Statistics and Probability seminar
Speaker: Prof. Remco van der Hofstad, Department of Mathematics and Computer Science, Eindhoven University of Technology
Host: Ayan Bhattacharya
Title: Network Science: Structure and Function
Time, day and date: 2:30:00 PM - 5:00:00 PM, Monday, November 24
Venue: Ramanujan Hall
Abstract: Many phenomena in the real world can be phrased in terms of networks. Examples include the World-Wide Web, social interactions and Internet, but also the interaction patterns between proteins, food webs and citation networks. Many large-scale networks have, despite their diversity in backgrounds, surprisingly much in common. Many of these networks are small worlds, in the sense that one requires few links to hop between pairs of vertices. Also, the variability of the number of connections between elements tends to be enormous, which is related to the scale-free phenomenon.

In this lecture series, we describe a few real-world networks and some of their empirical properties. We also describe the effectiveness of abstract network modelling in terms of graphs, and how these models help us to make sense to the empirical findings. We continue by discussing some random graph models for real-world networks and their properties, as well as their merits and flaws as network models. We further discuss the implications of some of the empirical findings on information diffusion, such as the spread of fake news, and competition on such scale-free networks, as well as the local and `almost local' structure of random graphs.

Statistics and Probability seminar
Speaker: Remco van der Hofstad, Department of Mathematics and Computer Science, Eindhoven University of Technology
Host: Ayan Bhattacharya
Title: Network Science: Structure and Function
Time, day and date: 2:30:00 PM - 5:00:00 PM, Tuesday, November 25
Venue: Ramanujan Hall
Abstract: Many phenomena in the real world can be phrased in terms of networks. Examples include the World-Wide Web, social interactions and Internet, but also the interaction patterns between proteins, food webs and citation networks. Many large-scale networks have, despite their diversity in backgrounds, surprisingly much in common. Many of these networks are small worlds, in the sense that one requires few links to hop between pairs of vertices. Also, the variability of the number of connections between elements tends to be enormous, which is related to the scale-free phenomenon.

In this lecture series, we describe a few real-world networks and some of their empirical properties. We also describe the effectiveness of abstract network modelling in terms of graphs, and how these models help us to make sense to the empirical findings. We continue by discussing some random graph models for real-world networks and their properties, as well as their merits and flaws as network models. We further discuss the implications of some of the empirical findings on information diffusion, such as the spread of fake news, and competition on such scale-free networks, as well as the local and `almost local' structure of random graphs.

Special Colloquium
Speaker: Prof. Remco van der Hofstad, Department of Mathematics and Computer Science, Eindhoven University of Technology
Host: Ayan Bhattacharya
Title: Surprises in percolation on random graphs
Time, day and date: 2:30:00 PM - 3:30:00 PM, Wednesday, November 26
Venue: Ramanujan Hall (
Abstract: Percolation is a model for random damage to a network. It is one of the simplest models that displays a phase transition: when the network is severely damaged, it falls apart in many small connected components, while if the damage is light, connectivity is hardly affected. We study the location and nature of the phase transition on random graphs. In particular, we focus on the connectivity structure close to, or below, criticality, where components display intricate scaling behaviour such that a typical connected component has a bounded size, while the maximal connected component sizes grow like powers of the network size.

We review the recent progress that has been made on percolation on random graphs whose expected adjacency matrix is close to being rank-1, the most prominent examples being the configuration model and rank-1 inhomogeneous random graphs. Time permitting, I will also discuss the surprising phase transition on dynamic random graphs, i.e., random graphs that grow with time, such as uniform attachment models. Remarkably, these two settings behave rather differently. In all cases, the inhomogeneity of the underlying random graph on which we perform percolation is of crucial importance.

In my presentation, I focus on the surprising behaviour of percolation on random graphs with infinite-variance degrees, and on growing random graphs.

[This is joint work with Sayan Banerjee, Shankar Bhamidi, Souvik Dhara, Rajat Hazra, Johan van Leeuwaarden, and Rounak Ray.]

Mathematics Colloquium
Speaker: Sudesh Kaur Khanduja, Panjab University and IISER Mohali
Host: Dipendra Prasad
Title: Newton Polygons and Irreducibility of Polynomials with Integer Coefficients
Time, day and date: 4:00:00 PM - 5:00:00 PM, Wednesday, November 26
Venue: Ramanujan Hall
Abstract: URL attached

Student Seminar
Speaker: Advaith Nair, IIT Bombay
Host: Rekha Santhanam
Title: Proof of when a fibre bundle is a fibration
Time, day and date: 10:30:00 AM – 11:30:00 AM, Thursday, November 27
Venue: Room 113
Abstract: -

Partial Differential Equations seminar
Speaker: Neeraj Rawat, IIT Bombay
Host: Harsha Hutridurga
Title: Stefan problems in dimension one with rapidly oscillating coefficients
Time, day and date: 10:30:00 AM – 11:30:00 AM, Thursday, November 27
Venue: Ramanujan Hall
Abstract: We examine a simple setting involving the one phase and the two-phase Stefan problems in dimension one. We prove existence and uniqueness of classical solutions to these free boundary problems. The novelty of the present work is that we are able to handle rapidly oscillating periodic coefficients (in space).

All interested re cordially welcome.

Student Seminar
Speaker: Ujjwal Kumar, IIT Bombay
Host: Rekha Santhanam
Title: Proof of Quillen's Theorem A.
Time, day and date: 10:00:00 AM – 11:00:00 AM, Friday, November 28
Venue: Room 113
Abstract: In this I talk will introduce concept of geometric realisation of simplicial sets, classifying space of category and then use lemma's related to geometric realisation to prove Quillen's Theorem A

Topology Seminar
Speaker: Aparajita Karmakar, IIT Bombay
Host: Rekha Santhanam
Title: Presheaves and Diagrams on the Burnside 2-categroy
Time, day and date: 11:00:00 AM – 12:00:00 PM, Friday, November 28
Venue: Room 113
Abstract: Mackey functors play a central role in equivariant algebraic topology: classically, they are additive (abelian-group-valued) functors on the Burnside category of a group. In this talk we introduce and explore higher analogues of Mackey functors. Concretely, we replace the Burnside category by the Burnside 2-category, and replace the target category of abelian groups by the 2-categorical world of strict symmetric monoidal (permutative) categories. Our objects of study are then enriched presheaves and diagrams on the Burnside 2-category.
Our principal goal is to establish an equivalence of homotopy theories between these enriched presheaf and diagram categories, paralleling the classical self-duality of the Burnside category. In the 1-categorical setting this self-duality yields both covariant and contravariant structure for Mackey functors. However, in the 2-categorical context the duality fails to hold strictly. To overcome this obstacle, we employ a strictification technique on coloured-operad pseudo-algebras restoring the duality up to equivalence. This approach builds on recent advances in the homotopy theory of enriched Mackey functors.
Thus, the talk will outline the construction of higher Mackey functors, explain why 2-categorical self-duality fails, and present the strictification via operadic methods that recovers an equivalence of homotopy theories — shedding light on how classical Mackey‐theoretic phenomena generalize in a higher-categorical setting.

PDE and Numerical Analysis seminar
Speaker: Chinmay Patwardhan, Karlsruhe Institute of Technology
Host: Harsha Hutridurga
Title: Computational aspects of radiative transfer: from asymptotics to uncertainty quantification
Time, day and date: 11:00:00 AM - 12:00:00 PM, Friday, November 28
Venue: Ramanujan Hall
Abstract: Thermal radiative transfer (TRT) governs phenomena ranging from supernovas in astrophysics to laser-driven fusion experiments in plasma physics. The interaction of radiation and matter involves prohibitively small-time scales, nonlinear coupling, and high-dimensional particle dynamics, making conventional numerical methods prohibitively expensive. Dynamical low-rank approximation (DLRA), combined with asymptotic-preserving discretizations, offers a promising direction, but until now its use for nonlinear TRT has been fundamentally limited: stability regions of existing DLRA integrators are unknown in realistic nonlinear regimes, and coefficient updates remain computationally costly. In this talk I present an asymptotic-preserving, locally conservative, rank-adaptive, and parallel integrator for a macro–micro decomposition-based DLRA of the nonlinear TRT equations. 

Moreover, since reality is rarely deterministic, including uncertainties, stemming from modelling errors, measurement errors, and device errors, in these models provides a more realistic description of the phenomena. Quantifying these is thus essential for robustness and reliability in applications. In this talk, I present a low-rank multilevel Monte Carlo method for quntifying uncertainties in the TRT equations.