Seminars and Colloquia by Series

Thursday, March 11, 2010 - 11:00 , Location: Van Leer Building Room W225 , Shannon Bishop , School of Mathematics, Georgia Tech , Organizer: Christopher Heil
This thesis addresses four topics in the area of applied harmonic analysis. First, we show that the affine densities of separable wavelet frames affect the frame properties. In particular, we describe a new relationship between the affine densities, frame bounds and weighted admissibility constants of the mother wavelets of pairs of separable wavelet frames. This result is also extended to wavelet frame sequences. Second, we consider affine pseudodifferential operators, generalizations of pseudodifferential operators that model wideband wireless communication channels. We find two classes of Banach spaces, characterized by wavelet and ridgelet transforms, so that inclusion of the kernel and symbol in appropriate spaces ensures the operator if Schatten p-class. Third, we examine the Schatten class properties of pseudodifferential operators. Using Gabor frame techniques, we show that if the kernel of a pseudodifferential operator lies in a particular mixed modulation space, then the operator is Schatten p-class. This result improves existing theorems and is sharp in the sense that larger mixed modulation spaces yield operators that are not Schatten class. The implications of this result for the Kohn-Nirenberg symbol of a pseudodifferential operator are also described. Lastly, Fourier integral operators are analyzed with Gabor frame techniques. We show that, given a certain smoothness in the phase function of a Fourier integral operator, the inclusion of the symbol in appropriate mixed modulation spaces is sufficient to guarantee that the operator is Schatten p-class.
Series: Other Talks
Wednesday, March 10, 2010 - 16:30 , Location: Skiles 269 , Matt Baker , Georgia Tech , Organizer:
Join math club for Dr. Baker's mathematical magic show.
Wednesday, March 10, 2010 - 11:00 , Location: Skiles 255 , Yuri Bakhtin , Georgia Tech , Organizer: Christine Heitsch
I will consider a class of mathematical models of decision
making. These models are based on dynamics in the neighborhood of
unstable equilibria and involve random perturbations due to small
noise. I will report results on the vanishing noise limit for these
systems, providing precise predictions about the statistics of
decision making times and sequences of unstable equilibria visited by
the process. Mathematically, the results are based on the analysis of
random Poincare maps in the neighborhood of each equilibrium point. I
will also discuss some experimental data.
Series: PDE Seminar
Tuesday, March 9, 2010 - 15:00 , Location: Skiles 255 , , Carnegie Mellon University , Organizer: Chongchun Zeng
A classic story of nonlinear science started with the
particle-like
water wave that Russell famously chased on horseback in 1834. I will
recount progress regarding the robustness of solitary waves in
nonintegrable model systems such as FPU lattices, and discuss progress
toward a proof (with Shu-Ming Sun) of spectral stability of small
solitary waves for the 2D Euler equations for water of finite depth
without surface tension.
Tuesday, March 9, 2010 - 12:00 , Location: Skiles 255 , Heinrich Matzinger , Professor, School of Mathematics , Organizer:

Hosted by: Huy Huynh and Yao Li

The Scenery Reconstruction Problem consists in trying to reconstruct
a coloring of the integers given only the observations made by
a random walk. For this we consider a random walk S and
a coloring of the integers X. At time $t$ we observe
the color $X(S(t))$. The coloring is i.i.d. and we show that
given only the sequence of colors
$$X(S(0)),X(S(1)),X(S(2)),...$$
it is possible to reconstruct $X$ up to translation
and reflection. The solution depends on the property of the
random walk and the distribution of the coloring.
Longest Common Subsequences (LCS) are widely used in genetics.
If we consider two sequences X and Y, then a common subsequence
of X and Y is a string which is a subsequence of X and of Y at the same
time. A Longest Common Subsequence of X and Y is a common
subsequence of X and Y of maximum length. The problem of the asymptotic
order of the flucutation for the LCS of independent random
strings has been open for decades. We have now been able to
make progress on this problem for several important cases.
We will also show the connection to the Scenery Reconstruction
Problem.
Monday, March 8, 2010 - 14:00 , Location: Skiles 171 , Mihran Papikian , Penn State , Organizer: Matt Baker
We discuss some arithmetic properties of modular varieties
of D-elliptic sheaves, such as the existence of rational points or
the structure of their "fundamental domains" in the Bruhat-Tits
building. The notion of D-elliptic sheaf is a generalization of the
notion of Drinfeld module. D-elliptic sheaves and their moduli
schemes were introduced by Laumon, Rapoport and Stuhler in their
proof of certain cases of the Langlands conjecture over function
fields.
Monday, March 8, 2010 - 13:00 , Location: Skiles 255 , Chun Liu , Penn State/IMA , Organizer:
Almost all models for complex fluids can be fitted into the energetic variational framework. The advantage of the approach is the revealing/focus of the competition between the kinetic energy and the internal "elastic" energies. In this talk, I will discuss two very different engineering problems: free interface motion in Newtonian fluids and viscoelastic materials. We will illustrate the underlying connections between the problems and their distinct properties. Moreover, I will present the analytical results concerning the existence of near equilibrium solutions of these problems.
Series: Other Talks
Monday, March 8, 2010 - 11:00 , Location: Room 129, Global Learning Center (behind the GA Tech Hotel) , Christine Franklin , University of Georgia , Organizer: