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Series: School of Mathematics Colloquium

Pre-reception at 2:30 in Room N201. If you would like to meet with Prof. Ashtekar while he is on campus (at the Center for Relativistic Astrophysics - Boggs building), please contact <A class="moz-txt-link-abbreviated" href="mailto:lori.federico@physics.gatech.edu">lori.federico@physics.gatech.edu</a>.

General relativity is based on a deep interplay between physics and mathematics: Gravity is encoded in geometry. It has had spectacular observational success and has also pushed forward the frontier of geometric analysis. But the theory is incomplete because it ignores quantum physics. It predicts that the space-time ends at singularities such as the big-bang. Physics then comes to a halt. Recent developments in loop quantum gravity show that these predictions arise because the theory has been pushed beyond the domain of its validity. With new inputs from mathematics, one can extend cosmology beyond the big-bang. The talk will provide an overview of this new and rich interplay between physics and mathematics.

Series: Analysis Seminar

We will survey recent developments in the area of two weight inequalities, especially those relevant for singular integrals. In the second lecture, we will go into some details of recent characterizations of maximal singular integrals of the speaker, Eric Sawyer, and Ignacio Uriate-Tuero.

Series: ACO Student Seminar

A central question in the theory of card shuffling is how quickly a deck of
cards becomes 'well-shuffled' given a shuffling rule. In this talk, I will
discuss a probabilistic card shuffling model known as the 'interchange
process'. A
conjecture from 1992 about this model has recently been resolved
and I will address how my work has been involved with this conjecture. I
will also discuss other card shuffling models.

Series: PDE Seminar

We prove that solutions of the Navier-Stokes equations of
three-dimensional, compressible flow, restricted to fluid-particle
trajectories, can be extended as analytic functions of complex time. One
important corollary is backwards uniqueness: if two such solutions agree
at a given time, then they must agree at all previous times.
Additionally, analyticity yields sharp estimates for the time
derivatives of arbitrary order of solutions along particle trajectories.
I'm going to integrate into the talk something like a "pretalk" in an
attempt to motivate the more technical material and to make things
accessible to a general analysis audience.

Series: CDSNS Colloquium

The Bendixson conditions for general nonlinear differential equations in Banach spaces are developed in terms of stability of associated compound differential equations. The generalized Bendixson criterion states that, if some measure of 2-dimensional surface area tends to zero with time, then there are no closed curves that are left invariant by the dynamics. In particular, there are no nontrivial periodic orbits, homoclinic loops or heteroclinic loops. Concrete conditions that preclude the existence of periodic solutions for a parabolic PDE will be given. This is joint work with Professor James S. Muldowney at University of Alberta.

Series: Combinatorics Seminar

In this lecture, I will explain the greedy approximation algorithm on submodular function maximization due to Nemhauser, Wolsey, and Fisher. Then I will apply this algorithm to the problem of approximating an monotone submodular functions by another submodular function with succinct representation. This approximation method is based on the maximum volume ellipsoid inscribed in a centrally symmetric convex body. This is joint work with Michel Goemans, Nick Harvey, and Vahab Mirrokni.

Series: Combinatorics Seminar

In this lecture, I will review combinatorial algorithms for minimizing submodular functions. In particular, I will present a new combinatorial algorithm obtained in my recent joint work with Jim Orlin.

Tuesday, August 18, 2009 - 14:00 ,
Location: Skiles 255 ,
Justin W. L. Wan ,
Computer Science, University of Waterloo ,
Organizer: Sung Ha Kang

In image guided procedures such as radiation therapies and computer-assisted surgeries, physicians often need to align images that are taken at different times and by different modalities. Typically, a rigid registration is performed first, followed by a nonrigid registration. We are interested in efficient registrations methods which are robust (numerical solution procedure will not get stuck at local minima) and fast (ideally real time). We will present a robust continuous mutual information model for multimodality regisration and explore the new emerging parallel hardware for fast computation. Nonrigid registration is then applied afterwards to further enhance the results. Elastic and fluid models were usually used but edges and small details often appear smeared in the transformed templates. We will propose a new inviscid model formulated in a particle framework, and derive the corresponding nonlinear partial differential equations for computing the spatial transformation. The idea is to simulate the template image as a set of free particles moving toward the target positions under applied forces. Our model can accommodate both small and large deformations, with sharper edges and clear texture achieved at less computational cost. We demonstrate the performance of our model on a variety of images including 2D and 3D, mono-modal and multi-modal, synthetic and clinical data.

Series: Combinatorics Seminar

In this lecture, I will explain connections between graph theory and submodular optimization. The topics include theorems of Nash-Williams on orientation and detachment of graphs.

Series: Dissertation Defense