IITG Mathematics Seminar Series
| Lecture Number: | 349 |
| Title: | Probabilistic aspects of complex networks: a spectral view |
| Speaker: | Dr. Rajat Subhra Hazra (Awarded Shanti Swarup Bhatnagar Prize 2020 in Mathematical Science) |
| Affiliation: | Associate Professor, Theoretical Statistics and Mathematics Unit, Indian Statistical Institute, Kolkata |
| Date: | 6th October, 2020 (Tuesday) |
| Time: | 04:00 PM (Venue: Microsoft Teams) |
Abstract: We will discuss about the probabilistic nature of complex networks and we will discuss a few important features of huge networks. We will then briefly look in the adjacency matrix of these networks and see some properties of the spectrum, linking the beautiful theory of random graphs, random matrices, and operator algebras. The talk will be accessible to a general audience.
| Lecture Number: | 348 |
| Title: | Partitioning a Reaction-Diffusion Ecological Network for Dynamic Stability |
| Speaker: | Prof. Soumyendu Raha |
| Affiliation: | Computational and Data Sciences, Indian Institute of Science, Bengaluru |
| Date: | 26th June, 2020 (Friday) |
| Time: | 04:00 PM (Venue: Microsoft Teams) |
Abstract: The loss of dispersal connections between habitat patches may destabilize the populations in a patched ecological network. This work studies the stability of the populations when one or more communication links get removed. An example is finding the alignment of a highway through a patched forest containing a network of metapopulations in the patches. This problem is modeled as that of finding a stable cut of the graph induced by the metapopulations network, where nodes represent the habitat patches and the weighted edges model the dispersal between the habitat patches. A reaction-diffusion system on the graph models the dynamics of the predator-prey system over the patched ecological network. The graph Laplacian's Fiedler value which indicates the well-connectedness of the graph, is shown to affect the stability of the metapopulations. We show that when the Fiedler value is sufficiently large, the removal of edges without destabilizing the dynamics of the network is possible. We give an exhaustive graph partitioning procedure, which is suitable for smaller networks and uses as criterion both the local and global stability of populations in the partitioned networks. An heuristic graph bisection algorithm that preserves the preassigned lower bound for the Fiedler value is proposed for larger networks and illustrated with examples.
| Lecture Number: | 347 |
| Title: | Coercive quasilinear elliptic systems: existence and asymptotic behaviour of radial solutions |
| Speaker: | Prof. Jacques Giacomoni |
| Affiliation: | Laboratory of Mathematics and its Applications of PAU , University of Pau (France) |
| Date: | 19th February, 2020 (Wednesday) |
| Time: | 10:00 AM |
Abstract: In this talk we discuss the existence and asymptotic behaviour of the radial solutions of some coercive quasilinear elliptic system. Here we use the methods of dynamical systems to get the precise asymptotic behaviour of the global solution.
| Lecture Number: | 346 |
| Title: | One uniform random variable can do a lot |
| Speaker: | Prof. K.B. Athreya |
| Affiliation: | Distinguished Professor Emeritus, Iowa State University |
| Date: | 18th February, 2020 (Tuesday) |
| Time: | 04:00 PM |
Abstract: Out of one uniform (0, 1) random variable U it will be shown that we can generate any random variable and any sequence of random variables.