## Seminars and Colloquia by Series

### Dynamical Path Planning Methods For Control Problems in Unknown Environment

Series
SIAM Student Seminar
Time
Monday, November 27, 2017 - 15:10 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Haoyan ZhaiSchool of Mathematics, Georgia Institute of Technology
In this talk, we provide a deterministic algorithm for robotic path finding in unknown environment and an associated graph generator use only potential information. Also we will generalize the algorithm into a path planning algorithm for certain type of optimal control problems under some assumptions and will state some approximation methods if certain assumption no longer holds in some cases. And we hope to prove more theoretical results for those algorithms to guarantee the success.

### Local Hausdorff dimension and measure

Series
SIAM Student Seminar
Time
Friday, February 12, 2016 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 114
Speaker
John DeverGeorgia Institute of Technology
A local Hausdorff dimension is defined on a metric space. We study its properties and use it to define a local measure. We show that in many circumstances we can recover the global Hausdorff dimension from the local one. We give an example of a compact metric space with a continuum of local dimension values. We define the dimension of a measure and connect the definition to that of local Hausdorff dimension and measure for a class of spaces called (variable) Ahlfors Q-regular. Very little background knowledge, aside from basic familiarity with metric spaces, will be assumed.

### THE EIGENVALUES OF THE LAPLACIAN ON DOMAINS WITH SMALL SLITS

Series
SIAM Student Seminar
Time
Tuesday, November 24, 2015 - 16:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Hagop TossounianGeorgia Institute of Technology
This is a summary of result of LUC HILLAIRET AND CHRIS JUDGE.

### On the inverse of some sign matrices and on the Moments sliding vector field on the intersection of several manifolds: nodally attractive case

Series
SIAM Student Seminar
Time
Friday, October 23, 2015 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Fabio DifonzoGeorgia Institute of Technology
In this paper, we consider selection of a sliding vector fieldof Filippov type on a discontinuity manifold $\Sigma$ of co-dimension 3(intersection of three co-dimension 1 manifolds). We propose an extension of the “moments vector field”to this case, and - under the assumption that $\Sigma$ is nodally attractive -we prove that our extension delivers a uniquely definedFilippov vector field. As it turns out, the justification of our proposed extension requiresestablishing invertibility of certain sign matrices. Finally,we also propose the extension of the moments vector field todiscontinuity manifolds of co-dimension 4 and higher.

### Periodic Eigendecomposition and its application in nonlinear dynamics

Series
SIAM Student Seminar
Time
Friday, October 17, 2014 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Xiong DingSchool of Physics, Georgia Tech
Periodic eigendecomposition algorithm for calculating eigenvectors of a periodic product of a sequence of matrices, an extension of the periodic Schur decomposition, is formulated and compared with the recently proposed covariant vectors algorithms. In contrast to those, periodic eigendecomposition requires no power iteration and is capable of determining not only the real eigenvectors, but also the complex eigenvector pairs. Its effectiveness, and in particular its ability to resolve eigenvalues whose magnitude differs by hundreds of orders, is demonstrated by applying the algorithm to computation of the full linear stability spectrum of periodic solutions of Kuramoto-Sivashinsky system.

### A proof of the sharp Sobolev inequality

Series
SIAM Student Seminar
Time
Thursday, September 18, 2014 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Rohan GhantaSchool of Mathematics, Georgia Tech
By showing a duality relation between the Sobolev and Hardy-Littlewood-Sobolev inequalities, I discuss a proof of the sharp Sobolev inequality. The duality relation between these two inequalities is known since 1983 and has led to interesting recent work on the inequalities (which may be the topic of future talks).

### Mark Kac's Master Equation and Propagation of Chaos

Series
SIAM Student Seminar
Time
Thursday, March 6, 2014 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Hagop TossounianSchool of Mathematics, Georgia Tech
In 1956 Mark Kac introduced an equation governing the evolution of the velocity distribution of n particles. In his derivation, he assumed a stochastic model based on binary collisions which preserves energy but not momentum. In this talk I will describe Kac's model and the main theorem of Kac's paper : that solutions with chaotic initial data can be related to the solutions Boltzmann type equation.

### New model for cell phone signal problem

Series
SIAM Student Seminar
Time
Friday, January 24, 2014 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Li WuchenSchool of Mathematics, Georgia Tech
We introduce a new model for cell phone signal problem, which is stochastic van der Pol oscillator with condition that ensures global boundedness in phase space and keeps unboundedness for frequency. Also we give a new definition for stochastic Poincare map and find a new approximation to return time and point. The new definition is based on the numerical observation. Also we develop a new approach by using dynamic tools, such as method of averaging and relaxation method, to estimate the return time and return point. Thus we can show that the return time is always not Gaussian and return point's distribution is not symmetric under certain section.

### TBA by Albert Bush

Series
SIAM Student Seminar
Time
Wednesday, October 9, 2013 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Albert Bush School of Mathematics, Georgia Tech
Erdos and Szemeredi conjectured that if one has a set of n numbers, one must have either the sumset or product set be of nearly maximal size, cn^2/log(n). In this talk, he will introduce the sum-product problem in the reals, show previous, beautiful geometric proofs by Solymosi and Elekes, and discuss some recent progress by Amirkhanyan, Croot, Pryby and Bush.

### A characterization of 4-ordered cycle in planar graphs

Series
SIAM Student Seminar
Time
Friday, April 29, 2011 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 246
Speaker
Jie MaSchool of Mathematics, Georgia Tech
Fix k vertices in a graph G, say a_1,...,a_k, if there exists a cycle that visits these vertices with this specified order, we say such a cycle is (a_1,a_2,...,a_k)-ordered. It is shown by Thomas and Wollan that any 10k-connected graph is k-linked, therefore any 10k-connected graph has an (a_1,a_2,...,a_k)-ordered for any a_1,...,a_k. However, it is possible that we can improve this bound when k is small. It is shown by W. Goddard that any 4-connected maximal planar graph has an (a_1,...,a_4)-ordered cycle for any choice of 4 vertices. We will present a complete characterization of 4-ordered cycle in planar graphs. Namely, for any four vertices a,b,c,d in planar graph G, if there is no (a,b,c,d)-ordered cycle in G, then one of the follows holds: (1) there is a cut S separating {a,c} from {b,d} with |S|\leq 3; (2) roughly speaking, a,b,d,c "stay" in a face of G with this order.