Seminars and Colloquia by Series

On the product of differences of sets in finite fields

Series
Combinatorics Seminar
Time
Friday, January 22, 2016 - 16:00 for 1 hour (actually 50 minutes)
Location
Skiles 154
Speaker
Georgios Petridis – University of Rochester –
We show that there exists an absolute constant c>0 with the following property. Let A be a set in a finite field with q elements. If |A|>q^{2/3-c}, then the set (A-A)(A-A) consisting of products of pairwise differences of elements of A contains at least q/2 elements. It appears that this is the first instance in the literature where such a conclusion is reached for such type sum-product-in-finite-fileds questions for sets of smaller cardinality than q^{2/3}. Similar questions have been investigated by Hart-Iosevich-Solymosi and Balog.

High-dimensional change-point detection: kernel-based method and sketching

Series
Stochastics Seminar
Time
Thursday, January 21, 2016 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Yao Xie – Georgia Inst. of Technology, ISYE
Detecting change-points from high-dimensional streaming data is a fundamental problem that arises in many big-data applications such as video processing, sensor networks, and social networks. Challenges herein include developing algorithms that have low computational complexity and good statistical power, that can exploit structures to detecting weak signals, and that can provide reliable results over larger classes of data distributions. I will present two aspects of our recent work that tackle these challenges: (1) developing kernel-based methods based on nonparametric statistics; and (2) using sketching of high-dimensional data vectors to reduce data dimensionality. We also provide theoretical performance bounds and demonstrate the performance of the algorithms using simulated and real data.

Hybrid simulation methods: simulating the world around you

Series
Job Candidate Talk
Time
Thursday, January 21, 2016 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Craig Schroeder – UCLA
Hybrid particle/grid numerical methods have been around for a long time, andtheir usage is common in some fields, from plasma physics to artist-directedfluids. I will explore the use of hybrid methods to simulate many differentcomplex phenomena occurring all around you, from wine to shaving foam and fromsand to the snow in Disney's Frozen. I will also talk about some of thepractical advantages and disadvantages of hybrid methods and how one of theweaknesses that has long plagued them can now be fixed.

The Kelmans-Seymour conjecture

Series
Combinatorics Seminar
Time
Wednesday, January 20, 2016 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Yan Wang – Math, GT
Seymour and, independently, Kelmans conjectured in the 1970s that every 5-connected nonplanar graph contains a subdivision of $K_5$. This conjecture was proved by Ma and Yu for graphs containing $K_4^-$. Recently, we proved this entire Kelmans-Seymour conjecture. In this talk, I will give a sketch of our proof, and discuss related problems. This is joint work with Dawei He and Xingxing Yu.

Exponential bases and frames on fractals

Series
Analysis Seminar
Time
Wednesday, January 20, 2016 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
ChunKit Lai – San Francisco State University –
We study the construction of exponential bases and exponential frames on general $L^2$ space with the measures supported on self-affine fractals. This problem dates back to the conjecture of Fuglede. It lies at the interface between analysis, geometry and number theory and it relates to translational tilings. In this talk, we give an introduction to this topic, and report on some of the recent advances. In particular, the possibility of constructing exponential frames on fractal measures without exponential bases will be discussed.

A General Framework for High-Dimensional Inference and Multiple Testing

Series
Job Candidate Talk
Time
Tuesday, January 19, 2016 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Yang Ning – Princeton University –
We consider the problem of how to control the measures of false scientific discoveries in high-dimensional models. Towards this goal, we focus on the uncertainty assessment for low dimensional components in high-dimensional models. Specifically, we propose a novel decorrelated likelihood based framework to obtain valid p-values for generic penalized M-estimators. Unlike most existing inferential methods which are tailored for individual models, our method provides a general framework for high-dimensional inference and is applicable to a wide variety of applications, including generalized linear models, graphical models, classifications and survival analysis. The proposed method provides optimal tests and confidence intervals. The extensions to general estimating equations are discussed. Finally, we show that the p-values can be combined to control the false discovery rate in multiple hypothesis testing.

Deterministic Random Walk on Finite Graphs

Series
Joint ACO and ARC Seminar
Time
Tuesday, January 19, 2016 - 13:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Shuji Kijima – Kyushu University
The rotor-router model, also known as the Propp machine, is a deterministic process analogous to a simple random walk on a graph. In this talk, we are concerned with a generalized model, functional-router model, which imitates a Markov chain possibly containing irrational transition probabilities. We investigate the discrepancy of the number of tokens between the functional-router model and its corresponding Markov chain, and give some upper bounds in terms of the mixing time of the Markov chain.

Sparsified Cholesky and Multigrid Solvers for Connection Laplacians

Series
ACO Student Seminar
Time
Friday, January 15, 2016 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Richard Peng – Georgia Tech
We introduce the sparsified Cholesky and sparsified multigrid algorithms for solving systems of linear equations. These algorithms accelerate Gaussian elimination by sparsifying the nonzero matrix entries created by the elimination process.We use these new algorithms to derive the first nearly linear time algorithms for solving systems of equations in connection Laplacians, a generalization of Laplacian matrices that arise in many problems inimage and signal processing.We also prove that every connection Laplacian has a linear sized approximate inverse. This is an LU factorization with a linear number of nonzero entries that is a strong approximation of the originalmatrix. Using such a factorization one can solve systems of equations in a connection Laplacian in linear time. Such a factorization was unknown even for ordinary graph Laplacians.Joint work with Rasmus Kyng, Yin Tat Lee, Sushant Sachdeva, and Daniel Spielman. Manuscript at http://arxiv.org/abs/1512.01892.

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