This is the page where I put links and things related to my mathematical work at Rutgers.

POLYPROB is a program I wrote for a Spring 2001 VIGRE rotation. It takes a PORTA input file defining a polytope whose vertices are generators of a monomial ideal; runs PORTA to produce inequalities bounding the polytope; and estimates the multiplicity of the ideal by probabilistically estimating the volume of the polytope. It will also run the 'vinci' program to calculate the polytope volume exactly. If you don't know what I'm talking about, you don't want this program.

If you do know what I'm talking about, click here to download a tarball containing the C++ source. The syntax is:

to call PORTA on foo.poi and use the resulting output to do a probabilistic estimate run with 100000 trials; or

to do the same estimate run, but read the PORTA output from foo.poi.ieq instead of calling PORTA; or

to get an exact computation by calling 'vinci'. WARNING: the vinci option will only give a correct answer if the polytope really is contained within the bounding simplex.

For more complete documentation, refer to the file readme.txt and the source code file polyprob.C. There is a makefile, so you should be able to compile the program just by typing "make"; this has so far been tested only on Solaris 2.7 and Linux (Debian and Red Hat).

multcalc performs the same task exactly, using the program 'lrs' to get an exact volume using arbitrary-precision rational arithmetic and then computing an exact multiplicity from that (it depends on the GNU multiple-precision library libgmp). Click here to download it; the readme.txt file has documentation.

If you have questions or problems, email me at nweininger@pobox.com.

Homepages of various mathematicians who have some useful papers up on their pages:

• Graham Brightwell
• Jim Fill
• Geoffrey Grimmett
• Olle Ha"ggstro"m
• Thomas M. Liggett
• Russell Lyons
• Robin Pemantle
• James Propp
• David Wilson

Some other math links I've found useful.

• MathSciNet, every literature searcher's best friend
• IRIS-- search the Rutgers libraries
• The online searchable Encyclopedia of Integer Sequences
• A preprint book I've been reading, Probability on Trees and Networks
• The Electronic Journal of Combinatorics
• The Electronic Journal of Probability

This part of the page collects info on random things that I've done as a student of mathematics, in hopes that one day some of these things will be helpful on job applications, although they don't really seem to be appropriate for my resume.

• Teaching stuff: in fall 2002 I TA'd a section of Math 115 (precalculus) and two sections of Math 135 (Calculus I). In summer 2003 I taught a section of Math 244 (Differential Equations for Engineers). In fall 2003 I TA'd three sections of Math 251 (Multivariable Calculus). In summer 2004 I am teaching Math 428 (Graph Theory).
• In spring 2004 I gave a talk at the DIMACS/DIMATIA/Renyi Workshop on Algebraic and Geometric Methods in Combinatorics at the Renyi Institute in Budapest, entitled "On correlation properties of some random colorings."
• I periodically give talks at the Graduate Student Combinatorics Seminar at Rutgers. In spring 2004 I gave one called "Generating Random Spanning Trees". In fall 2003 I gave one called "Correlations and Influence in Discrete Probability Models". In spring 2003 I gave two expository talks, one on Shannon and Sperner capacities of graphs and the other on graph entropy.
• In summer 2001 I co-mentored a DIMACS REU project with Prof. Mario Szegedy. In summer 2002 I co-mentored another such project with Prof. Eric Allender.
• I've given talks at the Rutgers pizza seminar: "On Computing the Volumes of Convex Bodies" in fall 2001, "Gauging the Henstock Integral" in fall 2000
• And I've talked at the VIGRE program's seminar: "Random Walks and Electrical Networks" in spring 2002, "Markov Chains and the FKG Inequality" in fall 2001, "Monomial Ideals and the Computation of Multiplicities" in spring 2001
• I've given a couple of short presentations to Rutgers undergraduates about my views on applying to and getting through grad school, at Math Club meetings in fall 2001 and spring 2002