NishMath - #logic

Research at the intersection of logic, descent theory, and category theory is currently underway, focusing on advanced mathematical concepts. Key areas of exploration include Galois descent in algebraic contexts, a concept with applications in algebraic geometry as detailed in texts by James Milne and lecture notes by Keith Conrad and Joshua Ruiter. Additionally, researchers are investigating equivariant bicategorical shadows and traces, aiming to generalize topological Hochschild homology.

This research extends to first-order categorical logic and quantum observables, contributing to a broader understanding of these abstract mathematical structures. A recent seminar at Vanderbilt University highlighted "Equivariant Bicategorical Shadows and Traces," where the presenter discussed a new framework of equivariant bicategorical shadows and explained why twisted THH is a g-twisted shadow, also exploring g-twisted bicategorical traces. This work builds upon the foundations laid by Ponto in defining bicategorical shadows, offering potential advancements in algebraic K-theory.


References :

• Diagonal Argument: Prev TOC Next MW: Last time we justified some equations and inequalities for our adjoints: they preserve some boolean operations, and “half-preserveâ€� some others.
• nLab: Updated by David Corfield on 2025-02-28 at 15:33:46Z.
• Math Department: Zhonghui Sun - Michigan State University

Classification:

• HashTags: #Logic #CategoryTheory #GaloisTheory
• Company: University
• Target: Abstraction
• Product: Logic
• Feature: Descent
• Type: Research
• Severity: Medium

Recent discussions in mathematical concepts and programming tools cover a range of topics, including theoretical foundations and practical applications. Peter Cameron highlighted the Compactness Theorem for first-order logic, explaining its consequences and connections to topology. Also, a beginner's guide to sets has been published to explain how they work and some applications.

Noel Welsh presented a talk at Imperial College on dualities in programming, exploring the relationships between data and codata, calls and returns, and ASTs and stack machines. The use of adjoints in boolean operations was justified, and Daniel Lemire published an overview of parallel programming using Go. These discussions bridge the gap between abstract mathematical principles and their concrete uses in software development and programming paradigms.


References :

• Diagonal Argument: Some equations and inequalities for adjoints: they preserve some boolean operations, and “half-preserveâ€� some others.

Classification:

• HashTags: #Mathematics #Logic #Programming
• Target: Development
• Product: Math
• Feature: Mathematical Concepts
• Type: Research
• Severity: Medium