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Theory of Ferromagnetism and Chemotaxis

Mathematics Colloquium | Debopriya Mukherjee | Oct 18th, 2022

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In my talk, I will address several mathematical questions about the constrained Stochastic Partial Differential Equations (SPDEs) arising from (i) Dynamics of ferromagnetism, (ii) Chemotaxis. Landau-Lifshitz-Gilbert equations (LLGEs) arise in the theory of the magnetization of ferromagnetic materials below a certain temperature (called the Curie temperature) and the constraint arises from the physical “saturation” property of the material. Here one usually seeks a “solution” to this problem such that the so-called “solution” lies on the three-dimensional unit sphere for all time. Next, I will specify the mechanisms for spatial pattern formation in systems of coupled reaction-diffusion equations with underlying chemotaxis. This system will be perturbed by a stochastic noise term, modeling neglected fluctuations or random perturbations from outside. Analysis of these kinds of PDEs with constraints under random perturbation is non-trivial and we adopt non-conventional but intriguing methods.

About Speaker:

Dr. Debopriya Mukherjee, is a Visiting Scientist at Indian Statistical Institute (ISI) Bangalore.  Previously, she was enrolled (from the 1st of April 2020 – the 31st of July 2022) as a recipient of the Marie Sklodowska-Curie Individual Fellowship 2020 at Montanuniversitaet Leoben, Austria. Before this, she was a postdoctoral fellow at the University of New South Wales, Sydney, Australia under the supervision of Prof Thanh Tran and Prof Benjamin Goldys. She obtained her doctorate degree on 16th July 2018 under the supervision of Prof Utpal Manna, affiliated with the Indian Institute of Science Education and Research (IISER) Thiruvananthapuram, India. Her research is at the interface of stochastic partial differential equations, time-dependent systems, and mathematical biological systems arising from Turing Patterns with some numerical implementations. The principal strength of her research is its broad focus and the crossover between stochastic analysis, analysis of PDEs, and mathematical biological models.


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