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Superfluidity and random media
(Massachusetts Institute of Technology, 1993)
Results on spectral sequences for monopole and singular instanton Floer homologies
(Massachusetts Institute of Technology, 2018)
We study two gauge-theoretic Floer homologies associated to links, the singular instanton Floer homology introduced in [15] and the monopole Floer homology, which is explained in the book [16]. For both cases, we study in ...
Cardy embedding of random planar maps and a KPZ formula for mated trees
(Massachusetts Institute of Technology, 2018)
The Schramm-Loewner evolution (SLE) is a random fractal curve which describes the scaling limit of interfaces in a wide range of statistical physics models. Liouville quantum gravity (LQG) is a random fractal surface which ...
Matrix estimation with latent permutations
(Massachusetts Institute of Technology, 2018)
Motivated by various applications such as seriation, network alignment and ranking from pairwise comparisons, we study the problem of estimating a structured matrix with rows and columns shuffled by latent permutations, ...
Hyperarithmetical real numbers and hyperarithmetical analysis
(Massachusetts Institute of Technology, 1962)
Incidence Problems for Slabs
(Massachusetts Institute of Technology, 2023-09)
In this thesis, I prove incidence estimates for slabs which are formed by intersecting small neighborhoods of well-spaced hyperplanes in R superscript 𝑑 with the unit cube [0, 1] superscript 𝑑 . My work is an analogue ...
Transport methods and universality for [beta]-ensembles
(Massachusetts Institute of Technology, 2018)
In this thesis, we investigate the local and global properties of the eigenvalues of [beta]-ensembles. A lot of attention has been drawn recently on the universal properties of [beta]-ensembles, and how their local statistics ...
Studies on quasisymmetric functions
(Massachusetts Institute of Technology, 2016)
In 1983, Ira Gessel introduced the ring of quasisymmetric functions (QSym), an extension of the ring of symmetric functions and nowadays one of the standard examples of a combinatorial Hopf algebra. In this thesis, I ...
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 ...
The theory of linear lattices
(Massachusetts Institute of Technology, 1984)