William Abikoff 
Department of Mathematics
University of Connecticut
Storrs, CT 06269-3009
Office: MSB 210
Telephone: (860) 486-2003
Fax: (860) 486-4238
email:abikoff@math.uconn.edu


B.S. 1965 Electrical Engineering, the Unified Honors Program, Polytechnic Insitute (now of New York University)
M.S. 1966 Electrical Engineering, Polytechnic Institute
Ph.D. 1971 Mathematics, Polytechnic Institute

Research Interests

Riemann surfaces, Teichmueller theory and Kleinian groups, visual realization of geometric structures and applications.


For a short version of my Lifestory just click.

You can also find my Curriculum Vita  here.
My Publication List  graces the this page.

Office hours: My office hours are on this list.


The courses I'm teaching in Spring, 2013 are Math 2142 (Advanced Calculus II) and Math 2360 (Geometry). If you're interested, click on the course number and you will be transported to the homepage for that course.

The Advanced Calculus Sequence (Math 2141,2142,2413,2144) is a rapidly maturing offering of the math department. A detailed description can be found in many places: as a starting point, you could try our undergraduate course offerings or the course homepages; further information is available using the links found in those places.

Early in my career, I was an engineer. As students, a couple of us developed a control system to assist people with disabilities. It got lots of publicity. If you'd like to see what engineering was like in the age of Neanderthals, click here. At that time, older people were astounded that young people could do anything valuable; we were featured in the press, magazines and even the Voice of America.

Now young people don't have to carve out their place in research or creative activity --- it is a natural part of the university experience. I think that's great.

Here are some pictures of the Barycentric (Douady-Earle) extension of some mappings of the circle. Recently Cliff Earle (Cornell) and I have extended the methods used to produce the images to higher dimensional real and complex hyperbolic spaces.

Bill Harvey (King's College, London) and I have a history; I should refer to him as my dissertation supervisor but --- for now --- only in spirit. We've worked together, almost forever, on geometric structures. We use analysis, algebra and topology as tools to gain insight into geometry.

I like to think that hyperbolic manifolds approximate the universe in which we live. I'm still trying to find a physicist who will abandon the notion of a simple space with complicated properties in favor of a complicated space with simple properties. I also like to visualize those spaces. If that interests you, again, we should talk.

Ultimately, I'm a geometric function theorist. I study the interaction between a space (that's the geometry) and its phenomenology (that's its functions or what can happen in that space). If you find this interesting, contact me.