Mathematics

 

Recent Submissions

  • Marinov, Kaloyan
    In this work, we study the stability aspect of two inverse boundary-value problems (IBVPs) on an infinite slab with partial data. The uniqueness aspects of these IBVPs were considered and studied by Li and Uhlmann for the ...
  • Tadic, Tvrtko
    We study continuous processes indexed by a special family of graphs. Processes indexed by vertices of graphs are known as probabilistic graphical models. In 2011, Burdzy and Pal proposed a continuous version of graphical ...
  • Robinson, Richard
    The positive semidefinite (psd) rank of a nonnegative <italic>p</italic> × <italic>q</italic> matrix <italic>M</italic> is defined to be the smallest integer <italic>k</italic> such that there exist <italic>k</italic> × ...
  • Sisodia, Gautam
    Let <italic>k</italic> be a field and <italic>B</italic> either a finitely generated free <italic>k</italic>-algebra, or a regular <italic>k</italic>-algebra of global dimension two with at least three generators, generated ...
  • Fan, Wai Tong
    This thesis studies the <italic>hydrodynamic limit</italic> and the <italic>fluctuation limit</italic> for a class of interacting particle systems in domains. These systems are introduced to model the transport of positive ...
  • Johnson, Tobias Lee
    One of the major themes of random matrix theory is that many asymptotic properties of traditionally studied distributions of random matrices are <italic>universal</italic>. We probe the edges of universality by studying ...
  • Drugan, Gregory
    We construct new examples of self-shrinking solutions to mean curvature flow. We first construct an immersed and non-embedded sphere self-shrinker. This result verifies numerical evidence dating back to the 1980's and shows ...
  • Lou, Shuwen
    In this thesis we introduce and study Brownian motion with or without drift on state spaces with varying dimension. Starting with a concrete such state space that is the plane with an infinite pole on it, we construct a ...
  • Slivken, Erik Dustin
    In this thesis we present three problems. The first problem is to find a good description of the number of fixed points of a 231-avoiding permutation. We use a bijection from Dyck paths to 231-avoiding permutations that ...
  • Ward, Matthew J
    This thesis develops a theory of arithmetic Fourier-Mukai transforms in order to obtain results about equivalences between the derived category of Calabi-Yau varieties over non-algebraically closed fields. We obtain answers ...
  • Deines, Alyson Laurene
    A crowning achievement of Number theory in the 20th century is a theorem of Wiles which states that for an elliptic curve E over <bold>Q</bold> of conductor N, there is a non-constant map from the modular curve of level N ...
  • Roberts, Austin
    In 2007 Sami Assaf introduced dual equivalence graphs as a method for demonstrating that a quasisymmetric function is Schur positive. The method involves the creation of a graph whose vertices are weighted by Ira Gessel's ...
  • Tran, Huy Vo
    The Loewner differential equation, a classical tool that has attracted recent attention due to Schramm-Loewner evolution (SLE), provides a unique way of encoding a simple 2-dimensional curve into a continuous 1-dimensional ...
  • Aponte Roman, Camil Ivette
    We define graded group schemes and graded group varieties and develop their theory. We give a generalization of the result that connected graded bialgebras are graded Hopf algebra. Our result is given for a broader class ...
  • Wang, Xingting
    We classify all connected Hopf algebras up to p^3 dimension over an algebraically closed field of characteristic p>0 under the mild restriction such that in dimension p^3, we only work over odd primes p when the primitive ...
  • Erickson, Lindsay
    Rational pairs, recently introduced by Kollár and Kovács, generalize rational singularities to pairs (X,D). Here X is a normal variety and D is a reduced divisor on X. Integral to the definition of a rational pair is the ...
  • Chiecchio, Alberto
    In this thesis we do the first steps towards a non-Q-Gorenstein Minimal Model Program. We extensively study non-Q-factorial singularities, using the techniques introduced by [dFH09]. We introduce a new class of singularities, ...
  • Lewis, Stephen
    In this thesis we develop the theory of Local Set Approximation (LSA), a framework which arises naturally from the study of sets with singularities. That is, we describe the local structure of a set A in Euclidean space ...
  • Yang, Yang
    Inverse problems arise in various areas of science and engineering including medical imaging, computer vision, geophysics, solid mechanics, astronomy, and so forth. A wide range of these problems involve elliptic operators. ...
  • Pawlowski, Brendan
    A fundamental invariant of a permutation is its inversion set, or diagram. Natural machinery in the representation theory of symmetric groups produces a symmetric function from any finite subset of <bold>N</bold><super>2</super>, ...

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