Quantum Complexity and L-functions

Explore the intersection of quantum complexity theory and L-functions in this 55-minute lecture by Kiran Kedlaya from the University of California, San Diego. Delve into topics such as the Hasse-Weil zeta function, classical and quantum complexity results, cohomology, modular forms, and the Mordell-Weil theorem. Examine the role of crystalline and étale cohomology in quantum algorithms, and investigate Fourier coefficients of modular forms of various weights. Consider the challenges and potential solutions in generating compact representations, including the use of Heegner points. Gain insights into cutting-edge research connecting number theory, algebraic geometry, and quantum computing.

Intro
The Hasse-Weil zeta function of a variety
Examples
A word of warning
Some classical complexity results
A quantum complexity result
The role of cohomology
Crystalline cohomology
Étale cohomology and quantum Schoof-Pila?
Fourier coefficients of modular forms
Modular forms of weight 1
Half-integral weight
The L-function of a modular form
The Mordell-Weil theorem
Generators of Mordell-Weil
An analogous problem
Heegner points
Alternate sources of compact representations?