|William J. Keith|
Michigan Tech University Math Department
Tenure-track Assistant Professor
In the fall of 2012 I am teaching:
|Outside of my office hours, students should get in touch with me using my MTU email, wjkeith [at] mtu.edu (no spaces).|
|My office hours this semester are Tuesday and Thursday 3-5pm. My office is Fisher 316. I am generally available at other times if a student emails me well in advance. This and other class information is available on the syllabus for each class, which is also on the course webpages linked above.|
|My research centers on partition theory and related q-series and symmetric function identities. Over the course of my postdoctorate at the University of Lisbon, I expanded my areas of interest to other enumerative combinatorics questions, though I remain primarily interested in partitions.|
Selected Publications and Preprints
A few of my more recent papers (and my thesis). I link to the published versions of these papers when possible, but preprints of all my work are available on the arXiv.
These are a few of the ongoing research questions which interest me. I am always happy to receive comments from interested colleagues, and would be pleased to collaborate with someone who has useful ideas in these directions. Graduate students considering combinatorics who find some of these questions interesting are encouraged to contact me as well.1.) I continue with great interest to study more about the polynomials described in the "Ramanujan congruence analogue" paper, which I think are fascinating combinatorial objects with properties that deserve exploration.
2.) In non-partition work, I am presently interested in another conjecture of Amdeberhan, Manna and Moll, this one their open conjecture on the 2-adic valuation of the Stirling numbers of the second kind.
3.) As mentioned above, I have recently become interested in m-regular partitions, espycially their low-modulus congruences.
4.) Of the famous problems that interest me, I would name the Borwein Conjecture, on the positivity of coefficients of a series defining a certain weighted sum over specialized partitions, and Lehmer's Conjecture on the non-zeroness of the coefficients of Ramanujan's tau function.