It is the end of the spring semester and our graduating Ph.D. in mathematics students have now submitted their theses. See a detailed list of all Theses defended in 2013, below, following a few words from our graduating majors.
Kelly Bickel, Ph.D. in Mathematics, advised by John McCarthy, Agler Decompositions on the Bidisk and Derivatives of Matrix Functions.
"My research concerns function theory on polydisks," says Kelly. "I am especially interested in the structure of bounded analytic functions on the bidisk and associated operators and reproducing kernel Hilbert spaces. I have also started studying multi-parameter harmonic analysis and its connections to bounded analytic functions on the polydisk." Asked about her plans, Kelly answered that she will be a postdoc at the Georgia Institute of Technology in Atlanta, next year and "the following fall, I will join the faculty at Bucknell University in Lewisburg, PA."
The other proposed theses in mathematics and statistics this year were:
Timothy Chumley, Ph.D. in Mathematics, advised by Renato Feres, Limit theorems for random billiard models.
Qingyun Wang, Ph.D. in Mathematics, advised by John McCarthy, Tracial Rokhlin property and non-commutative dimension.
Safdar Quddus, Ph.D. in Mathematics, advised by Xiang Tang, On the homology of noncommutative toroidal orbifolds.
Lan Andrea Xu, M.A. in Statistics, advised by Jimin Ding, An Empirical Analysis of the Effect of Diversification on Value.
Yuanxin Hu, M.A. in Statistics, advised by Edward Spitznagel, Survival Analysis of Cardiovascular Diseases
Wei Deng, Ph.D. in Mathematics, advised by Mohan Kumar, Four Generated Rank 2 Arithmetically Cohen-Macaulay Bundles on General Sextic Surfaces
All 2013 Theses:
Survival Analysis of Cardiovascular Diseases
Yuanxin Hu, Department of Mathematics, Washington University in St. Louis
December 16, 2013
1:00 pm - 3:00 pm
M.A. in Statistics with Thesis.
Abstract: The Cardiovascular diseases are leading causes of death in populations worldwide. The current investigation is applying survival analysis to identify risk factors, and their impacts on hazard functions or survival function. The methods of Kaplan-Meier nonparamtric method, Cox proportional hazard regression, and Accelerated Failure time model have been used.
Location: Cupples I, Room 207
Host: Prof. Ed. Spitznagel
Four Generated Rank 2 Arithmetically Cohen-Macaulay Bundles on General Sextic Surfaces
Wei Deng, Department of Mathematics, Washington University in St. Louis
August 28, 2013
1:10 pm - 3:00 pm
Abstract: We compute the dimension of the moduli of four generated indecomposable rank 2 arithmetically Cohen-Macaulay (ACM) bundles on a general sextic surface. Firstly we prove on a general sextic surface, every four generated indecomposable rank 2 ACM bundle belongs to one of fourteen cases. Next we prove for each of the fourteen cases, there exists an indecomposable rank 2 ACM bundle of that case on a general sextic surface. Finally we compute for each case, the dimension of its moduli on a general sextic surface.
Location: Cupples I, Room 6
Host: Prof. Mohan Kumar
Agler Decompositions on the Bidisk and Derivatives of Matrix Functions
Kelly Bickel, Department of Mathematics, Washington University in St. Louis
April 26, 2013
4:00 pm - 6:00 pm
Abstract: We examine two distinct problems about multivariate functions and their associated operators.
First, we discuss the structure of Agler decompositions, which give a useful way to represent two-variable Schur functions on the bidisk. We will discuss an elementary proof of the existence of Agler decompositions that uses special shift-invariant subspaces of the Hardy space. These shift-invariant subspaces are specific cases of Hilbert spaces that can be defined from Agler decompositions and we will outline several properties of such Hilbert spaces. Time permitting, we will touch on the situation for rational inner functions and highlight how related analyses can be used to characterize stable polynomials on the polydisk. Second, we consider differentiation of matrix-valued functions. Specifically, multivariate, real-valued functions induce matrix-valued functions defined on the space of d-tuples of n-times-n pairwise-commuting self-adjoint matrices. We will briefly discuss the geometry of this space of matrix tuples and highlight reasons why a suitable notion of differentiation of these matrix-valued functions is differentiation along curves. We will then discuss our proof that real-valued C^m functions induce matrix-valued functions that can be m-times continuously differentiated along C^m curves.
Location: Cupples I, Room 199
Host: Prof. John McCarthy
Limit theorems for random billiard models
Timothy Chumley, Department of Mathematics, Washington University in St. Louis
April 24, 2013
3:00 pm - 5:00 pm
Abstract: The central objects of study in this dissertation are random billiard systems. These are Markov chain systems with general state spaces derived from deterministic billiard systems by selecting one or more dynamical variables and replacing them with random variables with fixed probability distributions. In particular, we study two specific model systems; one which models gas diffusion through cylindrical channels whose walls have a microscopic structure, and another which models a minimalistic heat engine. The main results for the gas diffusion model, a series of probabilistic limit theorems, allow us to express transport characteristics such as mean exit times of the gas from the channel in terms of characteristics of the channel walls. Preliminary results for the heat engine model present some beginning steps in the study of stochastic thermodynamics of billiard-like mechanical systems.
Location: Cupples I, Room 199
Host: Prof. Renato Feres
An Empirical Analysis of the Effect of Diversification on Value
Lan Andrea Xu, Department of Mathematics, Washington University in St. Louis April 24, 2013
10:00 am - 12:00 pm
M.A. in Statistics with Thesis
Abstract: I use longitudinal and quantile analysis to study the effect of diversification on firm value. By characterizing the entire distribution of firm value for each group, I provide a more complete picture than a mean effect given by least-squares analysis.
Location: Cupples I, Room 6
Host: Prof. Jimin Ding
On the homology of noncommutative toroidal orbifolds
Safdar Quddus, Department of Mathematics, Washington University in St. Louis
April 22, 2013
9:00 am - 11:00 pm
Abstract: The noncommutative torus was studied in the early 80's as a fundamental example of noncommutative geometry. Connes calculated its cyclic and Hochschild cohomology. In this thesis, we study noncommutative toroidal orbifolds generated by actions of finite subgroups of $ SL (2,\mathbb Z) $ on a noncommutative torus. In the first part, we calculate the Hochschild and cyclic homology of $\mathcal A_\theta^{alg} \rtimes \Gamma $ for all finite subgroups $\Gamma \subset SL (2,\mathbb Z)$. In the second part, we analyze the cohomology of these algebras and compute the pairing of $K_0$-elements of $\mathcal A_\theta^{alg}\rtimes \mathbb{Z}_2$ with explicit cyclic cocycles as a generalization of index theory. We will end with discussing some partial results and conjectures about the corresponding smooth orbifolds.
Location: Danforth University Center, Room 217
Host: Prof. Xiang Tang
Tracial Rokhlin property and non-commutative dimension
Qingyun Wang , Department of Mathematics, Washington University in St. Louis
April 2, 2013
3:00 pm - 5:00 pm
Abstract: This dissertation focuses on finite group actions with the tracial Rokhlin property and the structure of the corresponding crossed products. It consists of two major parts. For the first part, we study several different aspects of finite group actions with certain versions of the Rokhlin property. We are able to give an explicit characterization of product-type actions with the tracial Rokhlin property or strict Rokhlin property. We also show that, in good circumstances, the actions with the tracial Rokhlin property are generic.
In the second portion of this dissertation, we introduce the weak tracial Rokhlin property for actions on non-simple C*-algebras. The main results are as follows. Let A be a unital non-simple C*-algebra and ? be an action of G on A with the weak tracial Rokhlin property. Assume that the crossed product C*(G,A, ?) is simple. Suppose A has either of the following property: tracial rank ? k, stable rank one, real rank zero. Then C*(G,A, ?) has the same property.
Location: Cupples I, room 199
Host: Prof. John McCarthy
Looking to contact a past graduate? Visit our Recent Ph.D.'s page⇨
2013 Mathematics Theses from WUSTL's Open Scholarship are soon to appear. Meanwhile, you can download a 2012 Mathematics Theses from WUSTL's Open Scholarship⇨
—Math news, stories, videos, and interviews by Marie C. Taris, http://www.math.wustl.edu/marietaris/math.html⇨
Liked this story? See also 2012 Theses in Mathematics and Statistics⇨ and 2011 Theses in Mathematics and Statistics⇨