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.