Posted December 17, 2018
Last modified March 17, 2019
Timo Richarz, Technische Universitat Darmstadt
Smoothness of Schubert varieties in affine Grassmannians
The geometry in the reduction of Shimura varieties, respectively moduli spaces of Drinfeld shtuka plays a central role in the Langlands program, and it is desirable to single out cases of smooth reduction. This question reduces to the corresponding Schubert variety which is defined in terms of linear algebra, and thus easier to handle.
We consider Schubert varieties which are associated with a reductive group G over a Laurent series local field, and a special vertex in the Bruhat-Tits building. If G splits, a strikingly simple classification is given by a Theorem of Evans-Mirkovic and Malkin-Ostrik-Vybornov. If G does not split, the analogue of their theorem fails: there is a single surprising additional case of "exotic smoothness". In my talk, I explain how to obtain a complete list of the smooth and rationally smooth Schubert varieties. This is joint work with Thomas J. Haines from Maryland.
Posted February 14, 2019
Last modified March 15, 2019
Hongbo Dong, Washington State University
On structured sparsity learning with affine sparsity constraints
Abstract: We introduce a new constraint system, namely affine sparsity constraints (ASC), as a general optimization framework for structured sparse variable selection in statistical learning. Such a system arises when there are nontrivial logical conditions on the sparsity of certain unknown model parameters to be estimated. One classical nontrivial logical condition is the heredity principle in regression models, where interaction terms of predictor variables can be introduced into the model only if the corresponding linear terms already exist in the model. Formally, extending a cardinality constraint, an ASC system is defined by a system of linear inequalities of binary indicators, which represent nonzero patterns of unknown parameters in estimation. We study some fundamental properties of such a system, including set closedness and set convergence of approximations, by using tools in polyhedral theory and variational analysis. We will also study conditions under which optimization with ASC can be reduced to integer programs or mathematical programming with complementarity conditions (MPCC), where algorithms and efficient implementation already exist. Finally, we will focus on the problem of regression with heredity principle, with our previous results, we derive nonconvex penalty formulations that are direct extensions of convex penalties proposed in the literature for this problem.
Posted January 27, 2019
Last modified March 13, 2019
Federico Salmoiraghi, Department of Mathematics, LSU
Posted March 15, 20193:30 pm - 4:30 pm Lockett 232
Yichuan Zhao, Georgia State University
Empirical likelihood for the bivariate survival function under univariate censoring
Abstract: The bivariate survival function plays an important role in multivariate survival analysis. Using the idea of influence functions, we develop empirical likelihood confidence intervals for the bivariate survival function in the presence of univariate censoring. It is shown that the empirical log-likelihood ratio has an asymptotic standard chi-squared distribution with one degree of freedom. A comprehensive simulation study shows that the proposed method outperforms both the traditional normal approximation method and the adjusted empirical likelihood method in most cases. The Diabetic Retinopathy Data are analyzed for illustration of the proposed procedure. This is joint work with Haitao Huang.
Posted March 13, 20195:30 pm Keiser Math Lounge (Lockett 321)
ASA Club Meeting
Cabe Chadick, who is an LSU alumnus and the President & Managing Principal of Lewis & Ellis, Inc Dallas, Texas, will be our speaker.
Pizza will be served.
Posted January 9, 2019
Last modified March 18, 2019
Amarjit Budhiraja, UNC Chapel Hill
On Some Calculus of Variations Problems for Rare Event Asymptotics
The theory of large deviations gives decay rates of probabilities of rare events in terms of certain optimal control problems. In general these control problems do not admit simple form solutions and one needs numerical methods in order to obtain useful information. In this talk I will present some large deviation problems where one can use methods of calculus of variations to give explicit solutions to the associated optimal control problems. These solutions then yield explicit asymptotic formulas for probability decay rates in several settings.