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Category: mathematics
| | www.galoisrepresentations.com
Test Your Intuition: p-adic local Langlands edition | Persiflage
Travel
| | [AI summary] The blog post discusses a mathematical problem related to the surjectivity of certain maps in the context of Galois representations and modular forms. It references a conjecture about the structure of the mod-p deformation ring and its connection to the Hecke algebra. The author explores the implications of this conjecture on the properties of the deformation ring and its relation to the cohomology of arithmetic groups. The post also touches on the use of completed cohomology and the patched module in understanding these structures. The author acknowledges the complexity of the problem and the need for further research and collaboration to resolve it.
| | igorpak.wordpress.com
The power of negative thinking: Combinatorial and geometric inequalities | Igor Pak's blog
Travel
| | The equality cases of Stanley inequality are not in the polynomial hierarchy. How come? What does that tell us about geometric inequalities?
| | jaydaigle.net
A Fictional History of Numbers, Part 4: Imagination, Complexity, and the Fundamental Theorem of Algebra
Travel
| We continue our exploration of what numbers are, and where mathematicians keep finding weird ones. In the first three parts we extended the natural numbers in two ways: algebraically and analytically. Those approaches gave overlapping but distinct sets of numbers. This week we combine them to get the complex numbers, and see some hints of why the complex numbers are so useful-and so frustrating.

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