Our world is messy, unpredictable, and packed with rich sensory stimuli. While precise modeling and careful engineering have powered robots to revolutionize the factory floor, getting such robots to robustly manipulate everyday objects in everyday environments is a largely unsolved problem. Consider the seemingly easy task of opening an unlocked door – a feat effortlessly … Continued
We are at a pivotal moment in our history. Large-scale AI models like DALL·E2 are transforming our society, making content creation accessible to all. However, this raises many pressing questions. Will AI replace human creators’ jobs? Is AI stealing artists’ work? How can AI and human creators work together? Who should get credited? My vision … Continued
My research uses the tools of theoretical computer science to answer fundamental questions about the security of widely deployed cryptography. Much of my work focuses on the foundations of post-quantum cryptography, that is, classical cryptographic schemes that are secure even against an adversary with a quantum computer. This particular line of research has added urgency … Continued
Cameras have become a ubiquitous interface between the real world and computers. Although their applications span across disciplines, today’s cameras acquire information in the same way they did in the 19th century: they aim to record an ideal image of the scene with a complex stack of lenses, while computation is only performed after the … Continued
My research focuses on a core question in theoretical computer science: What can be computed efficiently? The study of algorithms and computational complexity is a mathematical discipline that lies at the foundation of Computer Science. It introduces a “Computational Lens” that helps explain phenomenon in areas that are seemingly unrelated to computing, including phenomenon in … Continued
My research aims to develop general-purpose optimization algorithms that are optimal in theory and efficient in practice. I combine ideas from continuous and discrete mathematics to substantially advance state-of-the-art algorithms that tackle foundational problems in computer science and optimization, such as the maximum flow problem and linear programming. In the future, I plan to study … Continued
This proposal focuses on mathematical, computational, and mechanical foundations for designing complex 3D structures that can be built from shape-shifting 2D materials. New kinds of dynamic, shape-shifting matter such as programmable metamaterials, self-folding robotics, and active hydrogels driven by changes in heat, light, or humidity open up an abundance of new possibilities for applications. But … Continued
Nonconvex learning algorithms are enabling transformative societal changes by revolutionizing how we process data. Despite wide empirical success, a satisfactory understanding of the behavior of these algorithms is still lacking. In particular, as systems and processes become increasingly automated with algorithms aiding or replacing human judgment, the importance of more reliable learning methodologies coupled with … Continued
Much of my research effort is devoted to the topic of quantum computation. Is it possible for a quantum computer to function in thermal equilibrium? How does one design realistic tests for quantum behavior in a given device? What can one learn about quantum mechanics in general by taking a “quantum information” perspective?
My research aims to settle the complexity status of central problems in combinatorial optimization, such as the Unique Games problem and Sparsest Cut. Candidate methods are poorly understood semidefinite programming hierarchies. For any significant progress a deeper understanding of the underlying geometry has to be developed, bridging several areas of mathematics and theoretical computer science.