IITG Mathematics Seminar Series

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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.


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