Evan Chen • Problems & Solutions

http://web.evanchen.cc/problems.html

Mirror Symmetry

https://www.claymath.org/library/monographs/cmim01c.pdf

Dirichlet Branes and Mirror Symmetry

http://www.claymath.org/library/monographs/cmim04.pdf

The Schrödinger Equation for the Hydrogen Atom: A generalization

This is a two-body problem (diatomic molecule) and formulation of the problem is possible:

https://chem.libretexts.org/Courses/University_of_California_Davis/UCD_Chem_110A%3A_Physical_Chemistry_I/Text/06%3A_The_Hydrogen_Atom/6.01%3A_The_Schrodinger_Equation_for_the_Hydrogen_Atom_Can_Be_Solved_Exactly

And its solution is using Spherical Harmonics:

http://mathworld.wolfram.com/SphericalHarmonic.html

So how about 3-body, or n-body system?

How complexity creeps in arising from n-bodies to n-1 bodies interaction?

https://gereshes.com/2018/05/07/what-is-the-n-body-problem/   

https://www.youtube.com/watch?v=09iTidqkriw  (very good video on the history)

and the github for the codes mentioned above is here:

https://github.com/winsmith/n-body-problem

Complex, but simulation is possible:

https://jheer.github.io/barnes-hut/  (this is interactive)

https://en.wikipedia.org/wiki/N-body_simulation

https://arxiv.org/abs/astro-ph/0503600 

 https://www.americanscientist.org/article/the-100-billion-body-problem

https://sites.math.washington.edu/~morrow/336_13/papers/peter.pdf 

http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.762.6900&rep=rep1&type=pdf 

http://users.wfu.edu/choss/CUDA/docs/Lecture%2012.pdf 

http://www.math.harvard.edu/archive/118r_spring_05/handouts/nbody.pdf 

https://www.cs.cmu.edu/~guyb/realworld/nbody.html 

https://www.math.arizona.edu/~dwang/485home-10/N-body.pdf

The Golden Ratio

http://assets.press.princeton.edu/chapters/s8446.pdf

http://jwilson.coe.uga.edu/EMAT6450/Class%20Projects/Foy/goldenratio.pdf

https://bib.irb.hr/datoteka/658280.215-FP.pdf

https://www.ias.ac.in/article/fulltext/reso/022/01/0051-0060

https://www.ijera.com/papers/Vol6_issue8/Part-%204/A0608040107.pdf

https://www.math.cuhk.edu.hk/~pschan/uged1533/markowsky.pdf

https://www.math.ust.hk/~machas/fibonacci.pdf

Abstract Algebraic Topology

https://www.maths.ed.ac.uk/~v1ranick/papers/maybook.pdf

https://www.math.uni-hamburg.de/home/schweigert/ss16/atskript.pdf

http://www.math.nus.edu.sg/~matwujie/ma5209.pdf

http://www.mit.edu/~sanathd/main.pdf

http://www.pdmi.ras.ru/~olegviro/topoman/e-part1.pdf

http://www.pdmi.ras.ru/~olegviro/topoman/e-part2.pdf

http://www.pdmi.ras.ru/~olegviro/topoman/e-part3.pdf

Category Theory: its concepts and applications

https://www.cl.cam.ac.uk/teaching/1819/L108/

Less abstract:

http://chalkdustmagazine.com/features/an-invitation-to-category-theory/

https://raw.githubusercontent.com/jwbuurlage/category-theory-programmers/master/doc/categories_for_programmers.pdf

https://unglueit-files.s3.amazonaws.com/ebf/e90890f0a6ea420c9825657d6f3a851d.pdf

Types reasoning:

http://www.lambdadays.org/static/upload/media/1456307974627874bartoszlambdadays2016.pdf

Category Theory Applied to Functional Programming

http://www1.eafit.edu.co/asr/pubs/others/cain-screen.pdf

https://media.readthedocs.org/pdf/pycategories/latest/pycategories.pdf

https://teki-con.com/wp-content/uploads/2018/04/anat-category_theory_teki_con.pdf   

Categories for the working Hackers:

https://homepages.inf.ed.ac.uk/wadler/papers/categories/qcon-sf.pdf 

https://cukic.co/files/presentations/2014-12--monads-in-chains--ivan-cukic--meeting-cpp.pdf 

http://yowconference.com.au/slides/yowlambdajam2018/Hopkins-AllOfBasicCategories.pdf 

http://www.worldcolleges.info/sites/default/files/C%2B%2B_In_Action.pdf 

http://gpu.wigner.mta.hu/user/pages/03.events/02.lectures-on-modern-scientific-programming/04.lectures-on-modern-scientific-programming-2015/Session6_DeepMagic2.pdf