Friday, September 25, 2009 - 13:00 , Location: Skiles 255 , Benjamin Webb , School of Mathematics, Georgia Tech , Organizer:
In the study of one dimensional dynamical systems one often assumes that the functions involved have a negative Schwarzian derivative. In this talk we consider a generalization of this condition. Specifically, we consider the interval functions of a real variable having some iterate with a negative Schwarzian derivative and show that many known results generalize to this larger class of functions. The introduction of this class was motivated by some maps arising in neuroscience
Friday, September 11, 2009 - 13:00 , Location: Skiles 255 , Ruoting Gong , Georgia Tech , firstname.lastname@example.org , Organizer:
We develop a stochastic control system from a continuous-time Principal-Agent model in which both the principal and the agent have imperfect information and different beliefs about the project. We attempt to optimize the agent’s utility function under the agent’s belief. Via the corresponding Hamilton-Jacobi-Bellman equation we prove that the value function is jointly continuous and satisfies the Dynamic Programming Principle. These properties directly lead to the conclusion that the value function is a viscosity solution of the HJB equation. Uniqueness is then also established.
Friday, September 4, 2009 - 13:00 , Location: Skiles 255 , Maria Reguera Rodriguez , Georgia Tech , email@example.com , Organizer:
In this talk we will review some of the classical weighted theory for singular integral operators, and discuss some recent progress on finding sharp bounds in terms of the A_p constant associated with the weight
Friday, April 10, 2009 - 12:30 , Location: Skiles 269 , Tianjun Ye , School of Mathematics, Georgia Tech , Organizer:
Linear algebra method is a very useful method in combinatorics. Lovas Theorem (a very deep theorem about perfect graph) is proved by using this way. The idea is, if we want to come up with an upper bound on the size of a set of objects, associate them with elements in a vector space V of relatively low dimension, and show that these elements are linearly independent. Then we cannot have more objects in our set than the dimension of V. We will show we can use this way to solve some combinatorics problem, such as odd town problem and two-distance sets problem.
Friday, April 3, 2009 - 12:30 , Location: Skiles 269 , Sergio Almada , School of Mathematics, Georgia Tech , Organizer:
Suppose b is a vector field in R^n such that b(0) = 0. Let A = Jb(0) the Jacobian matrix of b at 0. Suppose that A has no zero eigenvalues, at least one positive and at least one negative eigenvalue. I will study the behavior of the stochastic differential equation dX_\epsilon = b(X_\epsilon) + \epsilon dW as \epsilon goes to 0. I will illustrate the techniques done to deal with this kind of equation and make remarks on how the solution behaves as compared to the deterministic case.
Friday, March 27, 2009 - 12:30 , Location: Skiles 255 , Huy Huynh , School of Mathematics, Georgia Tech , Organizer:
This is due to the paper of Dr. Christian Houdre and Trevis Litherland. Let X_1, X_2,..., X_n be a sequence of iid random variables drawn uniformly from a finite ordered alphabets (a_1,...,a_m) where a_1 < a_2 < ...< a_m. Let LI_n be the length of the longest increasing subsequence of X_1,X_2,...,X_n. We'll express the limit distribution of LI_n as functionals of (m-1)-dimensional Brownian motion. This is an elementary case taken from this paper.
Friday, March 6, 2009 - 12:30 , Location: Skiles 269 , Kai Ni , School of Mathematics, Georgia Tech , Organizer:
In this talk, I will briefly introduce some basics of mathematical learning theory. Two basic methods named perceptron algorithm and support vector machine will be explained for the separable classification case. Also, the subgaussian random variable and Hoeffding inequality will be mentioned in order to provide the upper bound for the deviation of the empirical risk. If time permits, the Vapnik combinatorics will be involved for shaper bounds of this deviation.
Friday, February 27, 2009 - 12:30 , Location: Skiles 269 , Weizhe Zhang , School of Mathematics, Georgia Tech , Organizer:
This talk will follow Peter Lax on the linear algebraic fact of the index of Fredholm operators such as the product formula and stability, all of which are totally elementary.
Friday, February 20, 2009 - 12:30 , Location: Skiles 269 , Ke Yin , School of Mathematics, Georgia Tech , Organizer:
In this introductory talk, I am going to derive the basic governing equations of fluid dynamics. Our assumption are the three physical principles: the conservation of mass, Newton's second law, and the conservation of energy. The main object is to present Euler equations (which characterize inviscid flow) and Navier-Stokes equations (which characterize viscid flow).
Friday, February 13, 2009 - 12:30 , Location: Skiles 269 , Yi Huang , School of Mathematics, Georgia Tech , Organizer:
Let V be a vector space over the field C of complex numbers and let GL(V) be the group of isomorphisms of onto itself. Suppose G is a finite group. A linear representation of G in V is a homomorphism from the group G into the group GL(V). In this talk, I will give a brief introduction to some basic theorems about linear representations of finite groups with concentration on the decomposition of a representation into irreducible sub-representations, and the definition and some nice properties of the character. At the end of the talk, I will re-prove the Burnside lemma in the group theory from the representation theory approach. Since I began learning the topic only very recently, hence an absolute novice myself, I invite all of you to the talk to help me learn the knowledge through presenting it to others. If you are familiar with the topic and want to learn something new, my talk can easily be a disappointment.