Seminars and Colloquia by Series

The Kelmans-Seymour conjecture II: 2-vertices in K_4^- (Intermediate structure and finding TK_5)

Series
Graph Theory Seminar
Time
Wednesday, March 2, 2016 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Yan Wang – Math, GT
We use K_4^- to denote the graph obtained from K_4 by removing an edge,and use TK_5 to denote a subdivision of K_5. Let G be a 5-connected nonplanar graph and {x_1, x_2, y_1, y_2} \subseteq V (G) such that G[{x_1,x_2, y_1, y_2}] = K_4^- with y_1y_2 \in E(G). Let w_1,w_2,w_3 \in N(y_2)- {x_1,x_2} be distinct. We show that G contains a TK_5 in which y_2 is not a branch vertex, or G - y_2 contains K_4^-, or G has a special 5-separation, or G' := G - {y_2v : v \in {w_1,w_2,w_3, x_1, x_2}} contains TK_5.In this talk, we will obtain a substructure in G' and several additional paths in G', and then use this substructure to find the desired TK_5.

Commutators and BMO

Series
Analysis Seminar
Time
Wednesday, March 2, 2016 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Brett Wick – GT and Washington University St Louis
In this talk we will discuss the connection between functions with bounded mean oscillation (BMO) and commutators of Calderon-Zygmund operators. In particular, we will discuss how to characterize certain BMO spaces related to second order differential operators in terms of Riesz transforms adapted to the operator and how to characterize commutators when acting on weighted Lebesgue spaces.

Index theory for symplectic matrix paths and periodic solutions of Hamiltonian systems with prescribed energy

Series
CDSNS Colloquium
Time
Wednesday, March 2, 2016 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Yiming Long – Nankai University
One of the major tools in the study of periodic solutions of Hamiltonian systems is the Maslov-type index theory for symplectic matrix paths. In this lecture, I shall give first a brief introduction on the Maslov-type index theory for symplectic matrix paths as well as the iteration theory of this index. As an application of these theories I shall give a brief survey about the existence, multiplicity and stability problems on periodic solution orbits of Hamiltonian systems with prescribed energy, especially those obtained in recent years. I shall also briefly explain some ideas in these studies, and propose some open problems.

Geometric understanding and analysis of unstructured data

Series
School of Mathematics Colloquium
Time
Monday, February 29, 2016 - 16:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Hongkai Zhao – University of California, Irvine
One of the simplest and most natural ways of representing geometry and information in three and higher dimensions is using point clouds, such as scanned 3D points for shape modeling and feature vectors viewed as points embedded in high dimensions for general data analysis. Geometric understanding and analysis of point cloud data poses many challenges since they are unstructured, for which a global mesh or parametrization is difficult if not impossible to obtain in practice. Moreover, the embedding is highly non-unique due to rigid and non-rigid transformations. In this talk, I will present some of our recent work on geometric understanding and analysis of point cloud data. I will first discuss a multi-scale method for non-rigid point cloud registration based on the Laplace-Beltrami eigenmap and optimal transport. The registration is defined in distribution sense which provides both generality and flexibility. If time permits I will also discuss solving geometric partial differential equations directly on point clouds and show how it can be used to “connect the dots” to extract intrinsic geometric information for the underlying manifold.

Strong reductions for extended formulations

Series
ACO Student Seminar
Time
Friday, February 26, 2016 - 13:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Aurko Roy – Georgia Tech
We generalize the existing reduction mechanism due to Braun, Pokutta and Zink (2014)for linear programming problems and semidefinite programming problems in two ways 1) relaxing the requirement of affineness2) extending to fractional optimization problems As applications we prove several new LP-hardness and SDP-hardnessresults, e.g., for the (non-uniform) Sparsest Cut problem with bounded treewidth on the supply graph, the Balanced Separator problem with bounded treewidth onthe demand graph, the Max Cut problem and the Matching problem on 3-regular graphs.We also provide a new, very strong Lasserre integrality gapfor the Independent Set problem, which is strictly greater than thebest known LP approximation, showing that the Lasserre hierarchydoes not always provide the tightest SDP relaxation.Joint work with Gabor Braun and Sebastian Pokutta.

Introduction to stochastic processes

Series
Dynamical Systems Working Seminar
Time
Friday, February 26, 2016 - 13:05 for 1 hour (actually 50 minutes)
Location
Skiles 170
Speaker
Hongyu Cheng – Georgia Tech
We present some basic results from the theory of stochastic processes and investigate the properties of some standard continuous-time stochastic processes. Firstly, we give the definition of a stochastic process. Secondly, we introduce Brownian motion and study some of its properties. Thirdly, we give some classical examples of stochastic processes in continuous time and at last prove some famous theorems.

Central Limit Theorems and Bootstrap in High Dimensions

Series
Stochastics Seminar
Time
Thursday, February 25, 2016 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Victor Chernozhukov – MIT

Please Note: Paper available on arXiv:1412.3661

This paper derives central limit and bootstrap theorems for probabilities that sums of centered high-dimensional random vectors hit hyperrectangles and sparsely convex sets. Specifically, we derive Gaussian and bootstrap approximations for probabilities Pr(n−1/2∑ni=1Xi∈A) where X1,…,Xn are independent random vectors in ℝp and Ais a hyperrectangle, or, more generally, a sparsely convex set, and show that the approximation error converges to zero even if p=pn→∞ as n→∞ and p≫n; in particular, p can be as large as O(eCnc) for some constants c,C>0. The result holds uniformly over all hyperrectangles, or more generally, sparsely convex sets, and does not require any restriction on the correlation structure among coordinates of Xi. Sparsely convex sets are sets that can be represented as intersections of many convex sets whose indicator functions depend only on a small subset of their arguments, with hyperrectangles being a special case.

Dynamical systems and beyond

Series
School of Mathematics Colloquium
Time
Thursday, February 25, 2016 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Stefan Siegmund – TU Dresden –
From theoretical to applied, we present curiosity driven research which goes beyond classical dynamical systems theory and (i) extend the notion of chaos to actions of topological semigroups, (ii) model how the human bone renews, (iii) study transient dynamics as it occurs e.g. in oceanography, (iv) understand how to protect houses from hurricane damage. The talk introduces concepts from topological dynamics, mathematical biology, entropy theory and mechanics.

The Kelmans-Seymour conjecture II: 2-vertices in K_4^- (Non-separating paths)

Series
Graph Theory Seminar
Time
Wednesday, February 24, 2016 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Yan Wang – Math, GT
We use K_4^- to denote the graph obtained from K_4 by removing an edge,and use TK_5 to denote a subdivision of K_5. Let G be a 5-connected nonplanar graph and {x_1, x_2, y_1, y_2} \subseteq V (G) such that G[{x_1,x_2, y_1, y_2}] = K_4^- with y_1y_2 \in E(G). Let w_1,w_2,w_3 \in N(y_2)- {x_1,x_2} be distinct. We show that G contains a TK_5 in which y_2 is not a branch vertex, or G - y_2 contains K_4^-, or G has a special 5-separation, or G - {y_2v : v \in {w_1,w_2,w_3, x_1, x_2}} contains TK_5.In this talk, we will show the existence of a path X in G whose removal does not affect connectivity too much.

Multicommutators

Series
Analysis Seminar
Time
Wednesday, February 24, 2016 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Danqing He – University of Missouri, Columbia –
We generalize the Calderon commutator to the higher-dimensional multicommutator with more input functions in higher dimensions. For this new multilinear operator, we establish the strong boundedness of it in all possible open points by a new multilinear multiplier theorem utilizing a new type of Sobolev spaces.

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