### Recent Submissions

• #### Type theoretic weak factorization systems ﻿

(2017-06-01)
This thesis presents a characterization of those categories with weak factorization systems that can interpret the theory of intensional dependent type theory with Σ, Π, and identity types. We use display map categories ...
• #### On the main conjectures of Iwasawa theory for certain elliptic curves with complex multiplication ﻿

(2017-05-30)
The conjecture of Birch and Swinnerton-Dyer is unquestionably one of the most important open problems in number theory today. Let $E$ be an elliptic curve defined over an imaginary quadratic field $K$ contained in $\mathbb{C}$, ...
• #### Exploring Random Geometry with the Gaussian Free Field ﻿

(2016-10-01)
This thesis studies the geometry of objects from 2-dimensional statistical physics in the continuum. Chapter 1 is an introduction to Schramm-Loewner evolutions (SLE). SLEs are the canonical family of non-self-intersecting, ...
• #### On a Heegaard Floer theory for tangles ﻿

(2017-03-10)
The purpose of this thesis is to define a “local” version of Ozsváth and Szabó’s Heegaard Floer homology HFL^ for links in the 3-sphere, i.e. a Heegaard Floer homology HFT^ for tangles in the 3-ball. The decategorification ...