Shmuel Weinberger

Shmuel Weinberger is an American mathematician. His research interests include geometric topology, differential geometry, geometric group theory, and, in recent years, applications of topology in other disciplines. He has written a book on topologically stratified spaces and one on the application of mathematical logic to geometry. He irregularly keeps a blog on which you can read I am a math professor at University of Chicago. I mainly work in geometry and topology, but I am curious about all sorts of things. I think of myself as an optimist, but many others do not.

 

"Flows and walks on graphs": Suppose that a bacterium splits in two with probability 1/2 or otherwise dies, and we start with a small colony of 1000 bacteria. Can we expect to obtain an immortal colony? If I randomly walk on a line from a position one unit from my home, and I go in each direction with equal probability, how long will it take me to get home? What about in higher dimensional space? Is it possible to rearrange the assets of the points of a graph through trade among neighbors so that all profit? These are among the problems that I will explain and interrelate in this introduction to the geometric/probabilistic side of graphs.