Dissertation: Higher order extensions of the Boltzmann equation

Dissertation: Cusps and Codimension-1 Flats in Convex Projective Geometrey

Dissertation: Numerical Multiscale Methods for Boundary Layer Problems in Fluid Dynamics

Dissertation: On Poisson Follower Model

Dissertation: Numerical Methods for Averaging and Homogenization

Dissertation: Coordinate-Free Principles for Extension of Smooth Functions

Dissertation: The L2 Theory of Well-posedness for Hyperbolic Systems of Conservation Laws

Dissertation: Compactified Mirror Families for Positive Log Calabi-Yau Surfaces

Dissertation: Non-unique sofic entropy and a von Neumann algebra multiplicative ergodic theorem

Dissertation: Conservative Spectral Methods of Fokker-Planck-Landau Type Equations: Simulations, Long-time Behaviour and Error Estimates

Dissertation: Old and New Perspectives on Effective Equations: A Study of Quantum Many-Body Systems

Dissertation: The De Giorgi method: Applications to degenerate PDE

Dissertation: The Ooguri-Vafa as a moduli space of framed wild harmonic bundles

Dissertation: Extremal problems in Fourier analysis, Whitney's theorem, and the interpolation of data

Dissertation: Andre-Quillen (co)homology and equivariant stable homotopy theory

Dissertation: On Spatial Birth-Death and Matching Processes, and Poisson Shot-Noise Fields

Dissertation: Methods for Solving Hamilton-Jacobi-Equations

Dissertation: Coupling and Unimodularity in Stationary Settings

Dissertation: A Study of the Three-Dimensional Quasi-Geostrophic System

Dissertation: Repulsion of Determinantal Point Processes and Stationary Poisson Tessellations in High Dimesions

Dissertation: On the dual complexes of certain Log Calabi-Yau pairs

Dissertation: Knot traces and the slice genus

Dissertation: The moduli space of objects in differential graded categories glued along bimodules & a presentability result in the homotopy theory of commutative differential graded algebras

Dissertation: Curvature Blow-up in Doublywarped Product Metrics Evolving by Ricci Flow

Dissertation: Equivariant aspects of topological Hochschild homology

Dissertation: Regularity of fractional analogue of k-Hessian operators and a non-local one-phase free boundary problem

Dissertation: Comparison Theorems of Phylogenetic Spaces and Algebraic Fans

Dissertation: Admissible groups and cluster structures of families of log Calabi-Yau surfaces

Dissertation: Fast high dimensional approximation via random embeddings

Dissertation: Global LP Solutions to the Boltzmann Equation with an Angle-Potential Concentrated Collision Kernel

Dissertation: Rectifying Stable Infinity-Categories and Relative Koszul Duality for Operads

Dissertation: Cardinality Restrictions on Noetherian Spectra

Dissertation: Effective Equidistribution Results for Horospherical Actions on the Space of Lattices

Dissertation: Martingale-Generated Control Structures and a Framework for the Dynamic Programming Principle

Dissertation: A Weighty Theorem of the Heart for the Algebraic K-Theory of Higher Categories

Dissertation: Essays on Forward Portfolio Theory and Financial Time Series Modeling

Dissertation: Lagrangian Torus Fibrations for Symplectic Torid Degenerations

Dissertation: Academic Math Mindset Interventions in First Year College Calculus

Dissertation: Mapping Tori and Stable Pairs

Dissertation: Optimal Investment with High-Watermark Fee in a Multi-dimensional Jump Diffusion Model

Dissertation: GHK Mirror Symmetry and the Knutson-Tao Hive Cone

Dissertation: Least Action Principles with Applications to Gradient Flows and Kinetic Equations

Dissertation: Minimality and Stability Properties in Sobolev and Isoperimetric Inequalities

Dissertation: Differential FPPF Descent Obstructions

Dissertation: Relax, Descend, and Certify: Optimization Techniques for Typically Tractable Data Problems

Dissertation: Several Regularity Results for Nonlocal Elliptic Equations

Dissertation: Hybrid Inverse Problems in Molecular Imaging

Dissertation: Inverse Problems in Photoacoustic Imaging: Analysis and Computation

Dissertation: OBSTRUCTIONS TO THE INTEGRAL HASSE PRINCIPLE FOR GENERALIZED AFFINE CHATELET SURFACES

Dissertation: Rectifying Stable Infinity-Categories and Relative Koszul Duality for Operads

Dissertation: WARPING GEOMETRIC STRUCTURES AND ABELIANIZING SL2R LOCAL SYSTEMS

Dissertation: ASYMPTOTIC LIMITS IN THE HITCHIN MODULI SPACE

Dissertation: EXPLORATIONS IN ALGEBRA AND TOPOLOGY

Dissertation: THE WONDERFUL COMPACTIFICATION FOR QUANTUM GROUPS

Dissertation: RECOVERING THE PAYOFF STRUCTURE OF A UTILITY MAXIMIZING AGENT

Dissertation: MULTIPLICATIVE AND DYNAMICAL ANALYSIS ON IDELES AND IDELE CLASS GROUPS

Dissertation: REGULARITY ESTIMATES FOR SOME FREE BOUNDARY PROBLEMS OF OBSTACLE-TYPE

Dissertation: ASPECTS OF DERIVED KOSZUL DUALITY

Dissertation: Entropy theory for locally compact sofic groups

Dissertation: MITTAG-LEFFLER MOMENTS AND WEIGHTED POINTWISE ESTIMATES FOR SOLUTIONS TO THE BOLTZMANN EQUATION FOR HARD POTENTIALS WITHOUT CUTOFF