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Browsing Theses - Mathematics by Issue Date

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Browsing Theses - Mathematics by Issue Date

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  • Keating, Ailsa Macgregor (Massachusetts Institute of Technology, 2014)
    We present two results relating to the symplectic geometry of the Milnor fibres of isolated affine hypersurface singularities. First, given two Lagrangian spheres in an exact symplectic manifold, we find conditions under ...
  • Česnavičius, Kęstutis (Massachusetts Institute of Technology, 2014)
    Given a prime number p, Bloch and Kato showed how the p Selmer group of an abelian variety A over a number field K is determined by the p-adic Tate module. In general, the pm1-Selmer group Selpmn A need not be determined ...
  • Deckelbaum, Alan (Massachusetts Institute of Technology, 2014)
    The problem of constructing auctions to maximize expected revenue is central to mechanism design and to algorithmic game theory. While the special case of selling a single item has been well understood since the work of ...
  • Dubbs, Alexander (Massachusetts Institute of Technology, 2014)
    This thesis presents analytic samplers for the [beta]-Wishart and [beta]-MANOVA ensembles with diagonal covariance. These generalize the [beta]-ensembles of Dumitriu-Edelman, Lippert, Killip-Nenciu, Forrester-Rains, and ...
  • Park, Jennifer Mun Young (Massachusetts Institute of Technology, 2014)
    Faltings' theorem states that curves of genus g > 2 have finitely many rational points. Using the ideas of Faltings, Mumford, Parshin and Raynaud, one obtains an upper bound on the upper bound on the number of rational ...
  • Tsymbaliuk, Oleksandr (Massachusetts Institute of Technology, 2014)
    In the first part of this thesis, we obtain some new results about infinitesimal Cherednik algebras. They have been introduced by Etingof-Gan-Ginzburg in [EGG] as appropriate analogues of the classical Cherednik algebras, ...
  • Batson, Joshua (Massachusetts Institute of Technology, 2014)
    In this thesis, we use invariants inspired by quantum field theory to study the smooth topology of links in space and surfaces in space-time. In the first half, we use Khovanov homology to the study the relationship between ...
  • Culler, Lucas Howard (Massachusetts Institute of Technology, 2014)
    In this thesis, I study the relationship between the higher rank Donaldson invariants of a smooth 4-manifold X and the invariants of its blowup X#CP2 . This relationship can be expressed in terms of a formal power series ...
  • DeFranco, Mario A. (Mario Anthony) (Massachusetts Institute of Technology, 2014)
    Let G be a connected reductive group with a split maximal torus defined over a nonarchimedean local field. I evaluate a matrix coefficient of the unramified principal series of G known as the "Bessel function" at torus ...
  • Jackson-Hanen, David Sean (Massachusetts Institute of Technology, 2014)
    In 2004, Seidel and Smith proved that the Liouville manifold associated to Ramanujams surface contains a Lagrangian torus which is not displaceable by Hamiltonian isotopy, and hence that higher products of this manifold ...
  • Lesieutre, John (Massachusetts Institute of Technology, 2014)
    We construct counterexamples to a number of questions related to positivity properties of line bundles on algebraic varieties. The examples are based on studying the geometry of varieties that admit pseudo automorphisms ...
  • Ketover, Daniel (Massachusetts Institute of Technology, 2014)
    A Heegaard splitting of a 3-manifold gives rise to a natural set of sweepouts which by the Almgren-Pitts and Simon-Smith min-max theory generates a min-max sequence converging as varifolds to a smooth minimal surface ...
  • Liu, Tiankai (Massachusetts Institute of Technology, 2014)
    This thesis studies rational curves in the complex projective plane that are homeomorphic to their normalizations. We derive some combinatorial constraints on such curves from a result of Borodzik-Livingston in Heegaard-Floer ...
  • Oza, Anand Uttam (Massachusetts Institute of Technology, 2014)
    Yves Couder and coworkers have demonstrated that millimetric droplets walking on a vibrating fluid bath exhibit several features previously thought to be peculiar to the microscopic quantum realm, including single-particle ...
  • Lipson, Mark (Mark Israel) (Massachusetts Institute of Technology, 2014)
    In the last few decades, the study of human history has been fundamentally changed by our ability to detect the signatures left within our genomes by adaptations, migrations, population size changes, and other processes. ...
  • Tucker, George Jay (Massachusetts Institute of Technology, 2014)
    Biological systems are extremely complex, and our ability to experimentally measure interactions in these systems is limited by inherent noise. Technological advances have allowed us to collect unprecedented amounts of raw ...
  • Bélanger-Rioux, Rosalie (Massachusetts Institute of Technology, 2014)
    Absorbing layers are sometimes required to be impractically thick in order to offer an accurate approximation of an absorbing boundary condition for the Helmholtz equation in a heterogeneous medium. It is always possible ...
  • Singh, Bhairav (Massachusetts Institute of Technology, 2013)
    One of the fundamental results in geometric representation theory is the geometric Satake equivalence, between the category of spherical perverse sheaves on the affine Grassmannian of a reductive group G and the category ...
  • Molác̆ek, Jan, Ph. D. Massachusetts Institute of Technology (Massachusetts Institute of Technology, 2013)
    Coalescence of a liquid drop with a liquid bath can be prevented by vibration of the bath. In a certain parameter regime, a purely vertical bouncing motion may ensue. In another, this bouncing state is destabilized by the ...
  • Suh, Uhi Rinn (Massachusetts Institute of Technology, 2013)
    The first part of the thesis provides three equivalent definitions of a classical finite W-algebra Wfin(g, f) and two equivalent definitions of a classical affine W-algebra W(g, f, k) associated to a Lie algebra g, a ...
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