## Seminars and Colloquia by Series

### 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 ScurryGeorgia Tech

### Goodness-of-Fit Tests and Bilinear Model

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

### Topics in Sequence Analysis

Series
Dissertation Defense
Time
Monday, November 5, 2012 - 12:30 for 1.5 hours (actually 80 minutes)
Location
Skiles 005
Speaker
Jinyong MaSchool 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.

### Minor-Minimal Non-Projective Planar Graphs With an Internal 3-Separation

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

### On the Almost Axisymmetric Flows with Forcing Terms

Series
Dissertation Defense
Time
Tuesday, June 19, 2012 - 10:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Marc SedjroSchool 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.

### Symmetric Schemes for Efficient Range and Error-Tolerant Search on Encrypted Data

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

### Legendrian and Transverse Knots and Their Invariants

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

### Forbidden Subgraphs and 3-Colorability

Series
Dissertation Defense
Time
Monday, May 21, 2012 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Tianjun YeSchool 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.

### Estimating the Maximum Probability of Categorical Classes with Applications to Biological Diversity Measurements

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