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Texas Tech University, Department of Mathematics and Statistics

The field of Differential Geometry, Integrable Systems, and Applications has a long history and is currently as dynamic and vibrant as ever. Thus, the conference provides an exciting opportunity for the interested audience to learn cutting-edge research in a friendly atmosphere. The main objectives of this minisymposium can be summarized as follows: 1. Improve our understanding of recent significant developments in the field of Differential Geometry, Integrable Systems, and Applications. 2. Bring together mathematicians from different backgrounds and in various career stages to foster mutual understanding and lay out foundations for future research. 3. Advance engagement of diverse graduate students and early-career researchers interested in this expanding field.

Geometrie und Topologie,    Infinitesimalrechnung, Differentialgleichungen, Integralrechnung

ICERM

In spite of their omnipresence and importance, a number of questions about knots remain elusive. Addressing them solicits techniques from a range of mathematical disciplines at the interface of algebra, analysis, geometry, modeling, and low-dimensional topology. Some of the most exciting recent avenues of research include optimizing geometry, quantum knot invariants, and applications in material sciences, physics, and molecular biology. This workshop emphasizes bridging the gap between theoretical, computational, and experimental approaches in knot theory and its applications, including artificial intelligence.

Program Staff;     Tel.: [1-401-863-5030];     Email: programstaff@icerm.brown.edu

Geometrie und Topologie,    Algebra

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

Angewandte Mathematik (allgem.),    Computer-gestütztes Beweisen