Frontiers of Scientific Computing Lecture Series

Posted September 24, 2016

3:30 pm - 4:30 pm 1034 Digital Media Center
Dongbin Xiu, Ohio State University

Approximation Algorithms for Big Data

Abstract: One of the central tasks in scientific computing is to accurately approximate unknown target functions. This is typically done with the help of data samples of the unknown functions. In statistics this falls into the realm of regression and machine learning. In mathematics, it is the central theme of approximation theory. The emergence of Big Data presents both opportunities and challenges. On one hand, big data introduces more information about the unknowns and, in principle, allows us to create more accurate models. On the other hand, data storage and processing become highly challenging. Moreover, data often contain certain corruption errors, in addition to the standard noisy errors. In this talk, we present some new developments regarding certain aspects of big data approximation. More specifically, we present numerical algorithms that address two issues: (1) how to automatically eliminate corruption/biased errors in data; and (2) how to create accurate approximation models in very high dimensional spaces using stream/live data, without the need to store the entire data set. We present both the numerical algorithms, which are easy to implement, as well as rigorous analysis for their theoretical foundation.

Algebra and Number Theory Seminar
Questions or comments?

Posted September 28, 2016

Last modified October 20, 2016

Simon Riche, CNRS / Université de Clermont-Ferrand

Character formulas in the modular representation theory of reductive algebraic groups

Abstract

In this talk I will present a project (including joint works with Pramod

Achar, Shotaro Makisumi, Carl Mautner, and Geordie Williamson) which

aims at providing a character formula for simple representations of

reductive algebraic groups over fields of positive characteristic. This

formula is inspired by Lusztig's conjecture, but different, and is

expected to hold in all characteristics bigger than the Coxeter number.

We expect to prove this formula using a geometric approach involving

coherent sheaves on the Springer resolution and constructible sheaves on

the affine flag variety and the affine Grassmannian of the Langlands

dual group.

Posted September 26, 2016

Last modified October 12, 2016

Workshop: Math Communications

The workshop targeted towards mathematics will be organized by the College of Science: Dawn Jenkins and Paige Jarreau