Seminars, Colloquia, and Conferences
2013 Norbert Wiener Lectures
Professor of Mathematics and Computer Science,
William Morrill Professor of Mathematics and Computer Science, Dartmouth College
PROBABILITY AND INTUITION
(March 11-13, 2013)
Probability Puzzles that Boggle the Mind
Monday, March 11, 4:30pm; Pearson 104
Reception: 5:30-6:30pm, Alumnae Lounge
Humans are not born with perfect probabilistic intuition,
to say the least, yet most decisions we make are based on "feel",
not calculation. Today you will hear some probability puzzles
(some with solutions, some without) that are designed to help you
adjust your intuition when it's about to run off the rails.
New Directions in Random Walk on a Graph
Tuesday, March 12, 4:30pm; Bromfield-Pearson Building 2
Reception: 4:00pm, Mathematics Conference Room
Random walk on a graph is a beautiful and (viewed from today) classical
subject with elegant theorems, multiple applications, and a close connection
to the theory of electrical networks. The subject seems to be livelier
now than ever, with lots of exciting new results.
Recent progress has provided some answers that match our intuition and
others that make us raise our eyebrows. Questions include:
how long can it take to visit every edge of a graph, or to visit every
vertex a representative number of times, or to catch a random walker?
Can random walks be scheduled or coupled so that they don't collide?
Can moving targets be harder to hit than fixed targets?
Mentioned will be work by or with Omer Angel, Jian Ding, Agelos Georgakopoulos,
Ander Holroyd, Natasha Komarov, James Lee, James Martin, Yuval Peres,
Perla Sousi, and David Wilson.
Random Walk and the Gittins Index
Wednesday, March 13, 3:00pm; Barnum Hall 104
Reception: 4:00-5:00pm, Barnum Hall 8
Suppose you want to reach some goal in least expected time, and there
are several routes, each involving some randomness. Naturally, you
pick the route that offers least expected time to the goal.
Things would seem to me vastly more complicated if you are allowed to
change your mind as time progresses; then, for example, you might want
to choose a route that could work fast but if it doesn't, will fail
quickly so you have time to try something else.
Amazingly, there's a simple parameter – a variation of the "Gittins index"
– that tells you how to play this game optimally. We'll present
our adaptation of a fabulous proof, due to Richard Weber, that this really works.
(Joint work with Ioana Dumitriu and Prasad Tetali).
The Norbert Wiener Lectures were initially funded by an anonymous gift
to the Department of Mathematics. All talks are free and open to the
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