Fall 2021 Mathematics Colloquium

Time and Location:

Minard 212 at 3:00 PM (No refreshments this semester.)

Special Colloquia or Tri-College Colloquia venues and times may vary, please consult the individual listing.

Tuesday, October 19          Tri-College Colloquium
 Jessica Striker          at MSUM  

Promotion, rotation, and web invariant polynomials

TIME and ROOM : 3:00-4:00 in Bridges 268 (Meet and Greet with snacks: 2:30-3:00 in MacLean 268 – The President’s Board Room) 

Mask up!

Masks required in buildings on campus.


Abstract:  Algebraic combinatorics has been wildly successful in the last several decades in identifying and describing mathematical objects and actions that display extremely elegant properties. Many of the combinatorial objects with strikingly good enumerations and dynamical behavior have underlying algebraic meaning. This talk showcases such interactions between combinatorics and algebra. We first explore classical results on promotion of standard Young tableaux, rotation of matchings, and related invariant polynomials and symmetric group actions. We then discuss recent joint work with Rebecca Patrias and Oliver Pechenik involving the more general setting of increasing tableaux and webs.


Tuesday, November 9              Dana Sylvan (Hunter College, City University of New York)

Modeling and inference for probability distribution functions and quantiles of spatial-temporal processes with complex structures

Abstract: The study of probability laws or, equivalently, of quantiles of distribution functions, is fundamental in Mathematical Statistics. When the data are not independent, modeling distribution functions and quantiles become hard mathematical problems, with a wide area of applicability. The temporal and/or spatial dependence of many real-life processes may show significant departures from normality and stationary behavior. Examples include processes in atmospheric and environmental sciences, finance, public health, sports. An important practical problem is to be able to model effects of high order quantiles, say, rather than modeling mean effects, on the grounds that people are adversely affected only by very high values of temperature, precipitation, air pollution. For these reasons, policy makers have issued environmental standards that are based on more relevant distributional characteristics, such as quantiles or threshold exceedance probabilities. In this talk I will present statistical methodology for modeling and inference for probability distributions and quantiles in a wide class of space-time processes. I will discuss asymptotic properties of various estimators and predictors, and will also address computational and implementation issues. For illustration, I will show applications on precipitation and air pollution space-time data.


Tuesday, November 16             Sunil Dhar (New Jersey Institute of Technology)

Building Geometric Models, Characterization, Goodness-of-Fit, and Applications

Abstract:  The components of a reliability system broken down into mutually independent parts build geometric models. Considering environmental effects on these component probabilities results in additional new models. Conditional and total failure rates characterize the geometric models. The supremum of the absolute value of the standardized difference between the estimated probability generating function and its empirical counterpart serves as the test statistic. This test statistic evaluates the bivariate geometric model’s (BVGM’s) goodness-of-fit. One BVGM, for example, utilizes sports data as an application.

Tuesday, November 30          Tri-College Colloquium
Hongyan Hou                at NDSU   

Primitive study of Bayesian estimation of a product of several Bernoulli proportion

Abstract:  A two-stage method for estimating the lower bound of variance by allocation of sample size is introduced when estimating a product of means of independent Bernoulli population with the maximum likelihood estimator. A three-stage procedure is introduced for increasing the lower bound. A Bayesian estimator is studied and the sample size allocation is provided for the minimum Bayes risk.


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