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Is a Random Perfect Group Nontrivial? So it’s finals season, and earlier today some of the younger grad students were asking me for...
20th Mar 2026
1

Is a Random Perfect Group Nontrivial?

from Chris Grossack's Blog [alt+shift+b] in science

20th Mar 2026
So it’s finals season, and earlier today some of the younger grad students were asking me for help studying for their topology finals. One of their practice problems was to build a cell complex with one 0-cell, two 1-cells, and two 2-cells which has nontrivial $\pi_1$ but...
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Talk -- Factorization Homology and Quantum Character Stacks Today Yesterday in the Representation Theory Seminar at UCR I gave a talk about Factorization...
20th Feb 2026
2

Talk -- Factorization Homology and Quantum Character Stacks

from Chris Grossack's Blog [alt+shift+b] in science

20th Feb 2026
Today Yesterday in the Representation Theory Seminar at UCR I gave a talk about Factorization Homology and how it lets us compute a “Quantum Character Stack”. This is all based on a great paper, Integrating Quantum Groups Over Surfaces by Ben-Zvi, Brochier, and Jordan, which...
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$F_2 \times F_2$ is Incoherent -- A Polite Spectral Sequence Computation Yesterday I watched my friend Jialin Wang defend her thesis, and as part of her background section...
3rd Sep 2025
39

$F_2 \times F_2$ is Incoherent -- A Polite Spectral Sequence Computation

from Chris Grossack's Blog [alt+shift+b] in science

3rd Sep 2025
Yesterday I watched my friend Jialin Wang defend her thesis, and as part of her background section she mentioned that the group $F_2 \times F_2$ is incoherent in the sense that it has a subgroup that’s finitely generated and not finitely presented. I was curious how one might...
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Free Things Are Complicated (Especially the Sphere Spectrum!) I’ve spent the last week at CT2025, which has just come to a close. It was great getting to see so...
20th Jul 2025
40

Free Things Are Complicated (Especially the Sphere Spectrum!)

from Chris Grossack's Blog [alt+shift+b] in science

20th Jul 2025
I’ve spent the last week at CT2025, which has just come to a close. It was great getting to see so many old friends and meet so many new ones, and every time I go to a CT I’m reminded of just how much category theory there is in the world, as well as just how much I enjoy all...
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An Empty Product of Nonempty Sets A few days ago I saw a cute question on mse asking about a particularly non-intuitive failing of...
4th Jun 2025
43

An Empty Product of Nonempty Sets

from Chris Grossack's Blog [alt+shift+b] in science

4th Jun 2025
A few days ago I saw a cute question on mse asking about a particularly non-intuitive failing of the axiom of choice. I remember when I was an undergrad talking to a friend of mine about various statements equivalent to choice, and being particularly hung up on the same...
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Analytic Combinatorics Redux Earlier today I gave a talk in the graduate student seminar titled “Counting is Hard. Complex...
9th May 2025
37

Analytic Combinatorics Redux

from Chris Grossack's Blog [alt+shift+b] in science

9th May 2025
Earlier today I gave a talk in the graduate student seminar titled “Counting is Hard. Complex Analysis is Easy.” based in part on my recent blog post about analytic combinatorics and based in part on Varilly’s notes on Dirichlet’s Theorem, showing how to count the number of...
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Analytic Combinatorics -- A Worked Example Another day, another blog post that starts with “I was on mse the other day…”. This time, someone...
8th Apr 2025
98

Analytic Combinatorics -- A Worked Example

from Chris Grossack's Blog [alt+shift+b] in science

8th Apr 2025
Another day, another blog post that starts with “I was on mse the other day…”. This time, someone asked an interesting question amounting to “how many unordered rooted ternary trees with $n$ nodes are there, up to isomorphism?”. I’m a sucker for these kinds of combinatorial...
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A Cute Application of the Yoneda Lemma Every few weeks recently I’ve been putting a new fun problem on one of the whiteboards in the first...
17th Mar 2025
60

A Cute Application of the Yoneda Lemma

from Chris Grossack's Blog [alt+shift+b] in science

17th Mar 2025
Every few weeks recently I’ve been putting a new fun problem on one of the whiteboards in the first year office. These are often inspired by something I saw on MSE, and I’m usually choosing problems that force you to understand something fundamental really well. Then I usually...
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Where Do Those Undergraduate Divisibility Problems Come From? Oftentimes in your “intro to proofs” class or your first “discrete math” class or something...
16th Jan 2025
73

Where Do Those Undergraduate Divisibility Problems Come From?

from Chris Grossack's Blog [alt+shift+b] in science

16th Jan 2025
Oftentimes in your “intro to proofs” class or your first “discrete math” class or something similar, you’ll be shown problems of the form “prove that for $n^6 + n^3 + 2n^2 + 2n$ is a multiple of $6$ for every $n$”… But where do these problems come from? And have you ever...
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$\mathsf{B}\text{Diff}(\Sigma)$ Classifies $\Sigma$-bundles I’ve been trying to learn all about topological (quantum) field theories, the cobordism hypothesis,...
21st Dec 2024
120

$\mathsf{B}\text{Diff}(\Sigma)$ Classifies $\Sigma$-bundles

from Chris Grossack's Blog [alt+shift+b] in science

21st Dec 2024
I’ve been trying to learn all about topological (quantum) field theories, the cobordism hypothesis, and how to use $(\infty,n)$-categories. This is all in service of some stuff I’m doing with skein algebras (which are part of a “$3+1$ TQFT” often named after Crane–Yetter, but...
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