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The modeling and numerical simulation of complex wave propagation phenomena are discussed. The analysis and numerics of the associated partial differential equations are usually very challenging. Minor changes in the model can lead to qualitatively very different properties. The aim is therefore to find a model with mathematically good properties that is still physically justified. This requires close interaction between mathematical analysis and physical modeling. The topic is approached using examples from helioseismology, plasmonics and anisotropic wave propagation.

Since the early twentieth century, it has been understood that mathematical definitions and proofs can be represented in formal systems with precise grammars and rules of use. Building on such foundations, computational proof assistants now make it possible to encode mathematical knowledge in digital form. In this talk, I'll explore some of the ways that these and related technologies can help us do mathematics.
 
Jeremy Avigad is a professor of philosophy and a professor of mathematical sciences at Carnegie Mellon University. He received a B.A. in mathematics from Harvard University in 1989, and a Ph.D. in mathematics from the University of California at Berkeley in 1995 under the supervision of Jack Silver. He has contributed to the areas of mathematical logic and foundations, formal verification and interactive theorem proving, and the philosophy and history of mathematics. He became Director of the Hoskinson Center for Formal Mathematics at Carnegie Mellon University after Charles Hoskinson donated $20 Million in September 2021 to establish it.

3 day public event with lectures and talks, music and quiz, movie and cultural highlights - all on and around Mathematics. From 8 - 10 October 2024. Join us at Triangel Open Space in Karlsruhe to delve into the world of modeling, prediction & simulation.

MathSEE modeling week,tentatively planned from October 14 - 18, 2024 will be hands-on application of mathematical methods in the SEE disciplines. Participation can be credited as a seminar with 3 CP. Students of Mathematics, Computer science and SEE disciplines as well as doctoral candidates are most welcome to apply.