Joining Caltech this year:
Franca Karoline Olga (Franca) Hoffmann
Franca Karoline Olga (Franca) Hoffmann

Franca Hoffmann's research is focused on the interface between applied mathematics and data analysis, driven by the need to provide rigorous mathematical foundations for modeling tools used in applications. Franca Hoffmann is interested in (1) the theory of nonlinear and nonlocal partial differential equations, making use of gradient flows, entropy methods, functional inequalities, optimal transport techniques, kinetic theory, particle methods and relationships between different scales; and (2) the development of novel tools for data analysis and mathematical approaches to machine learning, involving graph based methods for unsupervised and semi-supervised learning, focusing on data clustering and classification, graph Laplacians and their continuum counterparts, spectral analysis, uncertainty quantification and consistency analysis. It is the intersection of these topics that allow for novel interesting mathematical frameworks, such as recently developed sampling algorithms combining ideas from (1) and (2) to create approximate samples from a posterior distribution solving general classes of inverse problems.

Franca will join Caltech in Fall 2022.


Eric Mazumdar Eric Mazumdar
Eric Mazumdar's research lies at the intersection of machine learning and economics. He is broadly interested in developing the tools and understanding necessary to confidently deploy machine learning algorithms into societal-scale systems. This requires understanding the theoretical underpinnings of learning algorithms in uncertain, dynamic environments where they must interact with other strategic agents, humans, and algorithms. Practically, he applies his work to work to problems in intelligent infrastructure, online markets, e-commerce, and the delivery of healthcare. Some of the topics addressed by his recent work include strategic classification, learning behavioral models of human decision-making from data, min-max optimization, learning in games, multi-agent reinforcement learning, distributionally robust learning, and learning for control.



Yaser S. Abu-Mostafa

Professor of Electrical Engineering and Computer Science

The Learning Systems Group at Caltech studies the theory and applications of Machine Learning (ML). The theory of ML uses mathematical and statistical tools to estimate the information (data and hints) needed to learn a given task. The applications are very diverse and continue to expand to every corner of science and technology. The group works on medical applications of ML, on e-commerce and profiling applications, and on computational finance, among other domains. These applications use the latest techniques of neural networks and other models, and often give rise to novel ML theory and algorithms. Our latest projects are data-driven approach to predicting the spread of COVID-19 in every U.S. county, and ML approach to medical diagnostics using low-resolution ultrasound.

Personal Page
Aaron Ames

Bren Professor of Mechanical and Civil Engineering and Control and Dynamical Systems

Professor Ames’ research interests center on robotics, nonlinear control, hybrid systems and cyber-physical systems, with special emphasis on foundational theory and experimental realization on robotic systems; his lab designs, builds and tests novel bipedal robots and prosthesis with the goal of achieving human-like bipedal robotic walking and translating these capabilities to robotic assistive devices.

Personal Page
Animashree (Anima) Anandkumar

Bren Professor of Computing and Mathematical Sciences

Professor Anandkumar's research interests are in the areas of large-scale machine learning, non-convex optimization and high-dimensional statistics. In particular, she has been spearheading the development and analysis of tensor algorithms for machine learning. Tensor decomposition methods are embarrassingly parallel and scalable to enormous datasets. They are guaranteed to converge to the global optimum and yield consistent estimates for many probabilistic models such as topic models, community models, and hidden Markov models. More generally, Professor Anandkumar has been investigating efficient techniques to speed up non-convex optimization such as escaping saddle points efficiently.

Personal Page
Alan H. Barr

Professor of Computer Science

Professor Barr's research involves (1) mathematical simulation methods for computer graphics (2) developing new types of mathematical and computational methods for the study of biophysical behaviors and structures, and (3) technological leveraging for medical health care and new medical devices. In addition, he has been collaborating with JPL researcher Dr. Martin Lo on new computational and mathematical methods for utilizing the InterPlanetary Superhighway for developing new missions in the Solar System. All of these research areas involve the development and application of new mathematical and computational methods in the context of new applications in the physical sciences.

Personal Page
Katherine L. (Katie) Bouman

Assistant Professor of Computing and Mathematical Sciences, Electrical Engineering and Astronomy; Rosenberg Scholar

Katie Bouman's research focuses on computational imaging: designing systems that tightly integrate algorithm and sensor design, making it possible to observe phenomena previously difficult or impossible to measure with traditional approaches. Imaging plays a critical role in advancing science. However, as science continues to push boundaries, traditional sensors are reaching the limits of what they can measure. Katie's group combines ideas from signal processing, computer vision, machine learning, and physics to find and exploit hidden signals for both scientific discovery and technological innovation. For example, in collaboration with the Event Horizon Telescope, Katie's group is helping to build a computational earth-sized telescope that is taking the first images of a black hole and is analyzing its images to learn about general relativity in the strong-field regime.

Personal Page
Oscar P. Bruno

Professor of Applied and Computational Mathematics

Prof. Bruno's work focuses on development of accurate, high-performance numerical PDE solvers capable of modeling faithfully realistic scientific and engineering configurations. Major theoretical and computational difficulties arise in associated areas of PDE theory, numerical analysis and computational science as a result of intricate and/or singular geometries as well as solution singularities, resonances, nonlinearities, high-frequencies, dispersion, etc. Recently developed Fourier Continuation (FC) and integral-equation techniques, which can successfully tackle such challenges, have enabled accurate solution of previously intractable PDE problems of fundamental importance in science and engineering.

Personal Page
Joel W. Burdick

Richard L. and Dorothy M. Hayman Professor of Mechanical Engineering and Bioengineering; Jet Propulsion Laboratory Research Scientist

Professor Burdick focuses on robotics, kinematics, mechanical systems and control. Active research areas include: robotic locomotion, sensor-based motion planning algorithms, multi-fingered robotic manipulation, applied nonlinear control theory, neural prosthetics, and medical applications of robotics.

Research Group
Venkat Chandrasekaran

Professor of Computing and Mathematical Sciences and Electrical Engineering

Chandrasekaran’s research interests broadly lie in mathematical optimization and its interface with topics in the information sciences.  Specific areas of interest include convex optimization, mathematical signal processing, graphs and combinatorial optimization, applied algebraic geometry, computational harmonic analysis, and statistical inference.

Personal Page
Soon-Jo Chung

Bren Professor of Aerospace and Control and Dynamical Systems; Jet Propulsion Laboratory Research Scientist

Professor Chung's research focuses on distributed spacecraft systems, space autonomous systems, and aerospace robotics, and in particular, on the theory and application of complex nonlinear dynamics, control, estimation, guidance, and navigation of autonomous space and air vehicles.

Research Group
Mathieu Desbrun

Carl F Braun Professor of Computing and Mathematical Sciences

Applied geometry (geometry processing, meshing, and computer graphics); Discrete differential modeling (differential, yet readily-discretizable tools for computational modeling); finite element modeling.

Personal Page
John Doyle

Jean-Lou Chameau Professor of Control and Dynamical Systems, Electrical Engineering, and Bioengineering

Doyle's research is on theoretical foundations for complex tech, bio, med, neuro, and social networks integrating control, communications, computing, and multiscale physics. Layered architectures such as brains integrate high level planning with fast lower level sensing, reflex, and action and facilitate learning, adaptation, augmentation (tools), and teamwork, despite being implemented in energy efficient hardware with sparse, quantized, noisy, delayed, and saturating sensing, communications, computing, and actuation, on time scales from milliseconds to minutes to days.  We are developing a mathematical framework that deals with all of these features and constraints in a coherent and rigorous way with broad applications in science, technology, ecology, and society.

Personal Page
Babak Hassibi

Mose and Lillian S. Bohn Professor of Electrical Engineering and Computing and Mathematical Sciences

Hassibi's research spans various aspects of information theory, signal processing, control theory, and machine learning. He has made contributions to the theory and practice of wireless communications and wireless networks, as well as to robust control, adaptive filtering and neural networks, network information theory, coding for control, phase retrieval, structured signal recovery, high dimensional statistics, epidemic spread in complex networks, and DNA micro-arrays. On the mathematical side, he is interested in linear algebra, with an emphasis on fast algorithms, random matrices, and group representation theory.

Research Group
Thomas Y. Hou

Charles Lee Powell Professor of Applied and Computational Mathematics

Professor Hou focuses on multiscale problems arising from geophysical applications and fluid dynamics, the Millennium Problem on the 3D incompressible Navier-Strokes equations, model reduction for stochastic problems with high dimensional input variables, and adaptive data analysis.

Personal Page
Victoria Kostina

Professor of Electrical Engineering and Computing and Mathematical Sciences

Victoria Kostina's research spans information theory, coding, and wireless communications. Her current efforts explore one of the most exciting avenues in today's information theory: the nonasymptotic regime. Leveraging tools from the theory of random processes and concentration of measure, she pursues fundamental insight into modern delay-constrained communication systems.

Research Group
Steven Low

Frank J. Gilloon Professor of Computing and Mathematical Sciences and Electrical Engineering

Power systems, cyber-physical systems, network architecture, energy-efficient networking.

Personal Page
Urmila Mahadev

Assistant Professor of Computing and Mathematical Sciences

Mahadev's broad theme of research is in cryptographic possibilities of quantum information, a topic of considerable interest in the field. She has built new quantum cryptographic primitives by adapting and extending techniques from modern classical cryptography and has pioneered two widely acclaimed fundamental breakthroughs: 1) Quantum homomorphic encryption (i.e., computing on encrypted data) and 2) Verifiable delegation of quantum computation. Mahadev plans to focus her future research efforts on exploring problems in the intersection of theoretical computer science and quantum computing.

Matilde Marcolli

Robert F. Christy Professor of Mathematics and Computing and Mathematical Sciences

Research Group
Dan Meiron

Fletcher Jones Professor of Aeronautics and Applied and Computational Mathematics

Professor Meiron's research focuses on computation and modelling of basic fluid mechanical phenomena. Particular interests include shock driven flow instabilities, turbulence, simulation approaches for high strain rate solid mechanics. He is also interested on development of adaptive numeriocal methods for such flows that are suitable for high performance computation.

Research Group
Richard M. Murray

Thomas E. and Doris Everhart Professor of Control and Dynamical Systems and Bioengineering; William K. Bowes Jr. Leadership Chair, Division of Biology and Biological Engineering

Research in Richard Murray's group is in the application of feedback and control to networked systems, with applications in biology and autonomy. Current projects include novel control system architectures, biomolecular feedback systems and networked control systems.

Personal Page
Houman Owhadi

Professor of Applied and Computational Mathematics and Control and Dynamical Systems

Professor Owhadi’s research concerns the exploration of interplays between numerical approximation, statistical inference and learning  from a game theoretic perspective. Whereas the process of discovery is usually based on a combination of trial and error,  insight and plain guesswork, his research is motivated by the facilitation/automation possibilities  emerging from these interplays.

Personal Page
Lior Pachter

Bren Professor of Computational Biology and Computing and Mathematical Sciences

Professor Patcher is a computational biologist working in genomics. His career began in comparative genomics, and initially was interested in genome alignment, annotation, and the determination of conserved regions using phylogenetic methods. More recently he's become focused on functional genomics, which includes answering questions about the function and interaction of DNA, RNA and protein products. He's particularly interested in applications of high-throughput sequencing to RNA biology. Genomics requires the development of algorithms, statistical methodology and mathematical foundations, and a major part of his research is therefore on methods.

Personal Page
Niles A. Pierce

Professor of Applied and Computational Mathematics and Bioengineering; Executive Officer for Biology and Biological Engineering

Engineering small conditional DNAs and RNAs for signal transduction in vitro, in situ, and in vivo; computational algorithms for the analysis and design of nucleic acid structures, devices, and systems; programmable molecular technologies for readout and regulation of the state of endogenous biological circuitry.

Research Group
Peter Schroeder

Shaler Arthur Hanisch Professor of Computer Science and Applied and Computational Mathematics

Professor Schröder is interested in the design of efficient and reliable algorithms for problems in computer graphics. These range from geometric modeling (effective methods to model the shape of objects) to animation (simulation of physical phenomena such as the deformation of cloth). His emphasis is on an area known as "Discrete Differential Geometry." Its goals are to rebuild the foundations of classical differential geometry in a discrete setting which makes it immediately useful for computation.

Leonard J. Schulman

Professor of Computer Science

Algorithms and Communication Protocols; Combinatorics and Probability; Coding and Information Theory; Quantum Computation.

Personal Page
Andrew Stuart

Bren Professor of Computing and Mathematical Sciences

Professor Stuart's research is focused on the development of mathematical and algorithmic frameworks for the seamless integration of models with data. He works in the Bayesian formulation of inverse problems, and in data assimilation for dynamical systems. Quantification of uncertainty plays a significant role in this work. Current applications of interest include a variety of problems in the geophysical sciences, and in graph-based learning.

Research Group
Joel A. Tropp

Steele Family Professor of Applied and Computational Mathematics

Joel Tropp's work lies at the interface of applied mathematics, electrical engineering, computer science, and statistics. This research concerns the theoretical and computational aspects of data analysis, sparse modeling, randomized linear algebra, and random matrix theory.

Research Group
Christopher Umans

Professor of Computer Science; Executive Officer for Computing and Mathematical Sciences

Professor Umans is interested in theoretical computer science, and especially computational complexity. He enjoys problems with an algebraic flavor, and this often leads to research questions in derandomization and explicit combinatorial constructions, algebraic algorithms, coding theory, and hardness of approximation.

Personal Page
Thomas Vidick

Professor of Computing and Mathematical Sciences

Professor Vidick’s research is situated at the interface of theoretical computer science, quantum information and cryptography. He is interested in applying techniques from computer science, such as complexity theory, to study problems in quantum computing. He has investigated the role of entanglement in multi-prover interactive proof systems and obtained the first substantial computational hardness results on the power of entangled provers. Entanglement also plays a major role in quantum cryptography, and he has made important contributions to the field of device-independent cryptography. He is also interested in using quantum information theory to shed new light on fundamental techniques in theoretical computer science such as semidefinite programming and approximation algorithms.

Personal Page
Adam Wierman

Professor of Computing and Mathematical Sciences; Director, Information Science and Technology

Adam Wierman's research interests center around resource allocation and scheduling decisions in computer systems and services. More specifically, his work focuses both on developing analytic techniques in stochastic modeling, optimization, machine learning, and game theory, and applying these techniques to application domains such as energy-efficient computing, the cloud, the smart grid, and social networks.

Personal Page
Erik Winfree

Professor of Computer Science, Computation and Neural Systems, and Bioengineering

Professor Winfree's research involves theoretical and experimental aspects of molecular programming. Models of computation are developed that incorporate essential features of molecular folding, molecular self-assembly, biochemical circuits, and molecular robotics. These models are studied to determine their expressiveness for programming molecular-level tasks including decision-making, memory, behavior, and morphogenesis.  Methods for compiling abstract molecular programs into actual molecules are developed and tested in the laboratory.

Personal Page
Yisong Yue

Professor of Computing and Mathematical Sciences

Yisong Yue's research interests lie primarily in the theory and application of statistical machine learning. He is particularly interested in developing novel methods for interactive machine learning and structured machine learning. In the past, his research has been applied to information retrieval, recommender systems, text classification, learning from rich user interfaces, analyzing implicit human feedback, clinical therapy, tutoring systems, data-driven animation, behavior analysis, sports analytics, experiment design for science, learning to optimize, policy learning in robotics, and adaptive planning & allocation problems. 

Personal Page

Affiliated Faculty

Fernando Brandao

Bren Professor of Theoretical Physics

Fernando Brandão's research is focused on quantum information science. He explores the interplay of physics, computer science and mathematics to study the role of quantum mechanics in computation and information transmission. He is also interested in the application of tools and concepts of quantum information to other branches of science, such as quantum many-body theory, complexity theory and thermodynamics/statistical mechanics. In recent years he has been exploring several directions in entanglement theory, from understanding the relation between entanglement and other physical properties (such as correlation length) in quantum many-body systems, to developing a sharper understanding of fundamental properties of entanglement such as its monogamous character (with applications in quantum cryptography, quantum Hamiltonian complexity, and even in convex optimisation).

Frederick Eberhardt

Professor of Philosophy

Frederick Eberhardt's research interests lie at the formal end of philosophy of science, the machine learning end of statistics and computer science, and the learning and modeling end of psychology and cognitive science. His work has focused primarily on methods for causal discovery from statistical data, the use of experiments in causal discovery, the integration of causal inferences from different data sets and the philosophical issues at the foundations of causality and probability. He has done some work on computational models in cognitive science and some historical work on the philosophy of Hans Reichenbach, especially his frequentist interpretation of probability.

Personal Page
Alexei Kitaev

Ronald and Maxine Linde Professor of Theoretical Physics and Mathematics

Professor Kitaev works in the field of quantum computation and related areas of theoretical physics. His main contribution was the concept of topological quantum computation, a scheme where quantum information is protected from errors due to special properties of the underlying physical system, which are generally related to topology. He currently focuses on topological classification of quantum phases (a nontrivial example being the 2-dimensional electron liquid in the quantum Hall regime).

Beverley J. McKeon

Theodore von Karman Professor of Aeronautics; EAS Division Deputy Chair

Professor McKeon explores new ways to manipulate or control the boundary layer—the thin layer between a material and flowing air—to improve flow characteristics, such as a reduction of drag, noise, and structural loading or expansion of vehicle performance envelopes during travel. The unifying theme to her work is an experimental and theoretical approach at the intersection of fluid mechanics, control, and materials science to investigate fundamental flow questions, address efficiency and performance challenges in aerospace vehicle design, and respond to the energy conservation imperative in novel and efficient ways.


Specific interests include:

Modeling and control of wall-bounded flows using smart, morphing surfaces. Resolvent analysis as a tool for modeling turbulent, transitional and controlled flows; rigorous, system-level tools for understanding flow physics and design of flow control schemes. Assimilation of experimental data for efficient low-order flow modeling.

Measurement, definition and description of high Reynolds number wall turbulence. Interdisciplinary approaches to experimental flow manipulation for performance enhancement and understanding of fundamental flow physics; application of new materials to flow control.

Research Group
Pietro Perona

Allen E. Puckett Professor of Electrical Engineering

Professor Perona's research focusses on vision: how do we see and how can we build machines that see.

Professor Perona is currently interested visual recognition, more specifically visual categorization. He is studying how machines can learn to recognize frogs, cars, faces and trees with minimal human supervision, and how machines can learn from human experts. His project `Visipedia' has produced two smart device apps (iNaturalist and Merlin Bird ID) that anyone can use to recognize the species of plants and animals from a photograph.

In collaboration with Professors Anderson and Dickinson, professor Perona is building vision systems and statistical techniques for measuring actions and activities in fruit flies and mice. This enables geneticists and neuroethologists to investigate the relationship between genes, brains and behavior.

Professor Perona is also interested in studying how humans perform visual tasks, such as searching and recognizing image content. One of his recent projects studies how to harness the visual ability of thousands of people on the web.

Personal Page
John P. Preskill

Richard P. Feynman Professor of Theoretical Physics; Allen V. C. Davis and Lenabelle Davis Leadership Chair, Institute for Quantum Science and Technology

Professor Preskill works on quantum computation and quantum information science. He is especially interested in methods for protecting quantum states from damage, and in applications of quantum information concepts to problems in physical science.

Personal Page
Lulu Qian

Professor of Bioengineering

The Qian lab is interested in designing and constructing nucleic-acid systems from scratch that exhibit programmable behaviors – at the basic level, such as recognizing molecular events from the environment, processing information, making decisions and taking actions; at the advanced level, such as learning and evolving – to explore the principles of molecular programs that nature creates, to embed control within biochemical systems that directly interact with molecules, and eventually, to re-create synthetic molecular programs that approach the complexity and sophistication of life itself.

Personal Page
Omer Tamuz

Professor of Economics and Mathematics

Omer Tamuz's work in Economics focuses on how people learn through social interaction, and on games and strategic behavior in networks. His mathematical interests lie in probability theory, ergodic theory, and their connections to group theory. He has also worked in machine learning and statistics, and in particular in combinatorial statistics, where the estimated parameter takes values in a finite set.

Research Group

Teaching Faculty

Adam Blank

Teaching Assistant Professor of Computing and Mathematical Sciences

Adam Blank’s teaching approach involves developing new technologies and techniques to enhance the learning of computer science students. They experiment with new techniques and technologies involving technology, human computation and collaboration to improve the classroom experience.  They are especially interested in broadening participation in computing via their teaching methods.

Personal Page
Melissa Hovik

Teaching Assistant Professor of Computing and Mathematical Sciences

Melissa Hovik’s teaching philosophy is one that encourages students to discover and explore interdisciplinary connections between computer science and other fields such as biology. Her primary teaching interests are in introductory CS, web development, and databases, though she also enjoys introducing students to other areas in CS including security, programming languages, and theory foundations. In all of her classes, she strives to motivate real-world applications into material, including accessibility, ethics, and security.

Eugene Lavretsky

Lecturer in Computing and Mathematical Sciences

Elizabeth Qian

von Karman Instructor in Computing and Mathematical Sciences

Elizabeth Qian’s research seeks to develop scalable computational methods to enable and enhance decision-making in engineering, scientific, and medical applications. In particular, her work focuses on the development of principled low-dimensional model approximations through model reduction and scientific machine learning, and on designing multi-fidelity formulations for optimization and uncertainty quantification that embed these approximations in decision-making settings.

Research Group
Claire Ralph

Lecturer in Computing and Mathematical Sciences; Director, Career Development Center

Michael Vanier

Teaching Professor of Computing and Mathematical Sciences

Research Group
Konstantin Zuev

Teaching Assistant Professor of Computing and Mathematical Sciences

Research Group

Research Faculty

Paul Rothemund

Research Professor of Bioengineering, Computing and Mathematical Sciences, and Computation and Neural Systems

Personal Page


James L. (Jim) Beck

George W. Housner Professor of Engineering and Applied Science, Emeritus

Professor Beck focuses on the development of theory and algorithms for stochastic system modeling, uncertainty propagation and Bayesian updating of dynamic systems and networks based on sensor data, treating both modeling and excitation uncertainty. The primary computational tools are advanced stochastic simulation algorithms based on Markov chain Monte Carlo concepts. Some applications of current interest are stochastic predictions of the performance of structural systems under earthquakes, reliability assessment of technological networks, fast automated decision making for mitigation actions based on earthquake early warning systems, earthquake source inversions from seismic sensor networks, damage detection and assessment from structural sensor monitoring networks, Bayesian compressive sensing, and a stochastic mechanics approach to quantum mechanics.

Personal Page
Kanianthra M. (Mani) Chandy

Simon Ramo Professor of Computer Science, Emeritus

Professor Chandy builds and analyzes systems that sense and respond to changes. He is currently working on systems that sense and respond to: (a) seismic events, (b) threat events such as the introduction of nuclear radiation material, (c) medical events such a fetal distress, and (d) events in the power grid. The systems use sensor networks, cloud computing and event-driven architecture. The theory is based on optimization, control, machine learning and game theory.

Personal Page
Alain J. Martin

Professor of Computer Science, Emeritus

Professor Martin focuses on asynchronous VLSI and parallel architecture.

Personal Page
Carver Mead

Gordon and Betty Moore Professor of Engineering and Applied Science, Emeritus

Personal Page