### GREETINGSfrom Wlodzimierz (Wlodek) KuperbergDepartment of Mathematics & Statistics Auburn University

I am a faculty member of the Department of Mathematics and Statistics, Auburn University. During the current Semester (Fall 2013), I am teaching Linear Differential Equations MATH 2650 and Discrete Geometry and Convexity I, MATH 7110. I can can be seen in my office on Mondays, Wednesdays and Fridays at 9:00-9:50 a.m. or by appointment made by e-mail or telephone (see below).

I can be reached by

• phone: (334)-844-6594
• FAX: (334)-844-6555
• E-mail: kuperwl@auburn.edu
• Paper mail:
Department of Mathematics
Auburn University
Auburn, AL 36849-5310
My interests in mathematics are GEOMETRY and TOPOLOGY. Click on either one of the two to see the list of my publications on the topic.

### A PROBLEM IN GEOMETRY

Here is a problem in geometry: What is the minimum number of unit cubes in d dimensions which can cover a larger cube? For example, three unit squares (in the plane) can cover a larger square, but two cannot. It is not hard to show that d+1 unit d-cubes can cover a larger d-cube, but is d+1 the smallest number possible? If you can answer this question, even in some special cases, please write to me about it.

By the way, a similar question can be asked about other solids in place of the cube. The d-ball is an interesting, yet fairly easy, example:

THEOREM: The smallest number of unit d-balls that can cover a larger d-ball is d+1.

The proof can be assigned to geometry students as a nice exercise.

### UNBELIEVABLE STUFF!

Despite my relatively old age (I am well over 40), I have recently won a

### FIELDS MEDAL!!!

If you don't believe me, see for yourself!

### Thank you for dropping in to this site and come back to visit again sometime!

DISCLAIMER. All and any (if any) views, opinions, statements of fact, jokes, etc., expressed on this Web page are solely those of the individual named and pictured above, and not necessarily of the Department of Mathematics, Auburn University, or any other institution or individual. A hard copy of this disclaimer, signed and sealed in the presence of a Notary Public, is being kept locked in a safe vault at an undisclosed location.
COPYRIGHT WARNING. Any unauthorized copying of the material included in this page or any portion thereof for monetary gain or other form of profit is stricly prohibited and will be prosecuted to the full extent of the law, although I can hardly imagine anyone foolish enough to attempt to gain a single penny by doing so in the first place. (This warning too is covered by the very same warning!)