William A. Cherry

Associate Professor (on modified service) of Mathematics

University of North Texas

Contact Information

Mailing Address:	Department of Mathematics
	University of North Texas
	1155 Union Circle #311430
	Denton, TX 76203-5017

Delivery Address:	Department of Mathematics
	General Academic Building, Room 435
	University of North Texas
	225 S. Avenue B (Avenue B at Mulberry)
	Denton, TX 76203

Research Interests

I have done work that can be considered complex analysis, number theory, and algebraic geometry. I am especially interested in connections between rational solutions and functional solutions to systems of algebraic equations. For instance, consider the equation of the unit circle, x²+y²=1. This equation has many rational solutions, such as (3/5)²+(4/5)²=1, coming from Pythagorean triples. The unit circle equation also has the "functional solution" (sin t)²+(cos t)²=1. On the other hand, if n>3, then xⁿ+yⁿ=1 has only a few rational solutions (this is Fermat's Last Theorem/Wiles's Theorem or the Mordell Conjecture/Faltings's Theorem, depending on what one means by "few" and "rational"). Similarly, xⁿ+yⁿ=1 has no non-constant "entire function" solutions -- this follows easily from, for instance, the Uniformization theorem. One area I often work in is a field called "p-adic" analysis. Working with functions of p-adic numbers is sort of halfway in between algebra and analysis, so the idea is it might help us understand how functional solutions are related to rational solutions. Another area I work in is Nevanlinna theory, which extends the Fundamental Theorem of Algebra to meromorphic functions. Finally, I have research interests in classical complex analysis, particularly using geometric methods to better understand various inequalities.

Graduate Advising

If you are a UNT mathematics graduate student looking for an advisor and are considering asking me, here is some basic information.

I can advise masters students on a variety of topics in complex analysis, number theory, algebra, or geometry. Former students have done projects with me in topics like elliptic curves with connections to primarility testing and factorization, and on algebraic points of small height. Feel free to drop by my office to discuss your interests with me.

Publications

click here for a list of my publications or click here to find my preprints on the arXiv.

Click here to see my author profile in Mathematical Reviews.

Click here to see my citations according to Google Scholar.

Look me up in the Mathematics Genealogy Project.

Educational/Professional History

click here for a brief description of my educational and professional background

Maple Tutorial

Click here for a brief introduction to the computer algebra system Maple

Fun and Games

Click here to generate some "fractal" graphics associated with Newton's method.

Miscellany

Beautiful Numbers, by John R. Swallow [American Scholar 64 (1995)]: A delightful essay written by a graduate school colleague of mine about his transformation from a first-year graduate student to a successful mathematician and scholar. I recommend this essay to new graduate students struggling with deciding what to study, who to choose as an advisor, and finding one's personal mathematical aesthetic.

Ludic Proof: Greek Mathematics and the Alexandrian Aesthetic, by Reviel Netz [Cambridge, 2009]: A book I am looking forward to reading about the literary qualities of mathematics and commonalities between writing mathematics (which I mostly understand) and writing poetry (which I mostly don't understand, but admire nonetheless).

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