Tenure-track opening @ U. Colorado Boulder Dept. of Math!

Esp. (but not only) looking for:
algebraic geometry
homotopy theory
foundations
functional analysis
number theory
interdisciplinary collab. b/w math & computer science or the math of quantum physics

https://www.mathjobs.org/jobs/list/27231

Please help spread the word!

#AlgebraicGeometry #HomotopyTheory #AlgebraicTopology #FoundationsOfMath #FunctionalAnalysis #NumberTheory #ComputerScience #Quantum #Math

MathJobs from the the American Mathematical Society

Mathjobs is an automated job application system sponsored by the AMS.

(Weak) Homotopy Equivalences

Previously: Fibrations and Cofibrations. In topology, we say that two shapes are the same if there is a homeomorphism– an invertible continuous map– between them. Continuity means that …

  Bartosz Milewski's Programming Cafe

I've kind of always wondered what the point of definitions like a group is a non-empty set \(G\) with a binary operation \(d\) satisfying \(d(d(d(z,d(x, d(x,x))),d(z,d(y,d(x,x)))),x) = y\) is, other than because we can, but https://math.stackexchange.com/a/4366021 offers one such answer in terms of homotopy type

#grouptheory #categorytheory #homotopytheory

Looking for 1952 paper of Higman and Neumann

I am looking for the paper Graham Higman and Bernhard Hermann Neumann, Groups as groupoids with one law, Publicationes Mathematicae Debrecen 2 (1952), 215–221. In it, the authors prove (among other

Mathematics Stack Exchange
My #blog this week is on the Blakers-Massey theorem, whose proof in homotopy type theory #HoTT is one of the key achievements of that community. https://blogs.fediscience.org/the-updated-scholar/2024/03/15/discussing-a-mechanization-of-the-blakers-massey-connectivity-theorem-in-homotopy-type-theory/ #TypeTheory #HomotopyTheory
Discussing “A Mechanization of the Blakers–Massey Connectivity Theorem in Homotopy Type Theory” – The Updated Scholar

Donald Yau and I have a new book out! 📘 🥳

It's called "Homotopy Theory of Enriched Mackey Functors", and I want to explain what those words mean!

https://arxiv.org/abs/2212.04276

[thread about #HomotopyTheory, #CategoryTheory, and #Mackey functors]

(0/11)

Homotopy Theory of Enriched Mackey Functors

Mackey functors provide the coefficient systems for equivariant cohomology theories. More generally, enriched presheaf categories provide a classification and organization for many stable model categories of interest. Changing enrichments along $K$-theory multifunctors provides an important tool for constructing spectral Mackey functors from Mackey functors enriched in algebraic structures such as permutative categories. This work gives a detailed development of diagrams, presheaves, and Mackey functors enriched over closed multicategories. Change of enrichment, including the relevant compositionality, is treated with care. This framework is applied to the homotopy theory of enriched diagram and Mackey functor categories, including equivalences of homotopy theories induced by $K$-theory multifunctors. Particular applications of interest include diagrams and Mackey functors enriched in pointed multicategories, permutative categories, and symmetric spectra.

arXiv.org