Musings on Math and Computing
The other day, I was looking at a problem of pattern matching. Today I am going to look at what goes in between the patterns, or more generally, what separators and what subtrings delineated by these separators give us the most likely matches.[December 3]
As I enter students grades, I thought of a simple problem. I use the search function on my spreadsheet to find a student before I enter their grade. How would I minimize the number of keystrokes? The solution goes through calculating the entropy of some projection functions.[November 12]
Graph Isomorphism is a difficult problem. The best known algorithms are of exponential complexity. However, the situation is rather simple for trees. In this post, I will describe and implement a simple polynomial time recursive algorithm to check if two trees are isomorphic.[October 23]
The Moebius function is an important function which became the centerpiece for few recent conjectures: see here and here. Today, I will give an additively recursive definition of the Moebius function which does not require a factorization of the input into its prime factors, nor does it appeal to a modified version of the Sieve of Eratosthenes. I will also give an implementation in C. [September 16]
Today's post is about taking uniformly distributed samples from parametrized submanifolds. If this sounds scary to you, think of taking uniform samples from a surface embedded in our good-old 3-dimensional space.[September 2]
I was reading a very informative blog post by Philipp Wagner on differences between PCA and LDA. I thought one might combine LDA with k-nearest neighbor algorithm to get better results and this post was born. [July 27]
A description of my research
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.