Conferences  >  Mathematics  >  Automated Theorem Proving

American Institute of Mathematics (AIM)

This workshop, sponsored by AIM and the NSF, will be devoted to solving open problems regarding the stability of nonlinear waves using computer assisted methods of proof. Some results using computer assisted methods of proof include Hilbert's 18th problem and Smale's 14th problem. Researchers have developed efficient methods for obtaining rigorous error bounds for numerical approximations of heteroclinic and homoclinic connections between fixed points in ODE systems. These rigorous computation methods establish the existence and uniqueness of the solution in addition to providing a tight, completely rigorous error bound. Thus, these rigorous computations can be used to prove Theorems. Similarly, researchers have developed efficient and robust numerical methods for computing quantities that relay information about the spectral stability of one-dimensional traveling wave solutions to PDEs, which in turn yields information regarding the nonlinear stability. This workshop will help researchers identify collaborative opportunities to use rigorous computation to prove theorems regarding open problems in nonlinear wave theory.

Computer assisted proofs for stability analysis of nonlinear waves. Stability of multi-dimensional non-planar traveling waves. Rigorous computation of center manifolds

Applied Mathematics (in general),    Analysis

Mathematical Sciences Research Institute (MSRI)

Computational proof assistants now make it possible to develop global, digital mathematical libraries with theorems that are fully checked by computer. This summer school will introduce students to the new technology and the ideas behind it, and will encourage them to think about the goals and benefits of formalized mathematics. Students will learn to use the Lean interactive proof assistant, and by the end of the session they will be in a position to formalize mathematics on their own, join the Lean community, and contribute to its mathematical library.

Courses and Events for Math Students and Early Career Researchers,    Algebra

in conjunction with ACNS 2023

Over the years, many automated methods have been proposed to help designers and cryptanalysts prove security bounds of symmetric-key primitives against various attacks such as differential or integral cryptanalysis. These include the use of mixed integer linear programming (MILP), Boolean satisfiability problem (SAT) solvers and their extension, satisfiability modulo theories (SMT) solvers, as well as constraint programming (CP) solvers. More recently, data-driven techniques that rely on machine and deep learning have also been proposed, leading to attacks that rival that of their classical counterparts. The aim of the ADSC workshop is to provide an international forum for researchers to explore and further push the boundaries of these automated and data-driven methods. We welcome submissions on the application, improvement and efficient implementation of these methods.

Mathematical Sciences Research Institute (MSRI)

This summer school will provide an introduction to the field of probabilistic proofs and the beautiful mathematics behind it, as well as prepare students for conducting cutting-edge research in this area.

Hausdorff Center for Mathematics – hcm (Universität Bonn)

The last decade has witnessed tremendous advances in both interactive and automated theorem proving, and we are arguably on the doorstep of a new era, in which interactive theorem provers validate ground-breaking mathematical research in a reasonably short time, as shown in Peter Scholze's Liquid Tensor Experiment. This new area is driven both by new software and by a growing community of users. In addition, we have seen the advent of new software that guides mathematicians in finding proofs, helps them develop new conjectures or even generates a proof or part of a proof with minimal human input. This HSM will highlight both these developments.

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)