Title: New theorems at the interface of number theory and representation theory

Abstract: Ramanujan’s first and last letters to Hardy have a breathtaking legacy. In representation theory alone they inspired the development of vertex operator algebras and the Fields medal winning work of Borcherds on Monstrous Moonshine. The speaker will recall this history, and then explain very recent developments which illustrate that these results are only glimpses of even larger theories.

Speaker: Plamen Iliev (Georgia Tech)

Title: Bispectrality and superintegrability

Abstract: The bispectral problem concerns the construction and the classification of operators possessing a symmetry between the space and spectral variables. Different versions of this problem can be solved using techniques from integrable systems, algebraic geometry, representation theory, classical orthogonal polynomials, etc. I will review the problem and some of these connections and then discuss new results related to the generic quantum superintegrable system on the sphere.

Speaker: Piper Harron (UH Manoa)

Title: Equidistribution of shapes of number fields of degree 3, 4, and 5.

Abstract: In her talk, Piper Harron will introduce the ideas that there are number fields, that number fields have shapes, and that these shapes are everywhere you want them to be. This result is joint work with Manjul Bhargava and uses his counting methods which currently we only have for cubic, quartic, and quintic fields. She will sketch the proof of this result and leave the rest as an exercise for the audience. (Check your work by downloading her thesis!).

Speaker: Gideon Zamba (U. Iowa)

Title: Applied Mathematics in Action through Biostatistics

PBRC Seminar
Title: Hydrodynamic reception and predator avoidance by free-swimming organisms

Dr. Daisuke Takagi
Dept. of Mathematics and PBRC

where: AgSc 219
When: Thurs, Jan 26, 4-5pm

Speaker: Gideon Zamba (U. Iowa)

Title: A Semi-parametric Random-cell type of goodness-of-fit Test when Observations are Recurrent

Abstract: Goodness-of-fit of the distribution function governing time to occurrence of recurrent events is considered. We develop a chi-square type of test based on the nonparametric maximum likelihood estimator (NPMLE) of the inter-event time distribution. The test is based on the minimum chi-squared estimator of a parametric family and compares the estimated parametric null to the NPMLE on k partitions of a calendar time over a study monitoring period. Small sample and asymptotic properties of the proposed statistic are investigated. Simulation results for Weibull lifetime models are discussed and large sample properties of the test statistic are established using empirical process tools. The approach is then applied to jet planes air conditioning system failures.