If you are a graduate student, please contact me as soon as possible and start attending my weekly CACAO seminar. This will give you a solid idea of what I do, how I work, etc. Normally, I expect work equivalent to a four credit course and a weekly report of what you did each week.
If you are an undergraduate student, please contact soon, but no later than your junior year. I run a popular undergraduate seminar too. Students take turns talking about their projects.
Here is a list of books I find useful and often recommend for students working with me. See also my list of publications:
a) Lectures on Polytopes, by G. Ziegler, Graduate texts in Mathematics,
vol 152, Springer, Berlin 1995
b) A course on Convexity, by A. Barvinok, Graduate studies in Mathematics, vol. 54, AMS, Providence, 2002
d) Enumerative Combinatorics vols. I and II, by R. P. Stanley, Cambridge University Press, Cambridge, 1997.
e) Grobner bases and Convex Polytopes, by B. Sturmfels, University texts, AMS, Providence, 1995.
f) Modern computer Algebra, by J. von zur Gathen and J. Gerhard., Cambridge Univ. Press, Cambridge, 1999.
g) A=B, by M. Petkovsek, H. Wilf, and D. Zeilberger, AK Peters, Wellesley MA, 1996.
h) Computers and Intractability: A Guide to the Theory of NP-Completeness, by M. R. Garey and D. S. Johnson, W. H. Freeman, 1979.
i) Applied and Computational Complex Analysis, v. 1,2,3, by P. Henrici, Wiley, New York, 1986.
j) Ideals, Varieties and Algorithms, by D. Cox, J. Little, and D. O'Shea, Undergraduate texts in Mathematics, Springer, second edition 1996.
High school students, if you want to learn about my research, you can access an elementary exposition of past research at the level of a smart high school student, with some activities even suitable for younger kids. In particular, if you are really curious, you can find there an explanation of the logo appearing in my main web page. As you can see there even in geometry my taste is discrete (as in finite). Indeed, sometimes I can be a VERY discrete mathematician.