Seminars and Colloquia by Series

Hardy-Sobolev-Maz'ya Inequalities for Fractional Integrals on Halfspaces and Convex Domains

Series
Dissertation Defense
Time
Tuesday, April 19, 2011 - 16:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Craig A. Sloane – School of Mathematics, Georgia Tech
Classical Hardy, Sobolev, and Hardy-Sobolev-Maz'ya inequalities are well known results that have been studied for awhile. In recent years, these results have been been generalized to fractional integrals. This Dissertation proves a new Hardy inequality on general domains, an improved Hardy inequality on bounded convex domains, and that the sharp constant for any convex domain is the same as that known for the upper halfspace. We also prove, using a new type of rearrangement on the upper halfspace, based in part on Carlen and Loss' concept of competing symmetries, the existence of the fractional Hardy-Sobolev-Maz'ya inequality in the case p = 2, as well as proving the existence of minimizers, at least in limited cases.

Two-dimensional Riemann problems for compressible Euler systems

Series
PDE Seminar
Time
Tuesday, April 19, 2011 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Prof. Yuxi Zheng – Penn State University and Yeshiva University, –
We consider Riemann problems for the compressible Euler system in aerodynamics in two space dimensions. The solutionsinvolve shock waves, hyperbolic and elliptic regions. There are also regions which we call semi-hyperbolic. We have shownbefore the existence of such solutions, and now we show regularity of the boundaries of such regions.

A combinatorial spanning tree model for delta-graded knot Floer homology

Series
Geometry Topology Seminar
Time
Monday, April 18, 2011 - 14:20 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
John Baldwin – Princeton
I'll describe a new combinatorial method for computing the delta-graded knot Floer homology of a link in S^3. Our construction comes from iterating an unoriented skein exact triangle discovered by Manolescu, and yields a chain complex for knot Floer homology which is reminiscent of that of Khovanov homology, but is generated (roughly) by spanning trees of the black graph of the link. This is joint work with Adam Levine.

A Piecewise Smooth Image Segmentation Using Gamma-Convergence Approximation in Medical Imaging

Series
Applied and Computational Mathematics Seminar
Time
Monday, April 18, 2011 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
JungHa An – California State University, Stanislaus
Medical imaging is the application of mathematical and engineering models to create images of the human body for clinical purposes or medical science by using a medical device. One of the main objectives of medical imaging research is to find the boundary of the region of the interest. The procedure to find the boundary of the region of the interest is called a segmentation. The purpose of this talk is to present a variational region based algorithm that is able to deal with spatial perturbations of the image intensity directly. Image segmentation is obtained by using a Gamma-Convergence approximation for a multi-scale piecewise smooth model. This model overcomes the limitations of global region models while avoiding the high sensitivity of local approaches. The proposed model is implemented efficiently using recursive Gaussian convolutions. The model is applied to magnetic resonance (MR) images where image quality depends highly on the acquisition protocol. Numerical experiments on 2-dimensional human liver MR images show that our model compares favorably to existing methods.This work is done in collaborated with Mikael Rousson and Chenyang Xu.

Oral Comprehensive Exam

Series
Geometry Topology Seminar
Time
Monday, April 18, 2011 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Becca Winarski – Georgia Tech

Please Note: The actual talk will be 40 minutes. Note the unusual time.

The theorem of Birman and Hilden relates the mapping class group of a surface and its image under a covering map. I'll explore when we can extend the original theorem and possible applications for further work.

Atlanta Lecture Series in Combinatorics and Graph Theory III

Series
Other Talks
Time
Saturday, April 16, 2011 - 13:00 for 4 hours (half day)
Location
Klaus 1456
Speaker
Atlanta Lecture Series – School of Mathematics, Georgia Tech
Emory University, the Georgia Institute of Technology and Georgia State University will host a series of 9 mini-conferences from November, 2010 - April 2013. The conferences will stress a variety of areas and feature one prominent researcher giving 2 fifty minute lectures and 4 outstanding southern researchers each giving one fifty minute lecture. There will also be several 30 minute lecturers by young researchers or graduate students. The featured speaker is Maria Chudnovsky, Columbia University. The lectures begin at 1:00 PM Saturday, April 16 and end at noon on Sunday, April 17.

Generic rectangulations and pattern-avoiding permutations

Series
Combinatorics Seminar
Time
Friday, April 15, 2011 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Nathan Reading – North Carolina State University
A rectangulation is a tiling of a rectangle by rectangles. The rectangulation is called generic if no four of its rectangles share a corner. We will consider the problem of counting generic rectangulations (with n rectangles) up to combinatorial equivalence. This talk will present and explain an initial step in the enumeration: the fact that generic rectangulations are in bijection with permutations that avoid a certain set of patterns. I'll give background information on rectangulations and pattern avoidance. Then I'll make the connection between generic rectangulations and pattern avoiding permutations, which draws on earlier work with Shirley Law on "diagonal" rectangulations. I'll also comment on two theories that led to this result and its proof: the lattice theory of the weak order on permutations and the theory of combinatorial Hopf algebras.

[Special Date] Iterative 3D/4D Cone Beam CT Reconstruction on GPU in Cancer Radiation Therapy

Series
Applied and Computational Mathematics Seminar
Time
Friday, April 15, 2011 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Xun Jia – University of California, San Diego, Department of Radiation Oncology
Cone Beam Computer tomography (CBCT) has been broadly applied incancer radiation therapy, mainly for positioning patients to align withtreatment radiation beams. As opposed to tomography reconstruction problemsfor diagnostic purposes, CBCT reconstruction in radiotherapy requires a highcomputational efficiency, since it is performed while patient is lying on acouch, waiting for the treatment. Moreover, the excessive radiation dosefrom frequent scans has become a clinical concern. It is therefore desirableto develop new techniques to reconstruct CBCT images from low dose scans. Inthis talk, I will present our recent work on an iterative low dose CBCTreconstruction technique via total variation regularization and tight frameregularization. It is found that 40~60 x-ray projections are sufficient toreconstruct a volumetric image with satisfactory quality in about 2min. Wehave also studied 4 dimensional CBCT (4DCBCT) reconstruction problem viatemporal non-local means (TNLM) and high quality 4DCBCT images can beobtained. Our algorithms have been fully implemented on a graphicsprocessing unit. Detailed implementation techniques will also be addressed.

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