decide the future step. The aforementioned work carried out heuristic calculations of variance, and conjectured phase transitions from diffusive to superdiffusive and from superdiffusive to ballistic regimes in the m=2 case. We have proved these conjectures rigorously (with mild corrections), and discovered a new regime at one of the transition boundaries. These results will be presented along with several open problems. (This talk is based on a joint work with Krishanu Maulik and Tamojit Sadhukhan.)
About the speaker: Dr. Parthanil Roy is a Professor in the Department of Mathematics at Indian Institute of Technology Bombay.
He joined IIT Bombay in 2024 after serving as a Professor at the Indian Statistical Institute (ISI), Bangalore, where he held various positions from Assistant Professor to Professor over more than a decade.
He obtained his Ph.D. from Cornell University in 2007 under the supervision of Gennady Samorodnitsky and held a postdoctoral position at ETH Zurich before beginning his academic career at Michigan State University.
His research interests lie in probability theory and related areas, including stable random fields, extreme value theory, ergodic theory, and stochastic processes. He is also a recipient of the SwarnaJayanti Fellowship (2017) in mathematical sciences.
More about him: https://sites.google.com/view/parthanilroy/
Abstract: Fix integers g, n, d and consider the space of all degree d maps from smooth projective curves of genus g to projective n-space. A theorem of Gromov and Kontsevich says that, in order to compactify this space, it suffices to allow the domains of our maps to be at-worst-nodal projective curves of arithmetic genus g. After recalling this theorem, I will discuss some results in the converse direction (obtained in joint work with Fatemeh Rezaee), i.e., given a map from a nodal curve, how can we tell if it actually arises as the limit of a sequence of maps from smooth curves?
About the speaker: Dr. Mohan Swaminathan is a Reader at the School of Mathematics at the Tata Institute of Fundamental Research, Mumbai.
Previously, he was a Szegö Assistant Professor at Stanford University (2022-2025), a graduate student at Princeton University (2017-2022) and an undergraduate at Chennai Mathematical Institute (2014-2017). His research interests are in Symplectic Topology and Enumerative Geometry.
More about him: https://sites.google.com/view/mohanswaminathan/home
Abstract: Subfactors arise naturally in the study of symmetries in mathematics and mathematical physics.
While a single subfactor already carries rich structure, considering two subfactors inside the same system leads to new and subtle questions: how do they interact, and how can this interaction be measured?
In this talk, I will describe two complementary viewpoints. One uses a notion of entropy to quantify the amount of information shared between subfactors. The other uses diagrammatic tools, known as planar algebras, to describe their structural compatibility. I will explain how these approaches illuminate each other and lead to a clearer picture of how subfactors relate and interact.
No prior background in subfactor theory will be assumed.
About the speaker: Dr. Keshab Chandra Bakshi is an associate professor at IIT Kanpur specializing in $C^{*}$-algebras and von Neumann algebras; more specifically in Jones' theory of subfactor and planar algebras. He received his Ph. D. from the Institute of Mathematical Sciences under the supervision of Professor V. S. Sunder. More about him: https://sites.google.com/view/keshab-bakshi/home
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About the speaker: Dr. Swarnendu Sil is an assistant professor at IISc Bangalore, specializing in geometric analysis, partial differential equations and calculus of variations. After transitioning from a background in engineering at Jadavpur University to a Ph. D. at EPFL, he held postdoctoral positions at both EPFL and ETH Zürich. More about him: https://math.iisc.ac.in//~ssil/
Abstract: Increasingly large and complex spatial datasets pose massive inferential challenges due to high computational and storage costs. Our study is motivated by the KAUST Competition on Large Spatial Datasets 2023, which tasked participants with estimating spatial covariance-related parameters and predicting values at testing sites, along with uncertainty estimates. We compared various statistical and deep learning approaches through cross-validation and ultimately selected the Vecchia approximation technique for model fitting. To overcome the constraints in the R package GpGp, which lacked support for fitting zero-mean Gaussian processes and direct uncertainty estimation, two features necessary for the competition, we developed additional R functions. Additionally, we implemented subsampling-based approximations and parametric smoothing for estimators with skewed sampling distributions. Our team, DesiBoys, comprised of Rishikesh Yadav, currently an Assistant Professor at IIT Mandi, Pratik Nag, currently a Postdoctoral Fellow at the University of Wollongong, and I from IIT Kanpur, secured first place in two of the four sub-competitions and second place in the other two, validating the effectiveness of our proposed strategies. Moreover, we extended our evaluation to a large, real-world spatial satellite-derived dataset of total precipitable water, comparing the predictive performance of different models using multiple diagnostics. If time permits, we will discuss additional experiences with various data challenge competitions that we successfully participated in over the last few years.
About the speaker: Dr. Arnab Hazra is an assistant professor at IIT Kanpur. He received his Ph. D. in 2018 from North Carolina State University, Raleigh. His research interests are too numerous to list in such a short introduction; please see his webpage for more details: https://sites.google.com/view/arnabhazra09/home
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