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Now showing items 1-10 of 228

#### Functional and cross-trait genetic architecture of common diseases and complex traits

(Massachusetts Institute of Technology, 2017)

In this thesis, I introduce new methods for learning about diseases and traits from genetic data. First, I introduce a method for partitioning heritability by functional annotation from genome-wide association summary ...

#### Instanton correction, wall crossing and mirror symmetry of Hitchin's moduli spaces

(Massachusetts Institute of Technology, 2011)

We study two instanton correction problems of Hitchin's moduli spaces along with their wall crossing formulas. The hyperkahler metric of a Hitchin's moduli space can be put into an instanton-corrected form according to ...

#### Connections on conformal blocks

(Massachusetts Institute of Technology, 2011)

For an algebraic group G and a projective curve X, we study the category of D-modules on the moduli space Bung of principal G-bundles on X using ideas from conformal field theory. We describe this category in terms of the ...

#### Negative answers to some positivity questions

(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 ...

#### Bounds on extremal functions of forbidden patterns

(Massachusetts Institute of Technology, 2015)

Extremal functions of forbidden sequences and 0 - 1 matrices have applications to many problems in discrete geometry and enumerative combinatorics. We present a new computational method for deriving upper bounds on extremal ...

#### Gaussian free field, Schramm-Loewner evolution and Liouville quantum gravity

(Massachusetts Institute of Technology, 2017)

Consider an instance h of the Gaussian free field on a simply connected domain ... We study several properties of the level lines: continuity, monotonicity, reversibility and target-independence ... In the second part, we ...

#### Mayer-Vietoris property for relative symplectic cohomology

(Massachusetts Institute of Technology, 2018)

In this thesis, I construct and investigate the properties of a Floer theoretic invariant called relative symplectic cohomology. The construction is based on Hamiltonian Floer theory. It assigns a module over the Novikov ...

#### Combinatorics of acyclic orientations of graphs : algebra, geometry and probability

(Massachusetts Institute of Technology, 2015)

This thesis studies aspects of the set of acyclic orientations of a simple undirected graph. Acyclic orientations of a graph may be readily obtained from bijective labellings of its vertex-set with a totally ordered set, ...

#### On planar rational cuspidal curves

(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 ...

#### Free resolutions, combinatorics, and geometry

(Massachusetts Institute of Technology, 2012)

Boij-Söderberg theory is the study of two cones: the first is the cone of graded Betti tables over a polynomial ring, and the second is the cone of cohomology tables of coherent sheaves over projective space. Each cone has ...