Davi Castro-Silva

About me

I am currently a Research Associate at the University of Cambridge, advised by Tom Gur and Sergii Strelchuk. I am a member of the Centre for Quantum Information and Foundations.

Previously I was a postdoc at CWI (Amsterdam) advised by Jop Briët, and member of the quantum computing group QuSoft. Before that, I was a PhD student in Applied Mathematics at the University of Cologne, advised by Frank Vallentin and Fernando de Oliveira Filho.

I obtained my Master in Mathematics at IMPA advised by Roberto Imbuzeiro Oliveira, and completed the Cycle Ingénieur (Bachelor + Master) at École Polytechnique.

Research interests

I have fairly broad research interests distributed around theoretical computer science, quantum computing and combinatorics.

Recently my research has been aimed at understanding the true extent of the power of quantum computation, exploring when it can offer significant speedup compared to classical computers and when it cannot. In particular, I wish to elucidate the relationship between large quantum speedups and the symmetries or structural properties of the problems in consideration.

More generally, I am interested in the following topics:

• Additive combinatorics (in particular higher-order Fourier analysis).

• Combinatorial optimisation (in particular semidefinite programming and applications of harmonic analysis).

• Computational complexity (in particular obtaining lower bounds on several notions of complexity).

• Extremal combinatorics (in particular Ramsey theory and extremal geometric problems).

• Quantum computing and quantum information (in particular their interactions with combinatorics and analysis).

See also my publications for the type of work I usually do.