## Musings on Math and Computing

Today, I would like write a recursive function which
counts the number of isomorphism classes of binary trees
with a given number of vertices. The implemention I gave
use a nice trick of memoization. **[Sep 18]**

I was watching Guy Steele’s talk subtitled foldl and foldr Considered Slightly Harmful.
He ends the talk with the words "Get rid of cons." Well… I am not ready to ditch the cons yet. **[Sep 7]**

I saw a nice algorithm by Vincent Granville that simulates samples
obeying Zipf’s Law using a nice physical process. Today I am
going to look at that, but I had to play with the parameters of the
simulation a bit. **[Aug 22]**

Today, I am going to develop an algorithm to generate uniformly random trees
with a given number of vertices. Bulk of the post is on showing that the trees I
generate with this algorithm are uniformly random. **[Aug 8]**

MD5 is a popular hashing algorithm. Today, I will investigate the effects on
truncating this hash function on the entropy. **[June 12]**

Today, I am posting a straightforward implementation of Bailey-Bowein-Plouffe
formula which calculates the hexadecimal digits of pi. **[June 8]**

In a previous post I investigated the effect of increasing the lengths
of n-grams on information gain. There I demonstrated the fact that after
a specific point increasing the length does not result in information gain.
However, there were some unresolved questions. Today, I will resolve
the remaining issues. **[February 12]**

A thesaurus is a dictionary which gives a list of somewhat equivalent words. A thesaurus path is a sequence of words

word_1, word_2, word_3, … , word_n

such that any two consecutive words appear in the list of entries of a third word, or of either word in a given thesaurus. I will define the thesaurus distance of a pair of words is the length of the shortest thesaurus path connecting one word to the other.

Today, I will implement the thesaurus distance in lisp.**[February 1]**

## A description of my research

### Mathematics

I do homological and homotopical algebra in the context of noncommutative geometry. You can find a detailed exposition of my past research, my present and future research interests in my research statement. Specifically I am interested in, Hopf equivariant cohomology theories, various flavors of Hochschild (co)homology, cyclic (co)homology and K-Theory. I am also intrested in abstract homotopical algebra, operads, PROPs and their algebras. For the visually inclined, I have a map of my slanted view of the noncommutative geometry landscape.

### Applied Statistics and History

As an ongoing project with Prof. Boğaç Ergene at University of Vermont, we investigate social mobility patterns in 18th Century Ottoman Empire. While he provided the historical context and the analysis of the results we obtained, I did the necessary data processing and performed the statistical analyses needed for the particular data set Prof. Ergene painstakingly generated from historical sources and archives. We wrote three papers together so far, with more to come in the future.