Modular Forms | Modular Forms; Section 1 2

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We define modular forms, and borrow an idea from representation theory to construct some examples.

Fourier Theory (0:00)
Definition of Modular Forms (8:02)
In Search of Modularity (11:38)
The Eisenstein Series (18:25)

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What I found great about this video is that, though this felt to me like it really jumped to a higher level and requires I fill many gaps to unpack it, you explain and lay things out in a way that I could take notes and encourages me to investigate further in many areas. I would love to see, at some point, a companion series on complex analysis that would help with some concepts in this video, particularly Laurent expansion and background on taking complex derivatives.

johnrobin

Oh wow so this is the direction I've needed to go to properly satisfy my curiosity regarding the stuff I noticed about inversions and projections while exploring complex analysis, projective geometry, conformal mapping, while trying in vain so far to properly represent a perpetual circular motion like (cos(t), sin(t)) but without explicit trig functions or like infinite sums, or imaginary numbers.

The vector version of sin and cos don't properly mimic that effect I'm looking for which keeps going around and around with the magnitude of some single variable parametrically

I've been thinking recently about trying to use y=x as representing infinity, and 1/x as infinitesimals, and const representing said const. Or maybe I'm wrong and should try using e and ln but whatever the idea is what matters. Where infinity then is now an obtainable and usable value which can be scaled in its own right and generating it's own graph at a different layer from const. (I'm also thinking x^2 would be another layer of infinity)

This representation or interpretation allows an object with all values to be different from another object with all values by simply comparing growth rates instead of the collection of values.

I'm glad I took a break from the two different lecture series on algebraic geometry to come here.

codatheseus

Crazy good videos. I just found your videos. I'm trying to figure out what the constants e_1, e_2, e_3 are, where 1, 2, &3 are subscript of e.

jeffreyhowarth

it was great!!
when will the next video come?

mansimarsingh

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