Calculus on Fractals: Resistance Scaling on Weighted Sierpinski Carpets
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Location
Gallaudet University - JSAC Multipurpose Room
Start Date
4-3-2024 10:30 AM
End Date
4-3-2024 11:00 AM
Description
Abstract - Most of this talk will be accessible to non-mathematicians. First, I will go through a brief, visual overview of the foundations of calculus and some of the ideas and motivation behind creating ‘nice’ function spaces. After that, I will discuss the construction and properties of some fractals, which are rough, intricate shapes, often with infinitely many holes. Lastly, I will go through some ideas needed for constructing the theory behind some calculus concepts on fractals, and a description of my own results on what I call weighted Sierpinski carpets. This gives some of the groundwork to discuss some mathematical versions of heat and electricity on those fractals.
Recommended Citation
Hayes, Christopher, "Calculus on Fractals: Resistance Scaling on Weighted Sierpinski Carpets" (2024). Global Year of STEM Sign Language Summit. 5.
https://ida.gallaudet.edu/global_STEM_signlanguage/STEM_signlanguagesummit/day_3/5
Calculus on Fractals: Resistance Scaling on Weighted Sierpinski Carpets
Gallaudet University - JSAC Multipurpose Room
Abstract - Most of this talk will be accessible to non-mathematicians. First, I will go through a brief, visual overview of the foundations of calculus and some of the ideas and motivation behind creating ‘nice’ function spaces. After that, I will discuss the construction and properties of some fractals, which are rough, intricate shapes, often with infinitely many holes. Lastly, I will go through some ideas needed for constructing the theory behind some calculus concepts on fractals, and a description of my own results on what I call weighted Sierpinski carpets. This gives some of the groundwork to discuss some mathematical versions of heat and electricity on those fractals.
