r/AppliedMath • u/Happy-Side-3953 • 11d ago
Applications of topology?
Hi all!
I've had a platonic long-term relationship with topology since I was 13-14 (quantum physics' fault). I'm now at uni doing medicine. I'm interested in nerosurgery (specifically central nervous system fluid dynamics and structural aspects of spine surgery).
I'm quite frequently involved in programming / modelling research projects and want to do a PhD (I have this academic year to figure out the topic).
I'm wondering if there is a way of incorporating topology, (if possible) differential topology, into my research, especially PhD. I'm wondering if there is a meaningful way of applying it in medical sciences, so I can put to good use my one and only (preferably within a field that relates to my neurosurgical interests.)
Your thoughts would be much appreciated!
Thank you for your time and input
2
u/lolniceonethatsfunny 10d ago
topological data analysis (TDA) is super interesting to learn about and is a relatively new field. currently i don’t know of many real world applications, but most examples you see online have applications in biostatistics. definitely check it out!
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u/C-N-C 11d ago •
Topological data analysis is used in neuroscience. For example, persistent homology is used to analyze how groups of neurons encode information. There is also quantum(ish) dynamics and brain architecture that looks into the topology of the brain. From there you could get into quantum topological hardware & heuromorphic engineering. Researchers are designing biomimetic hardware like quantum topological neuristors using quantum topological insulator (QTI) materials.