ESP Biography


Major: Not available.

College/Employer: Columbia University

Year of Graduation: Not available.

Picture of Avik Laha

Brief Biographical Sketch:

Not Available.

Past Classes

  (Look at the class archive for more.)

Labor Market with Search Frictions in Splash 2018 (Nov. 17 - 18, 2018)
We will try to derive a simple model of the Diamond-Mortensen-Pissarides (DMP) model for the labor market with search frictions. This model won its authors the 2010 Nobel Prize in Economics.

Basic Complexity Theory in Splash 2018 (Nov. 17 - 18, 2018)
We will define formal languages, (deterministic, one-tape) Turing machines, and give the verifier-based definition of NP. We will then discuss the ideas of undecidability (briefly), reduction, and completeness, giving several examples. A potential auxiliary topic, depending on interest, is the equivalence of the verifier-based and machine definitions of NP.

Why P vs. NP isn't trivial in Splash 2018 (Nov. 17 - 18, 2018)
We will begin with the basics, defining I/O Turing machines and discussing what it means for a problem to require some amount of time or space, and giving central foundational results/techniques like the hierarchy theorems and diagonalization, and some applications. Afterwards, we will define oracle Turing machines and discuss the concept of completeness. We will conclude the main part of the course by showing that techniques like diagonalization cannot separate P and NP - in particular, any proof of their inequivalence cannot relativize. As time permits, we will look at other notable complexity classes lying between P and PSPACE, e.g. PH, BQP, and IP.