Talks

In this talk, I will discuss the complexity of a fermionic analogue of Quantum k-SAT. In this Fermionic k-SAT problem, one is given the task to decide whether there is a fermionic state in the null-space of a collection of fermionic, parity-conserving, projectors on n fermionic modes, where each fermionic projector involves at most k fermionic modes. We prove that this problem can be solved efficiently classically for k = 2. In addition, we show that deciding whether there exists a satisfying assignment with a given fixed particle number parity can also be done efficiently classically for Fermionic 2-SAT: this problem is a quantum-fermionic extension of asking whether a classical 2-SAT problem has a solution with a given Hamming weight parity. We also prove that deciding whether there exists a satisfying assignment for particle-number-conserving Fermionic 2-SAT for some given particle number is NP-complete. Complementary to this, we show that Fermionic 9-SAT is QMA_1-hard. 

In 1914, Ramanujan wrote down 17 intriguing formulas for 1/pi, which motivated the modern-day machinery of computing trillions of digits of pi. Most of these formulas lay unproven until the 1980s. The Canadian Borwein brothers wrote a comprehensive treatise proving these formulas in the 1980s. We can now ask, “What is the physics behind Ramanujan’s pi”? I will argue that the physics connection can be found via logarithmic conformal field theories, for instance, those studied in the fractional quantum hall effect, polymers, and percolation. The CFT connection gives rise to an infinite number of new formulas for pi. In contrast, the myriad Ramanujan formulas provoke us into looking into faster converging basis for conformal correlators, which is, in turn, provided by the stringy dispersion relation mentioned above.

The cosmic neutrino background is like the cosmic microwave background, but less photon-y and more neutrino-ey. The CNB is also less talked about than the CMB, mostly because it's nearly impossible to detect directly. But if it could be detected, it would be interesting in several ways that are discussed.