### One and Two Weight Theory in Harmonic Analysis

- Series
- Dissertation Defense
- Time
- Tuesday, February 5, 2013 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- James Scurry – Georgia Tech

- You are here:
- Home
- News & Events

- Series
- Dissertation Defense
- Time
- Tuesday, February 5, 2013 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- James Scurry – Georgia Tech

- Series
- Dissertation Defense
- Time
- Tuesday, December 4, 2012 - 15:00 for 1.5 hours (actually 80 minutes)
- Location
- Skiles 005
- Speaker
- Huijun Feng – School of Mathematics, Georgia Tech

- Series
- Dissertation Defense
- Time
- Monday, November 5, 2012 - 12:30 for 1.5 hours (actually 80 minutes)
- Location
- Skiles 005
- Speaker
- Jinyong Ma – School of Mathematics, Georgia Tech

This work studies two topics in sequence analysis. In the first part, we
investigate the large deviations of the shape of the random RSK Young
diagrams, associated with a random word of size n whose letters are
independently drawn from an alphabet of size m=m(n). When the letters are
drawn uniformly and when both n and m converge together to infinity, m
not growing too fast with respect to n, the large deviations of the shape
of the Young diagrams are shown to be the same as that of the spectrum of
the traceless GUE. Since the length of the top row of the Young diagrams is
the length of the longest (weakly) increasing subsequence of the random
word, the corresponding large deviations follow. When the letters are drawn
with non-uniform probability, a control of both highest probabilities will
ensure that the length of the top row of the diagrams satisfies a large
deviation principle. In either case, speeds and rate functions are
identified. To complete this first part, non-asymptotic concentration bounds
for the length of the top row of the diagrams are obtained.
In the second part, we investigate the order of the r-th, 1\le r <
+\infty, central moment of the length of the longest common subsequence of
two independent random words of size n whose letters are identically
distributed and independently drawn from a finite alphabet. When all but one
of the letters are drawn with small probabilities, which depend on the size
of the alphabet, the r-th central moment is shown to be of order
n^{r/2}. In particular, when r=2, the order of the variance is linear.

- Series
- Dissertation Defense
- Time
- Thursday, November 1, 2012 - 13:30 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Arash Asadi – Math, GT

Please see http://www.aco.gatech.edu/dissert/asadi.html for further details.

- Series
- Dissertation Defense
- Time
- Tuesday, August 14, 2012 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Luke Postle – Math, GT

Details can be found at http://www.aco.gatech.edu/dissert/postle.html.

- Series
- Dissertation Defense
- Time
- Tuesday, June 19, 2012 - 10:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Marc Sedjro – School of Mathematics, Georgia Tech

This work is concerned with the Almost Axisymmetric Flows with Forcing
Terms which are derived from the inviscid Boussinesq equations. It is our hope that
these
flows will be useful in Meteorology to describe tropical cyclones. We show that
these
flows give rise to a collection of Monge-Ampere equations for which we prove an
existence and uniqueness result. What makes these equations unusual is the boundary
conditions they are expected to satisfy and the fact that the boundary is part of the
unknown. Our study allows us to make inferences in a toy model of the Almost Axisymmetric Flows with
Forcing Terms.

- Series
- Dissertation Defense
- Time
- Friday, June 15, 2012 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Klaus 3100
- Speaker
- Nathan Chenette – School of Mathematics, Georgia Tech

- Series
- Dissertation Defense
- Time
- Thursday, June 7, 2012 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Bulent Tosun – School of Mathematics, Georgia Tech

- Series
- Dissertation Defense
- Time
- Monday, May 21, 2012 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Tianjun Ye – School of Mathematics, Georgia Tech

Classical vertex coloring problems ask for the minimum number of colors needed
to color the vertices of a graph, such that adjacent vertices
use different colors. Vertex coloring does have quite a few practical applications
in
communication theory, industry engineering and computer science. Such examples can
be
found in the book of Hansen and Marcotte.
Deciding whether a graph is 3-colorable or not is a well-known NP-complete problem,
even for triangle-free graphs. Intutively, large girth may help reduce the chromatic
number.
However, in 1959, Erdos used the probabilitic method to prove that for any two
positive
integers g and k, there exist graphs of girth at least g and chromatic number at
least k.
Thus, restricting girth alone does not help bound the chromatic number. However, if
we
forbid certain tree structure in addition to girth restriction, then it is possible
to bound the
chromatic number. Randerath determined several such tree structures, and conjectured
that
if a graph is fork-free and triangle-free, then it is 3-colorable, where a fork is a
star K1,4
with two branches subdivided once.
The main result of this thesis is that Randerath's conjecture is true for graphs
with odd
girth at least 7. We also give an outline of a proof that Randerath's conjecture
holds for
graphs with maximum degree 4.

- Series
- Dissertation Defense
- Time
- Wednesday, May 2, 2012 - 11:00 for 2 hours
- Location
- Skiles 006
- Speaker
- Huy Huynh – School of Mathematics, Georgia Tech