Mathematics

Williams 17th in 2009 Putnam

Continuing our strong performance in last year’s Putnam Competition, the Williams team (comprised from Nick Arnosti, Carlos Dominguez, Jake Levinson and Wei Sun) placed 17th in North America, with all four scoring in the top 500 of over 3000 students. Click here for the problems and… Continue reading »

Geometry in Banff

I have been spending my sabbatical this year at MSRI and the University of California, Berkeley.  I cannot complain about the great interaction with faculty from all over the world, and the wonderful “sunny and 65” days in the Bay area.  So why did I spend… Continue reading »

Transferrific Day

Transferrific Day was January 22, 2010 for the Williams Math/Stat department. For a number of years we have taken a day (or  an afternoon) in January to learn together some area of math. This year we used as a springboard David Ruelle’s Dynamical Zeta Functions and Transfer Operators (… Continue reading »

Soap Bubbles Everywhere

Since soap bubbles minimizing surface area or energy provide the typical model for my research in the calculus of variations, I receive lots of related and unrelated reports from friends. My former student Kevin Hahm ’07 sent me a link to an amazing video of water droplets… Continue reading »

Symmetrization

Write-up of a departmental faculty seminar, October 2, 2009 Solutions to problems in geometry and physics and even in the social sciences tend to be symmetric. As prime example, the solution to the isoperimetric problem, which seeks the least-perimeter way to enclose given volume in R3, is a sphere, the most symmetric of all shapes. One way to prove this is to show that anything else improves as you make it more symmetric. For thousands of years, mathematicians have been looking for good ways to make shapes more symmetric and to prove that as they get more symmetric they “get better,” for example, enclose the same volume with less perimeter. My favorite references are Burago and Zalgaller [BZ, §9.2] and Ros [R1, §3.2]. This talk is based on [MHH]. Gromov [G, §9.4] provides some sweeping remarks and generalizations, including most of our results. 1. Steiner symmetrization [St, 1838] replaces every vertical slice of a region in R3 with a centered interval of the same length, as in Figure 1. By calculus, the volume does not change, but one can show that the perimeter decreases (or remains the same).             Figure 1. Steiner symmetrization replaces every vertical slice with a centered interval of the same length. www.math.utah.edu/~treiberg/Lect.html Continue reading »

Like Risk? Be an Actuary!

Do you like risk? Or, more precisely, do you like to assess and quantify risk and put a price on it (the premium that insurance collects)? If yes, consider becoming an actuary. This profession almost always makes the top 10 in the various best jobs lists (like this… Continue reading »

The UnKnot Conference

Two weeks ago, the first UnKnot Conference was held in Granville, Ohio at Denison University. And no, UnKnot does not stand for a conference devoted to the properties of the trivial knot, which would be short conference indeed, but rather for the Undergraduate Knot Theory Conference. Organized by… Continue reading »

Mathematics and the Iranian Elections

One of the many things I love about mathematics is that results initially discovered in one realm pop up in surprising places. A terrific example is Benford’s law of digit bias (those taking Math 341 in the fall will get to learn a lot more about this!). Benford’s… Continue reading »

Compactness

In my opinion, compactness is the most important concept in mathematics. Here’s an article, recently published in Pro Mathematica, that tracks compactness from the one-dimensional real line in calculus to infinite dimensional spaces of functions and surfaces. Continue reading »

Crocodilia, Sex Ratios, and Fisher’s Theorem

Crocodilia, the biological order that includes alligators and crocodiles, have the interesting property that the gender of offspring is not determined by random genetics but by the environment of the nesting site. Prime nesting sights, in wet marshes near water sources, produce nearly 80% female hatchlings. The… Continue reading »