Mushfeq Khan

khan@math.hawaii.edu
305 Physical Sciences Building
University of Hawai'i at Mānoa

My area of interest is logic, specifically computability theory. I did my PhD at the University of Wisconsin–Madison under the supervision of Joseph S. Miller.

Bjørn Kjos-Hanssen is my mentor at the University of Hawai'i.

Teaching: Fall 2016

Math 243

Math 351

Research

Research statement

Shift-complex sequences. Bulletin of Symbolic Logic, 2013.

Forcing with bushy trees. With J. S. Miller. Preprint.

Lebesgue density and \(\Pi^0_1\) classes. Journal of Symbolic Logic, to appear.

My thesis

Slides

Shift-complex sequences. ASL Meeting, UC Berkeley, 2011.

Density-one points of \(\Pi^0_1\) classes. CCR, Buenos Aires, 2013.

Density-one points of \(\Pi^0_1\) classes. Midwest Computability Seminar XIII, University of Chicago, 2013.

Lebesgue density and \(\Pi^0_1\) classes. Algorithmic Randomness and Complexity, Shonan Village Center, Japan, 2014.

Note: Many of the questions in the slides about density-one points have been answered since I gave these talks. The preprint is more current.

Mass problems and recursively bounded DNR functions. ASL Meeting, University of Illinois at Urbana-Champaign, 2015.

Effective bi-immunity and randomness. ASL Meeting, University of Connecticut-Storrs, 2016.

The Computability Menagerie

Joseph Miller and I have created an interactive web-based version of his "Computability Menagerie". It depicts relationships between downward closed classes of Turing degrees, and is inspired by Bjørn Kjos-Hanssen's original version, which can be found here.

The Menagerie generates its graph based on a database file that contains some key facts about the classes. It can make a few basic types of deductions from these facts and fill in missing information.

You can tell the Menagerie to display only the classes that you care about. For example, this is a part of the diagram showing some questions that might be open.

The code is available here.