Sadly the public has very little idea of what mathematicians do. Do they add bigger and bigger numbers? Do they balance big checkbooks? In this talk I will try to give you a taste of mathematical research through polyhedra. These are very pretty objects and are familiar to everyone from a young age: Polygons, triangles, squares, cubes, pyramids, Platonic solids have captivated humans attention for thousands of years and are familiar shapes from childhood. Polyhedra in high-dimensional versions turn out to be widely used in applied mathematics. Their beauty and simplicity appeal to all, but very few people know of the many easy-to-state but difficult-to-solve mathematical problems that hide behind their beauty. They illustrate well what a modern mathematician does everyday. This lecture will have lots of nice pictures and will introduce the audience to some fascinating unsolved questions at the frontier of mathematical research and its applications. No prior knowledge beyond your faint memory of high school geometry will be assumed.

#### About the Speaker

Jesús A. De Loera is a Professor of Mathematics at the University of California, Davis. In recognition of his contributions to Computational Discrete Mathematics and Optimization, he was elected Fellow of both the American Mathematical Society and the Society of Industrial and Applied Mathematics and is a winner of the Farkas Prize of the INFORMS Optimization Society. For his teaching and mentoring he won the Distinguished Teaching Award of the College of Letters and Science and the Golden Section Teaching award from the Mathematical Association of America. He is currently a vice-president of AMS and editor for SIAM and Sociedad Matematica Mexicana. He has mentored more than 20 Ph.D. students and dozens of undergraduates. He is eager to have more people like and enjoy mathematics.