To anyone in the Cambridge, MA area: a bunch of us will be organizing a learning seminar on higher categories and derived algebraic geometry at Harvard. Our goal is to understand some of the topics in the book “Higher Topos Theory” and some of the DAG papers. We will be having an organizational meeting (where we figure out what our goals and format will be) next Tuesday at 4:30. Let me know (at amathew (at) college (dot) harvard (dot) edu) if you are interested and can make it!

### random

September 2, 2011

## Derived algebraic geometry seminar

Posted by Akhil Mathew under random | Tags: advertisements, derived algebraic geometry |[2] Comments

July 7, 2010

## My adventure in live TeXing and some notes

Posted by Akhil Mathew under random | Tags: latex, liveblogging, Sergei Tabachnikov |[6] Comments

At the REU I’m at, we listen to daily lectures. The current topic is “geometry of polynomials,” by Sergei Tabachnikov; it will continue for two weeks. I’ve been live-TeXing notes in class.

It’s not something I anticipated doing—after all, typing is slower, right? I find that’s not really the case. First, out of concerns of laziness efficiency, I always predefine macros (e.g. \e = \mathbb) in my source files that reduce the amount of typing. Second, since this is a talk, there are pauses in the mathematical exposition that allow one to catch up. (I actually fall behind very rarely–even though I run pdflatex and scan the output every now and then.*) The most serious problem is that this is a *geometry* course. I may try whipping out an image editor and trying to copy down the various diagrams (and insert them as figures into the document later). But it’d be hard to keep up when there are so many figures, as seems to be the case in this course—and it’ll likely be even harder in the next course (“fractal geometry and dynamics”).

But, on balance, I think I’m pretty sold on live-TeXing. Mostly because my handwriting is awful, and I’m really bad at keeping organized sheaves of papers. By contrast, LaTeX output is pretty and computer files don’t (usually) vanish. I recommend it to others, as well as this post of Chris Schommer-Pries.

So, without further pontification, here are my notes from the past two days.

*On the subject, I definitely recommend using evince as a PDF viewer–it has the nice property of being able to update the document automatically without your having to close and reopen it.

February 21, 2010

## A few random things

Posted by Akhil Mathew under algebraic geometry, random | Tags: Eckmann-Hilton argument, future plans, GAGA, monoidal categories |[4] Comments

I don’t really anticipate doing all that much serious blogging for the next few weeks, but I might do a few posts like this one.

First, I learned from Qiaochu in a comment that the commutativity of the endomorphism monoid of the unital object in a monoidal category can be proved using the Eckmann-Hilton argument. Let be this object; then we can define two operations on as follows. The first is the tensor product: given , define , where is the isomorphism. Next, define . It follows that by the axioms for a monoidal category (in particular, the ones about the unital object), so the Eckmann-Hilton argument that these two operations are the same and commutative. (more…)

November 16, 2009

My name is Akhil Mathew. I’m currently a high school senior interested in mathematics. This is my mathematics blog.

I first became exposed to the blathosphere as a sophomore after a mentor of mine pointed me to Terence Tao’s blog. I soon discovered after clicking on the links that there were numerous blaths already on the web, many of which were accessible to me.

I joined the blathosphere in the summer of 2009 at the group blog Delta Epsilons, started by the mathematics students of that year’s Research Science Institute. Eventually, prodded by comments there, I found that my typical style of blogging, which often includes long series of posts and a textbookish style, was ultimately unsuitable for the motto of Delta Epsilons: mathematical research and problem solving.

So, while I’m going to remain a contributor to Delta Epsilons, I’ve started this to create an additional outlet where I can post to learn math better. I plan to post entries more suitable to Delta Epsilons–by which I mean resembling a crisp expository article than a chapter in a book–in both locations.

The tentative topics I intend to talk about in the future are diverse. Right now I’m in the middle of a MaBloWriMo sequence on differential geometry. But in the future I’m considering discussing topological K-theory, algebraic geometry, and harmonic analysis. In the long run, one of my ambitious hopes is to understand the Atiyah-Singer index theorem (and its proof), which may also become a topic. However, my interests change too quickly for me to predict with any reliability. I hope this will make it interesting.

Incidentally, you might be wondering why I have an introductory post after over sixty posts in the archives: those are the textbookish entries that I made at Delta Epsilons, copied here for completeness.