07-11-2025
Speaker: Om Milind Joglekar
Abstract: Moore graphs are the “perfect” examples in the degree–diameter problem — regular graphs that exactly meet the Moore bound for given degree k and diameter d. They’re extremely rare, and understanding when they can exist turns out to be a surprisingly rigid question. In this talk I’ll look at Moore graphs in general diameter and show how strong algebraic constraints narrow down the possibilities. Specializing to diameter 2, this leads to the famous condition that k can only be 3, 5, 7 or 57. *The asterisk in the title is because the k=57 case is still an unsolved problem. All in all, we know every Moore graph that exists except possibly the one corresponding to k=57.
Time: 5:30 PM–6:30 PM
Venue: Room 215
06-11-2025
Speaker: Suraj Mishra
Abstract: In this talk we will discuss a particular type of module over path algebra of a locally bound Quiver, called a rooted tree module and a combinatorial criterion for checking the indecomposability of the rooted tree module. If time permits we can also talk about the direct sum decomposition of a decomposable rooted tree module into indecomposable summands.
Time: 5:30 PM–6:30 PM
Venue: Room 215
15-10-2025
Speaker: Nirav Bhattad
Abstract: In this talk, I will present Rado’s Theorem, a fundamental result in complex analysis concerning the extension of holomorphic functions. The proof, which will be discussed in detail, relies on the maximum modulus principle. This talk will be accessible to anyone who has taken MA412 (Complex Analysis).
Time: 5:00 PM–6:00 PM
Venue: Room 114
Speaker: Aditya Dwivedi
Abstract: In this talk, we shall overview major and useful results on Grobner Bases and discuss the applications of them in free resolutions. We will also give a proof of Hilbert's basis theorem using the theory developed.
Time: 6:00 PM–7:00 PM
Venue: Room 215
Speaker: Kaushik Khamari
Abstract: This will be a continuation of the previous talk (Seminar 90)
Time: 6:00 PM–7:00 PM
Venue: Room 215
Speaker: Kaushik Khamari
Abstract: In this talk we will see an introduction to spectral sequences of bicomplexes and their applications in homological algebra and if time permit give a proof of Foxby's theorem.
Time: 6:30 PM–7:30 PM
Venue: Room 105
Speaker: Vishnu Ravi
Abstract: In this talk, we shall overview major and useful results on spanning trees, structural properties, enumeration and estimation. Then we shall talk about spanning forests, leading to the problem of estimating the ratio of spanning trees and spanning forests, which was proposed by Prof. Balachandran. We shall cover a few results and conjectures that we have made in this direction, and related problems worked on by others.
Time: 5:30 PM–6:30 PM
Venue: Room 105