UMass Amherst Math/Stat Seminars (Weekly Schedule)

Monday, Nov 23 at 4:00pm: Statistics and Probability Seminar - Daniel W. Chambers

Statistics and Probability Seminar
Forecasting with Hidden Markov Models
Daniel W. Chambers , Mathematics Department, Boston College

A hidden Markov model (HMM) consists of two random processes: a state sequence X_1, X_2, . . . and an observation sequence Y_1, Y_2 , . . . The state sequence is unknown (hidden), while the observation sequence is seen. The state sequence is a Markov chain and, at each time t, the observation Y_t depends on the state of the system- that is, the value of X_t . Hidden Markov models saw early use in speech recognition, but have seen applications in many other settings, including modeling ion channels, genetic sequences, and seismological activity. We will review HMM�s, including parameter estimation algorithms, and then give a straightforward extension that allows us to forecast future observations, given past observations. That is, we will give the (calculable) density of Y_t+k, conditional on the values of Y_1 , . . . , Y_t for any k ≥ 1. We will give two examples: (1) the �occasionally dishonest casino� of Durbin et al. (Biological Sequence Analysis), and (2) forecasting mainshock earthquake activity in southern California (joint work with John Ebel, Alan Kafka, and Jenny Baglivo).

Refreshments at 3:45

4:00pm-5:00pm, Monday, November 23, 2009 in LGRT 1634

Monday, Nov 23 at 4:00pm: Representation Theory - Ryan Reich

Representation Theory
Twisted geometric Satake correspondence
Ryan Reich, Harvard

Geometric Satake correspondence is a way to construct from a reductive group G its Langlands dual group G*. (One can think of it as a deep generalization of duality of vector spaces.) This is a bases of the geometric approach to ``Langlands program'' which is a unifying view on much of Number Theory, Representation Theory, Algebraic Geometry and more recently also some Quantum Field Theory. The ``twisted'' version is a recent development which extends the scope of Langlands program.

4:00pm-5:00pm, Monday, November 23, 2009 in LGRT 1234
Note special room

Tuesday, Nov 24 at 4:00pm: Five College Number Theory Seminar - Andrew Yang

Five College Number Theory Seminar
On the low-lying zeros of Dedekind zeta functions attached to cubic number fields
Andrew Yang, Dartmouth College

We study the distribution of low-lying zeros of Dedekind zeta functions attached to cubic number fields, in the sense of the Katz-Sarnak philosophy, using the work of Davenport and Heilbronn on counting cubic number fields, as well as recent work of Belabas, Bhargava, and Pomerance, on error terms in Davenport and Heilbronn's counts. In accordance with the predictions of the Katz-Sarnak philosophy, we find that the distribution of low-lying zeros predicts a symplectic symmetry type for the family of Dedekind zeta functions of cubic number fields.

Refreshments at 3:30pm in Seeley-Mudd 208

4:00pm-5:00pm, Tuesday, November 24, 2009 in Seeley-Mudd 207, Amherst College