Finite Geometry and Coding Theory Seminar
Speaker: Puspendu Pradhan, IIT Bombay
Host: Sudhir R. Ghorpade
Title: PGL_2(q)-orbits of lines of PG(3,q) and Higher weight spectra of some Reed-Muller codes
Time, day and date: 11:30:00 AM - 12:15:00 PM, Monday, September 29
Venue: Ramanujan Hall
Abstract: (https://drive.google.com/open?id=1mASoUTg688KdSHa7n-RVYKl51v32qIb8)
We shall divide the talk into two parts. In the first part, we focus on the problem of classifying the lines of the projective 3 space PG(3, q) over a finite field Fq into orbits under the action of the group PGL2(q), which represents the linear symmetries of the twisted cubic C. While this problem has been addressed in the literature for characteristic 2, in this talk we shall consider the case of characteristic 6= 2. We reduce this question to the classification of binary quartic forms over Fq into PGL2(q)-orbits. This part of the talk is based on joint works with Krishna Kaipa and Nupur Patanker. For non-negative integers ν and m, the Reed–Muller code RMq(ν, m) is defined as the subspace obtained by evaluating all polynomials of degree at most ν in m variables, with coefficients in Fq, at the points of the affine space AG(m, q). In the second part of the talk, we will present progress on determining the higher weight spectra of the Reed–Muller code RMq(2, 3) over the ternary field F3. This part of the talk is based on an ongoing joint work with Sudhir Ghorpade, Trygve Johnsen, Rati Ludhani, and Rakhi Pratihar.

APS
Speaker: Chayan Karmakar, IIT Bombay
Host: Ravi Raghunathan
Title: Geometry of the Tensor Product for SL(3,C)
Time, day and date: 4:00:00 PM – 5:00:00 PM, Monday, September 29
Venue: Ramanujan Hall
Abstract: We aim to study the geometric structure of tensor products of irreducible representations of $\mathrm{SL}(3, \mathbb{C})$. By plotting the highest weights of the irreducible components in the weight lattice, we observe that they form some convex regions. We also study additional structural properties of the tensor products, including a stability result in the resulting tensor diagrams