Life is becoming interesting as you discuss Math. I am yet to venture out new topics in my research. In particular, with PhD students or Post docotoral fellows or collaborators. With them, I focus on interplay between Harmonic Analysis and Geometric Measure theory.
However, being at IISER for almost 7 years, we come across students who are looking forward for more explorations. They are yet to decide being in Academia or non-academia. Especially the pandemic has changed the dynamics of MS thesis that I had visualized earlier. Deciding to help out an MS student for their thesis is a short collaboration for me. Depending on their short goal (be it exploring UPSC or MBA or PhD or any other future career path), we discuss and figure out some mutual topics that works for both of us to explore in the 10 months of their final BsMs period. Upcoming: together with Mr. Prateek, Ms. Shruti and Mr. Faizal, we are exploring Fractals in Finance, Difference Set vs Graphs and Wavelets respectively. Some of the BsMs Math students who I had interaction with in the past:
| NAME | PERIOD | STATUS | TOPIC |
| Mr. Mayank Agarwal | May 2024 – | Almost in completion (co-mentored) | Algorithmic Graph Theory |
| Mr. Saptarshi Gosh | May 2024 – | Almost in completion | Sum sets |
| Mr. S. Santosh | May 2023 – April 2024 | Graduated (Co-mentored) | Independence of Continuum Hypothesis, and some applications of Martin’s axiom |
| Mr. Milap Kumar Rajgor | May 2023 – April 2024 | Graduated (Co-mentored) | The Bergman Spaces and the Bergman Kernels |
| Mr. Neehar Verma | May 2022 – April 2023 | Graduated (Co-mentored) | Error distance distribution of Projective Reed-Solomon Codes from the perspective of Finite Geometry |
| Mr. Animesh Nayak | May 2022 – April 2023 | Graduated | Fractal dimension and density of s-sets |
| Mr. Pratik Sinha | May 2020 – April 2021 | Graduated | Steiner formula for convex bodies |
A few documents:
- The topics covered in the lectures that I delivered at IIT Tirupati for NCM Workshop on Ergodic theory and fractals can be found here.
(to be updated)
I will be updating this post based on the lectures I have given outside the teaching hours. The next update will be in April 2025.
Briefly, if you are interested in knowing any of the following, this space is for you to read.
“What are dimensions?” “”Are there fractional dimensions?” “How do we measure sets that do not have length or area or any dimensional volume?” “How do we formulate and attack problems to recognize patterns in the given set via measure theory?” “What do we mean by analytic and geometric properties of the given set?” “How to construct fractals?” “Why should we study fractals?” “Why do we have $\latex \epsilon,\delta$ while studying Real analysis?”
K. S. Senthil Raani 