Topology seminar
Speaker: Udit Mavinkure, IIT Bombay
Host: Rekha Santhanam
Title: Quasicategories vs. Segal Spaces, Part 3
Time, day and date: 2:30:00 PM – 3:30:00 PM, Thursday, August 20
Venue: Room 215
Abstract: This talk is the third installment in a four-part expository series on higher category theory. The goal of the series is to establish the following result of Joyal and Tierney: the Joyal model structure for quasicategories and the Rezk model structure for complete Segal spaces are Quillen equivalent. (NB: Newcomers are welcome; background from the April and May talks will not be assumed!)

We will begin with a brief recap of quasicategories: their definition, and how they generalize ordinary categories. We will then discuss the Joyal model structure, and its specific properties that enable a straightforward description of its simplicial completion, à la Cisinski.

PDE and Numerical Analysis seminar
Speaker: Ketan Savla, University of Southern California
Host: Harsha Hutridurga
Title: LQR for finite extent linear evolution PDEs.
Time, day and date: 4:00:00 PM – 5:00:00 PM, Thursday, August 20
Venue: Ramanujan Hall
Abstract: We consider the linear quadratic regulator (LQR) problem for linear evolution PDEs on a bounded spatial interval, with control entering as an additive forcing term and arbitrary boundary data. Classical frequency-domain approaches to LQR for PDEs rely on the real-frequency Fourier transform, and work cleanly only on unbounded domains or under homogeneous boundary conditions; applied naively on a finite interval, they produce a control law that depends on future, unspecified boundary values. We resolve this using the unified transform of Fokas, which extends the Fourier transform on a bounded domain to complex frequencies. Decoupling the PDE in this complex frequency variable and solving the resulting family of finite-dimensional LQR problems yields a closed form control law; deforming the associated frequency integrals onto suitable contours in the complex plane then eliminates all dependence on the unknown boundary data. For the reaction-diffusion equation, we show that the resulting integral representation is equivalent to a state-feedback law whose kernel splits into a Toeplitz part, as on the whole line, and a new Hankel part generated purely by the boundary.

Algebraic groups seminar
Speaker: Sabyasachi Dhar, IIT Bombay, Mumbai
Host: Shripad Garge
Title: Iwahori-Hecke Algebras. III
Time, day and date: 5:00:00 PM - 6:30:00 PM, Thursday, August 20
Venue: Room No .215
Abstract: We continue with the study of the Iwahori-Hecke algebras. We will be doing some examples in this lecture.