I've always been secretly fascinated with the rich structure and applications of finite-dimensional associative unital algebras over complete fields. In particular, I am very much interested in the structure and representations of commutative ones and their central extensions. My background is nu...

I'm very keen to deepen my understanding of arithmetic and diophantine problems. In the past I studied some algebraic, analytic and sieve based number theory. Recently I've been reading Weil - Basic Number Theory which covers some early results of Fermat and Euler in their original forms and then...

I am a senior Mathematics Major, and I am interesting in learning about Modular Forms. I have a layman's general sense of what they are but I was wondering if there is a lecture(I am willing to pay) or a book that explains Modular forms in Layman terms to in mathematical terms. I understand it's ...

There is a wikipedia article. There is a paper by Elisha Peterson. I tried reading these but they don't seem to click for me. Are there books or other resources for learning how to do linear algebra with trace diagrams?

I want to know a "knowledge road" to holomorphic foliations. I assume that differential geometry and complex analysis is needed, but, what else? For example, I want to be able to read Lins Neto's book "Folheacoes algebricas complexas".

I am a student of mathematics, and have some background in Algebraic Topology (Hatcher, Bott-Tu, Milnor-Stasheff), Differential Geometry (Lee, Kobayashi-Nomizu), Riemannian Geometry (Do Carmo), Symplectic Geometry (Ana Cannas da Silva) and Differential Topology (Hirsch, Minor (Morse Theory...

I have been lurking here for a long time just enjoying the scenery from my beginner's viewpoint. I have a math.SE account but I think this question is appropriate here based on the nature of the subject and similar questions I have seen. It also seems that some of those qualified to answer are mu...

Question Suppose you grasped and enjoyed reading Quillen's "Higher Algebraic K-theory I". Now, if you could go back in time to when you started studying algebraic topology and create a reading list / roadmap with the above paper as a goal, what would this plan look like? Here's another version ...

I want to learn the classification of finite simple groups. But it is often commented that it is a theorem spanning tens of thousands of pages of research papers. So it is quite intimidating to an outsider like me. Can someone please point me where to start and trace out atleast the first few bas...

Generative Adversarial Networks were introduced in http://papers.nips.cc/paper/5423-generative-adversarial-nets and has more than 20000 citations. The paper introduced key paradigm changes which require applications from modern areas of mathematics. I wanted to ask what are some the mathematics r...

I am a PhD student in algebraic topology, and I would like to learn something about group cohomology. The final goal would be to present one or two seminars on this topic, in order to give my mates a gently introduction to this subject and at the same time showing them some striking result/applic...

There are lots of introductions to number theory out there, but typically they are streamlined to assume as little prerequisite knowledge as possible. I'm looking for a text which does the opposite -- assumes you are fluent in algebraic geometry, and builds on that knowledge to introduce number t...

I am a 17 years old student and I am really interested in category theory due to its abstraction and beauty. I wanted to know if you'd have any advices to approach this theory and if you have papers to begin with this. Thank you in advance for your answer.