We will review the basics of vector bundles, sheafs, and sheaf cohomology

Nowadays the Big Data is all around us, and it is important to understand the tools and mechanisms on collecting and analysing it.

I will start my talk by reviewing real-life problems which scientists are facing when working with a Big Data. Then, I will continue discussing on how those problems can be solved using Wavelet Analysis, Graph Theory, Random Matrices, Probability and Statistics. In this part, I will present some of my past and ongoing research works in these areas of mathematics. Also, I will talk about applications of Big Data in Compressed Sensing, Wireless Communication and Speech Recognition.

The conclusion of the talk will be based on discussion of my future research questions concerning different applied problems of Big Data in the areas of Network Engineering, Financial Mathematics and Bio-Sciences, and their solutions with the help of different areas of mathematics.

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During the 1960s, Jennings, Golod, Shafarevich and Lazard introduced two sequences of integers a and c, closely related to a special filtration of a finitely generated pro-p group G, called Zassenhaus filtration. These sequences give the cardinality of G, and characterize its topology. Let us cite the famous Gocha's alternative: this is a condition on a and c equivalent for G to be analytic, i.e., a Lie group over p-adic fields. Recently in 2016, Minac, Rogelstad and Tan inferred an explicit relation between a and c.This talk will review these results, enrich them in an isotypical context, and give examples.

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https://westernuniversity.zoom.us/j/96866090477