Introduction to Modular Forms - Part 1 of 8

“Introduction to Modular Forms,” by Keith Conrad. Topics include Eisenstein series and q-expansions, applications to sums of squares and zeta-values, Hecke operators, eigenforms, and the L-function of a modular form.
This is a video from CTNT, the Connecticut Summer School in Number Theory that took place at UConn during August 8th - 14th, 2016, organized by Keith Conrad, Amanda Folsom, Alvaro Lozano-Robledo, and Liang Xiao. For more information, see
ctnt-summer.math.uconn.edu/

[@greg55666]

This teacher is really great. He is talking at the perfect level, motivating everything.

[@ernstvangelderen9537]

Absolutely. I did not understand modular forms. After this series of lectures I do understand at least the basics of modular forms,

[@travelgalaxy8291]

Excellent lecture by Prof Keith Conrad

[@MadHadda63]

Incredibly clear and well organized lecture!

[@keyyyla]

Jacob Gross have a look at his expositories. I have never read mathematical articles that clear and easy to understand (including proofs).

[@Suav58]

I did look up the first two. They are very good and, as is my slang about it "leave the doors and windows clearly visible if not open". What I mean, is, that, some lecturers lead you through the subject as through the dark corridor holding the torch of "enlightenment" clearly focused, while others let you into chambers full of light and open views to amazing countryside.

[@sahhaf1234]

Excellent lecture. But you need a better camera guy and thicker marker pen..

[@boyabundabasketball4988]

Amazing lecture indeed!

[@DynestiGTI]

6:32 me when I take my glasses off

[@CLSC_Outrun2SP_TA]

Huge fan of Prof. K.Conrad!

[@chinmayhegde5728]

This is just amazing sir. Tk you

[@pairadeau]

C'est magnifique!

[@alicialacueva6827]

very nice!

[@eddyhans5365]

06:45 Is the camera guy testing his camera??😂😂😂

[@prakashpanangaden1373]

Nice lecture but it was annoying that the camera was out of focus just when he was giving the main definition.

[@Distillations21]

how did i get here. EARTH TO HUMANS

[@greg55666]

Who knew Jon Lovitz knew math?

[@Achrononmaster]

Nice. But really, someone has to redo all this using Clifford algebra, the potential insights could be huge. SL(2,C) has a natural representation in real Clifford algebra, thus so do Mobius transformations. Whenever you are given matrix representations I think there is a more intuitive and more natural Clifford algebra representation that you should really be using for a first course. Matrix algebras stuff up our geometric intuitions. Blame the physicists, they started QM with a complex matrix algebra instead of a real Clifford algebra, and never bothered to fix this mistake. Pauli matrices are just the even subalgebra of 3-space, and Dirac matrices are basis vectors for the Cl(1,3) spacetime algebra. Spinors are just spacetime rotors, and Lorentz transforms are also rotors, so when you do QM properly, with Clifford algebra instead of matrix algebra, you get a lovely feature that the transformations are the same class of objects as the states on which they act. So even if this only amounts to a change in language, I think some insights could be gained. It makes it less a mystery that modular forms arise in String Theory for example, since they'd occur in even any classical theory that has non-trivial spacetime topology.

[@caspermadlener4191]

I assume you don't see yourself as a "somebody"?

[@tonicopm]

Pretty lousy camera displacement, and the sound sucks. The lecture, though, extremely interesting and well given. A pity...

[@Dec38105]

pfff... this is a pirate copy , bad quality + i can see peoples heads

[@bobman8192]

This is what is linked on the professors web page