Rationality Proofs by Curve Counting

Curve Counting and Instanton Counting

Intuitively, in four-dimensional gauge theories one counts instantons, and in twodimensional string theory one counts holomorphic curves. These correspond to the instanton counting and curve counting in the title. There is no obvious connection between them, but a remarkable physical idea called geometric engineering [9, 10, 11] dictates that they are indeed related. More precisely, the generat...

Counting proofs in propositional logic

We give a procedure for counting the number of different proofs of a formula in various sorts of propositional logic. This number is either an integer (that may be 0 if the formula is not provable) or infinite.

Proving Properties of Interactive Proofs by a Generalized Counting Technique

Counting-Based Impossibility Proofs for Distributed Tasks

A cornerstone result in distributed computing is the impossibility of solving consensus using only read and write operations in asynchronous systems where processes may fail. The impossibility of solving consensus led to the study of sub-consensus coordination tasks, namely tasks that are weaker than consensus. Two archetypal sub-consensus tasks are k-set agreement and M -renaming. In k-set agr...

Memory efficient hyperelliptic curve point counting

Let E be a hyperelliptic curve of genus g over a finite field of degree n and small characteristic. Using deformation theory we present an algorithm that computes the zeta function of E in time essentially cubic in n and quadratic memory. This improves substantially upon Kedlaya’s result which has the same time asymptotic, but requires cubic memory size. AMS (MOS) Subject Classification Codes: ...