## Overview

Our efforts in Theoretical Computer Science span traditional algorithms and complexity, and often make contact with pure math (algebra, combinatorics, geometry, probability). **Leonard Schulman** works on aspects of coding and communication, combinatorics and probability, theoretical machine learning, and algorithmic game theory. **Chris Umans** works on algorithms and complexity with connections to algebra, and has an ongoing interest in algorithms for matrix multiplication that employ group theory and representation theory. **Thomas Vidick** is known for his work in quantum complexity and cryptography, particularly in studying the power of quantum interactive proofs. **Urmila Mahadev** has established landmark results regarding the classical verification of quantum computation, and is interested in problems at the intersection of quantum computation and cryptography.

Caltech is a place that is infused with theory, and many CMS and affiliated faculty make contributions in TCS as part of their work, including **Babak Hassibi**, **Michelle Effros** and **Victoria Kostina** (coding and information theory), **Joel Tropp** (matrix concentration and randomized algorithms), **Erik Winfree** and **Lulu Qian** (molecular programming), **Fernando Brandao****,** **Alexei Kitaev**, and **John Preskill** (quantum information and computing), and **Omer Tamuz** (algorithmic economics, probability and statistics), and **Adam Wierman** (online algorithms and algorithmic economics).