Compressed Wannier Functions

Wannier functions are localized functions that form a complete orthogonal set. In solid state physics, we expand the electron wavefunction using Wannier functions to help interpret the distribution of electron probability in an environment. We utilize an \(l_1\)-regularization of the quantum variational method subject to orthogonality constraint to calculate sparse Wannier functions.

Skills: Mathematica, split Bregmann method, orthogonality constraint, projection, lasso, topology.

Learned Wannier Functions

The learned Wannier function method uses basis pursuit and a highly specialized Wannier basis to calculate new exponentially localized Wannier functions from the characteristics of known Wannier functions. In symmetrizing our Wannier dictionary, our basis functions act as symmetry generators and are capable of constraining symmetry.

Skills: Basis pursuit, dictionary learning, sparse coding, convex optimization, split Bregmann method, localization, symmetry constraint using group theory.

Electronic Bandstructure Classification

Electronic bandstructures are eigenspectra of solutions to Schrodinger’s equation. In some cases, the local spatial features of bandstructures are strong indicators of physical properties of the quantum system studied. Instead of representing bandstructures as matrices, we suggest using a classified representation that clusters common spatial features and builds a classification model for predicting the group index of a particular feature. Our method organizes bandstructures in a way that better fits the way we think about them, and introduces concepts from machine learning and computer vision to materials engineering.

Skills: Python, clustering, classification, computer vision, cross-validation, shilouette analysis, prediction metrics, scikit-learn, TensorFlow.

Mobile Application Development

Group vacations, bachelorette parties, roommate interactions; life gets complicated when you can’t pay for things separately. SPLRG is a simple solution to the complicated problem of sharing group expenses.

Skills: Swift, Objective-C, HTML, Firebase, Twitter API, Google Places API, GeoFire.

Web Development

When managing multiple web based projects setting up a personal database for every project creates redundant coding processes. We develop a javascript library that reduces this redundancy by automatically organizing the structure of a database to handle similar forms from different websites.

Skills: Javascript, css-frameworks, HTML, Firebase API

Deep Learning

Using a pre-trained CNN we can extract the content-representation and style-representation from images. Because these are seperate characteristics, we can produce new data by blending the content and style representations from different data via a non-linear optimization problem. We develop a framework based on a keras library for performing style transfer on images effectively and efficiently.

Skills: Python, Keras, Tensorflow, CNN, L-BFGS.

We perform fine-tunning on a pre-trained CNN to personalize the recognition of cellphones in images, from a small given dataset. This allows us to use a standard object detection tool, ImageAI, to detect the location of cellphones in images accurately.

Skills: ImageAI, fine-tunning, Python, Keras, Tensorflow, CNN.

Professional Experience

Download PDF