• The Complexity of Random Functions of Many Variables 

  Arous, Gérard Ben (Georgia Institute of Technology, 2016-08-31)

  A function of many variables, when chosen at random, is typically very complex. It has an exponentially large number of local minima or maxima, or critical points. It defines a very complex landscape, the topology of its ...

• Statistical inference for large matrices 

  Xia, Dong (Georgia Institute of Technology, 2016-07-29)

  This thesis covers two topics on matrix analysis and estimation in machine learning and statistics. The first topic is about density matrix estimation with application in quantum state tomography. The density matrices are ...

• Transverse Surgery on Knots in Contact Three-Manifolds 

  Conway, James (Georgia Institute of Technology, 2016-05-19)

  We study the effect of surgery on transverse knots in contact $3$-manifolds by examining its effect on open books, the Heegaard Floer contact invariant, and tightness in general. We first compare surgery on transverse ...

• A study of stochastic differential equations and Fokker-Planck equations with applications 

  Li, Wuchen (Georgia Institute of Technology, 2016-04-15)

  Fokker-Planck equations, along with stochastic differential equations, play vital roles in physics, population modeling, game theory and optimization (finite or infinite dimensional). In this thesis, we study three topics, ...

• Open book decompositions in high dimensional contact manifolds 

  Elmas, Gokhan (Georgia Institute of Technology, 2016-05-27)

  In this thesis, we study the open book decompositions in high dimensional contact manifolds. We focus on the results about open book decomposition of manifolds and their relationship with contact geometry.

• Numerical algorithms based on the back and forth error compensation and correction 

  Hu, Lili (Georgia Institute of Technology, 2014-12-18)

  In this thesis we carry out a further study of the back and forth error compensation and correction (BFECC) method. The first part discusses the time reversibility of numerical schemes. Motivated by the BFECC method, a ...

• Dynamics and variational problems 

  Loss, Michael; Carlen, Eric A. (Georgia Institute of Technology, 2010-06-01)

• Combinatorial problems for graphs and partially ordered sets 

  Wang, Ruidong (Georgia Institute of Technology, 2015-11-13)

  This dissertation has three principal components. The first component is about the connections between the dimension of posets and the size of matchings in comparability and incomparability graphs. In 1951, Hiraguchi proved ...

• Thermostated Kac models 

  Vaidyanathan, Ranjini (Georgia Institute of Technology, 2015-11-16)

  We consider a model of N particles interacting through a Kac-style collision process, with m particles among them interacting, in addition, with a thermostat. When m = N, we show exponential approach to the equilibrium ...

• The Filippov moments solution on the intersection of two and three manifolds 

  Difonzo, Fabio Vito (Georgia Institute of Technology, 2015-11-18)

  In this thesis, we study the Filippov moments solution for differential equations with discontinuous right-hand side. In particular, our aim is to define a suitable Filippov sliding vector field on a co-dimension $2$ ...

• Fields program on new trends in harmonic analysis - international U.S. participation 

  Lacey, Michael (Georgia Institute of Technology, 2008-08-01)

• The geometry and topology of the Jones polynomial 

  Garoufalidis, Stavros (Georgia Institute of Technology, 2009-05-01)

• Multivariable moments and factorizations and other problems in analysis 

  Geronimo, Jeffrey Stephen (Georgia Institute of Technology, 2008-08-01)

• Mathematical modeling of heterogeneous media 

  Goldsztein, Guillermo (Georgia Institute of Technology, 2008-05-01)

• A numerical study of vorticity-enhanced heat transfer 

  Wang, Xiaolin (Georgia Institute of Technology, 2014-06-26)

  In this work, we have numerically studied the effect of the vorticity on the enhancement of heat transfer in a channel flow. In the first part of the work, we focus on the investigation of a channel flow with a vortex ...

• Multifold sums and products over R, and combinatorial problems on sumsets 

  Bush, Albert (Georgia Institute of Technology, 2015-07-22)

  We prove a new bound on a version of the sum-product problem studied by Chang. By introducing several combinatorial tools, this expands upon a method of Croot and Hart which used the Tarry-Escott problem to build distinct ...

• Symmetric ideals and numerical primary decomposition 

  Krone, Robert Carlton (Georgia Institute of Technology, 2015-07-27)

  The thesis considers two distinct strategies for algebraic computation with polynomials in high dimension. The first concerns ideals and varieties with symmetry, which often arise in applications from areas such as algebraic ...

• Minimization problems involving polyconvex integrands 

  Awi, Romeo Olivier (Georgia Institute of Technology, 2015-06-02)

  This thesis is mainly concerned with problems in the areas of the Calculus of Variations and Partial Differential Equations (PDEs). The properties of the functional to minimize with respect to the given topology play an ...

• Complete nonnegatively curved spheres and planes 

  Hu, Jing (Georgia Institute of Technology, 2015-06-02)

  We study the space of complete Riemannian metrics of nonnegative curvature on the sphere equipped with C^{k+\alpha} topology. We show the space is homogenous for k>=2. If k is infinite, we show that the space is homeomorphic ...

• Small-time asymptotics of call prices and implied volatilities for exponential Lévy models 

  Hoffmeyer, Allen Kyle (Georgia Institute of Technology, 2015-01-08)

  We derive at-the-money call-price and implied volatility asymptotic expansions in time to maturity for a selection of exponential Lévy models, restricting our attention to asset-price models whose log returns structure is ...

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