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Aathreya's Reading List

Books I'm Reading

Here are some books I'm reading right now. I'd love any recommendations!

Stochastic Differential Equations by Brent Oksendal	I got to join a reading group on stochastic PDEs, and this is the book we're reading! So far, it's been really interesting, I've learned a lot about integration and I'm getting into solving differential equations.
After reading Millman and Parker's differential geometry book this semester, it's time I get into more modern ideas with Lee's triplets! I plan to try and finish as much Lee as I can this summer. I hear he has a new book coming out soon too!	Introduction to Smooth Manifolds by John M. Lee
Lectures on Algebraic Topology by Haynes Miller	It might just be me, but Hatcher's algebraic topology didn't really make too much sense to me. I couldn't even get past Chapter 0 (actually, with the help of a video series on YouTube following Hatcher, I think I've finally gotten it (yippee), but that's besides the point). As such, Professor Utiralova recommended that I check out Miller's notes. They must be good!

Selected Papers I've Been Reading

Are All Good Word Vector Spaces Isomorphic? by Ivan Vulic, Sebastian Ruder, and Anders Søgaard
Sur quelques points d’alg`ebre homologique by Alexander Grothendieck, the Tôhoku paper
Isomorphic Cross-lingual Embeddings for Low-Resource Languages by Sonal Sannigrahi and Jesse Read
$C^{1}$ Isometric Imbeddings by John Nash
LERF: Language Embedded Radiance Fields by Justin Kerr, Chung Min Kim, Ken Goldberg, Angjoo Kanazawa, and Matthew Tancik
NeRF: Representing Scenes as Neural Radiance Fields for View Synthesis by Ben Mildenhall, Pratul P. Srinivasan, Matthew Tancik, Jonathan T. Barron, Ravi Ramamoorthi, and Ren Ng
Strength and Hartshorne's Conjecture in High Degree by Daniel Erman, Steven V Sam, and Andrew Snowden

Selected Books I've Read Since May 13th, 2024

For all these books, I have solved at least 50% of the problems (usually more), and have at least read all problem statements. This is a change I implemented after my third semester at Berkeley. Ever since then, I have decided to make it a habit of finishing books more thoroughly.

Elements of Differential Geometry by Richard S. Millman, George D. Parker

The Springer GTM Test Results:

My answers:

You are lost in a forest. What do you do? Keep wandering -- you'll find your way out eventually!
At the grocery store, do you: try to get in and get out as quickly as possible.
What sort of colours do you prefer? Pastel shades.
Which of the following historic sites would you most like to visit? The Great Pyramid of Giza
In my morning newspaper, I always take a look at: The comics

If I were a Springer-Verlag Graduate Text in Mathematics, I would be Joe Harris's Algebraic Geometry: A First Course.

I am intended to introduce students to algebraic geometry; to give them a sense of the basic objects considered, the questions asked about them, and the sort of answers one can expect to obtain. I thus emphasize the classical roots of the subject. For readers interested in simply seeing what the subject is about, I avoid the more technical details better treated with the most recent methods. For readers interested in pursuing the subject further, I will provide a basis for understanding the developments of the last half century, which have put the subject on a radically new footing. Based on lectures given at Brown and Harvard Universities, I retain the informal style of the lectures and stresses examples throughout; the theory is developed as needed. My first part is concerned with introducing basic varieties and constructions; I describe, for example, affine and projective varieties, regular and rational maps, and particular classes of varieties such as determinantal varieties and algebraic groups. My second part discusses attributes of varieties, including dimension, smoothness, tangent spaces and cones, degree, and parameter and moduli spaces.

Which Springer GTM would you be? The Springer GTM Test

To be honest for the grocery store question I felt equally good about the first three, and for the color question I felt equally good about bright colors and pastel shades, so I could also be:

Frank Warner's Foundations of Differentiable Manifolds and Lie Groups
William S. Massey's A Basic Course in Algebraic Topology
Robin Hartshorne's Algebraic Geometry

I think this feels pretty accurate. ;) I think it's not a bad goal to have to try and finish all of the Springer GTM books. B-) So here is a list, see my progress!