MAA Joint Meeting of the Northeastern and Seaway Sections June 21-22, 2001, Williams College

Program Registration Contributed and Student Papers Directions Program Committee NES/MAA Home

Friday, June 21, 2002 2:00-2:45 pm Executive Committee Meeting 3:00-3:45 pm Tea (and Project NExT) 4:00-4:45 pm Thomas C. Hales, Mellon Professor of Mathematics, University of Pittsburgh "Computer and Proof in the Context of Discrete Geometry" 5:00-5:20 pm 5:30-5:50 pm 6:00-6:20 pm Future Colleagues Talks in parallel (This year, undergraduates as well as graduate students) 6:30 pm Dinner 8:00 pm Thomas Garrity, Professor of Mathematics, Williams College "On Writing Numbers: The Hermite Problem" Saturday, June 22, 2002 9:00-9:30 am Sean McLaughlin, graduate student in Computer Science, New York University "Verification of Free Choice" 9:45-10:15 am 10:30-11:00 am Contributed papers in parallel 11:30-11:55 am Business meeting 12:00-1:00 pm Lunch 1:15-2:15 pm Hike or visit to Clark Art Museum Abstracts and Biographies Thomas C. Hales, Battles Lecturer "Computer and Proof in the Context of Discrete Geometry" Abstract: Gian-Carlo Rota once wrote that mathematicians are ``on the lookout for an argument that will make all computer programs obsolete.'' At the other extreme is the elusive search for the computer program that will make all mathematicians obsolete. This lecture will discuss the interplay of computers and mathematical proof in the context of some large-scale computer-assisted proofs, such as the Kepler Conjecture. Hales is Mellon Professor of Mathematics at the University of Pittsburgh. After attending Stanford and Princeton, he took posts at MSRI, Harvard, IAS, Chicago, CNRS, and Michigan. He recently proved the 400-year-old Kepler Conjecture on sphere packing, as well as the 2000-year-old Hexagonal Honeycomb Conjecture on efficient partitions of the plane. The proof of the Kepler Conjecture used extensive and intricate computer calculations, and he is now looking at ways to use computers to prove other difficult theorems. Thomas Garrity, Dinner Speaker "On Writing Numbers: The Hermite Problem" Abstract: What is the best way of writing numbers? Rationals are easily identified by their periodic decimal expansions. Quadratic irrationals are easily identified by periodic continued fraction expansions. But what about cubics, etc? This is the Hermite Problem. Garrity is Professor of Mathematics and recent chair at Williams College. He was an undergraduate at the University of Texas at Austin, a graduate student at Brown, and an Evans Instructor at Rice before coming to Williams in 1989. He has spent leaves at Washington and Michigan. He works in algebraic and differential geometry and number theory, and has a new book on "All the Mathematics You Missed [But Need to Know for Graduate School]." Sean McLaughlin "Verification of Free Choice" Abstract: Verification is the process of mathematically proving that a computer program is correct. We will look at classical deterministic and probabilistic "free choice" algorithms for solving Dijkstra's notorious "Dining Philosophers problem" and present new results on how implementations can be proven correct. McLaughlin is a graduate student in Computer Science at New York University. While an undergraduate at The University of Michigan, he won the national Morgan Prize for undergraduate research for his work under Hales in proving the Dodecahedral Conjecture on local sphere packing.