Atabey Kaygun
@atabeykaygun.bsky.social
Mathematician. Frankenstein's monster. Incongruous bits and pieces coalesced accidentally instead of a plan. Apparently, also includes batteries.
https://kaygun.github.io
https://kaygun.github.io
Pinned
Atabey Kaygun
@atabeykaygun.bsky.social
· Mar 29
Resmi-tarihsel anlatıya karşı 'hatırlamak' radikal bir eylemdir. Ne olduğunu hatırlayın. Gerçekler mağdurlar için önemlidir, "alternatif gerçekler" ise failler için.
New post: "Higher–Degree Casimir Elements via Invariant Polynomials"
kaygun.github.io/clean/2025-1...
kaygun.github.io/clean/2025-1...
2025-12-01-general-casimir-elementsThe Kitchen Sink and Other Oddities
kaygun.github.io
December 2, 2025 at 1:04 AM
New post: "Higher–Degree Casimir Elements via Invariant Polynomials"
kaygun.github.io/clean/2025-1...
kaygun.github.io/clean/2025-1...
Generating Creative Chess Puzzles arxiv.org/abs/2510.23881
Generating Creative Chess Puzzles
While Generative AI rapidly advances in various domains, generating truly creative, aesthetic, and counter-intuitive outputs remains a challenge. This paper presents an approach to tackle these diffic...
arxiv.org
October 31, 2025 at 4:59 AM
Generating Creative Chess Puzzles arxiv.org/abs/2510.23881
Reposted by Atabey Kaygun
‘Verging on unwatchable’: Guardian writers on their most stressful movies
‘Verging on unwatchable’: Guardian writers on their most stressful movies
With the US release of Rose Byrne’s anxiety-inducing motherhood spiral If I Had Legs I’d Kick You, writers relive their most uncomfortable movie watches
www.theguardian.com
October 12, 2025 at 3:57 AM
‘Verging on unwatchable’: Guardian writers on their most stressful movies
Reposted by Atabey Kaygun
Reposted by Atabey Kaygun
"We sat down with Phil Wadler, one of the most influential folks in the Haskell community, functional programming, and programming languages, responsible for type classes, monads, and much more. We take a stroll down memory lane, starting from Haskell’s inception."
haskell.foundation/podcast/70/
haskell.foundation/podcast/70/
September 16, 2025 at 9:24 PM
"We sat down with Phil Wadler, one of the most influential folks in the Haskell community, functional programming, and programming languages, responsible for type classes, monads, and much more. We take a stroll down memory lane, starting from Haskell’s inception."
haskell.foundation/podcast/70/
haskell.foundation/podcast/70/
New post: "Strongly Depth Balanced Binary Trees" kaygun.github.io/clean/2025-0...
2025-09-10-strongly-balancedThe Kitchen Sink and Other Oddities
kaygun.github.io
September 10, 2025 at 7:17 PM
New post: "Strongly Depth Balanced Binary Trees" kaygun.github.io/clean/2025-0...
Reposted by Atabey Kaygun
Jiaming Luo
On the Log Hodge Theory of Toroidal Varieties and a Partial Proof of the Absolute Hodge Conjecture
https://arxiv.org/abs/2509.07672
On the Log Hodge Theory of Toroidal Varieties and a Partial Proof of the Absolute Hodge Conjecture
https://arxiv.org/abs/2509.07672
September 10, 2025 at 4:18 AM
Jiaming Luo
On the Log Hodge Theory of Toroidal Varieties and a Partial Proof of the Absolute Hodge Conjecture
https://arxiv.org/abs/2509.07672
On the Log Hodge Theory of Toroidal Varieties and a Partial Proof of the Absolute Hodge Conjecture
https://arxiv.org/abs/2509.07672
Reposted by Atabey Kaygun
There's a big mathematics and engineering story going on under the radar in Houston with some former Chevron engineers thinking big about category theory. Not academia. Hard engineering. Really interesting work at Holon Labs Foundation.
open.substack.com/pub/estebana...
open.substack.com/pub/estebana...
Category Theory is Being Co-opted
How Our World Shapes the Meaning of Mathematics While Mathematics Has the Potential to Reshape our World
open.substack.com
September 7, 2025 at 10:22 PM
There's a big mathematics and engineering story going on under the radar in Houston with some former Chevron engineers thinking big about category theory. Not academia. Hard engineering. Really interesting work at Holon Labs Foundation.
open.substack.com/pub/estebana...
open.substack.com/pub/estebana...
Reposted by Atabey Kaygun
New video about a piece by the modern artist Sol LeWitt, and the group theory behind it.
youtu.be/_BrFKp-U8GI
youtu.be/_BrFKp-U8GI
September 7, 2025 at 12:39 PM
New video about a piece by the modern artist Sol LeWitt, and the group theory behind it.
youtu.be/_BrFKp-U8GI
youtu.be/_BrFKp-U8GI
New post: "Böhm Trees and a Lazy λμ-Calculus" kaygun.github.io/clean/2025-0..., and the accompanying github repo for the implementation: github.com/kaygun/LazyL...
August 4, 2025 at 9:41 PM
New post: "Böhm Trees and a Lazy λμ-Calculus" kaygun.github.io/clean/2025-0..., and the accompanying github repo for the implementation: github.com/kaygun/LazyL...
New post: "A Strange Path to λ: Magmas and Catamorphisms" kaygun.github.io/clean/2025-0...
2025-07-30-magmas-and-catamorphismsThe Kitchen Sink and Other Oddities
kaygun.github.io
July 30, 2025 at 3:45 PM
New post: "A Strange Path to λ: Magmas and Catamorphisms" kaygun.github.io/clean/2025-0...
Reposted by Atabey Kaygun
The devastating funding cuts to mathematics research in the US will cut-short the careers of a generation of mathematicians. It really is disgraceful, and unbelievably shortsighted. #MathSky
www.scientificamerican.com/article/can-...
www.scientificamerican.com/article/can-...
Math Is Quietly in Crisis over NSF Funding Cuts
A 72 percent reduction in federal funding is devastating to math research. The American Mathematical Society is offering $1 million in backstop grants—but it’s likely not enough
www.scientificamerican.com
July 25, 2025 at 7:20 AM
The devastating funding cuts to mathematics research in the US will cut-short the careers of a generation of mathematicians. It really is disgraceful, and unbelievably shortsighted. #MathSky
www.scientificamerican.com/article/can-...
www.scientificamerican.com/article/can-...
Reposted by Atabey Kaygun
I've got a new paper that I'm proud of: arxiv.org/abs/2507.17936. While teaching discrete math, we got some results about the topology of finite subsets, finite tuples, and compact subsets of a given space. I was teaching combinatorics, so I wondered about ordered compact subsets. This is the result
An Adaptation of the Vietoris Topology for Ordered Compact Sets
We introduce a natural topology on powers of a space that is inspired by the Vietoris topology on compact subsets. We then place this topology in context with other product topologies; specifically, w...
arxiv.org
July 25, 2025 at 11:46 AM
I've got a new paper that I'm proud of: arxiv.org/abs/2507.17936. While teaching discrete math, we got some results about the topology of finite subsets, finite tuples, and compact subsets of a given space. I was teaching combinatorics, so I wondered about ordered compact subsets. This is the result
Reposted by Atabey Kaygun
Theorem of the day: Löb's theorem!
Löb proved that in Peano arithmetic, if you can prove that the proof of a proposition implies the proposition itself, then you can prove the proposition 🤪
So when I have a statement P, if I can prove the provability of P implies the truth of P, then I can prove P
Löb proved that in Peano arithmetic, if you can prove that the proof of a proposition implies the proposition itself, then you can prove the proposition 🤪
So when I have a statement P, if I can prove the provability of P implies the truth of P, then I can prove P
July 25, 2025 at 3:40 PM
Theorem of the day: Löb's theorem!
Löb proved that in Peano arithmetic, if you can prove that the proof of a proposition implies the proposition itself, then you can prove the proposition 🤪
So when I have a statement P, if I can prove the provability of P implies the truth of P, then I can prove P
Löb proved that in Peano arithmetic, if you can prove that the proof of a proposition implies the proposition itself, then you can prove the proposition 🤪
So when I have a statement P, if I can prove the provability of P implies the truth of P, then I can prove P
Reposted by Atabey Kaygun
I hope you can join me at this conference 24-26 October at University of Minnesota celebrating the work and 60th birthday of my PhD advisor, Igor Kriz!
cse.umn.edu/math/events/... 🧮
cse.umn.edu/math/events/... 🧮
Equivariant, Motivic, and Physical Topology in the Midwest
This three-day conference celebrates the 60th birthday and influential career of Igor Kriz, whose groundbreaking contributions have shaped modern perspectives in homotopy theory and its interactions w...
cse.umn.edu
July 26, 2025 at 12:22 AM
I hope you can join me at this conference 24-26 October at University of Minnesota celebrating the work and 60th birthday of my PhD advisor, Igor Kriz!
cse.umn.edu/math/events/... 🧮
cse.umn.edu/math/events/... 🧮
Reposted by Atabey Kaygun
It turns out the convention $B_{1}=+1/2$ is the "correct" definition for Bernoulli numbers...
luschny.de/math/zeta/Th...
luschny.de/math/zeta/Th...
The Bernoulli Manifesto
A definition of the Bernoulli numbers based on the Bernoulli function as introduced by Helmut Hasse.
luschny.de
July 26, 2025 at 1:18 AM
It turns out the convention $B_{1}=+1/2$ is the "correct" definition for Bernoulli numbers...
luschny.de/math/zeta/Th...
luschny.de/math/zeta/Th...
Reposted by Atabey Kaygun
arxiv.org/abs/2507.18230
/Rowmotion and Echelonmotion/
Colin Defant, Yuhan Jiang, Rene Marczinzik, Adrien Segovia, David E Speyer, Hugh Thomas, Nathan Williams
/Rowmotion and Echelonmotion/
Colin Defant, Yuhan Jiang, Rene Marczinzik, Adrien Segovia, David E Speyer, Hugh Thomas, Nathan Williams
Rowmotion and Echelonmotion
Given a linear extension $σ$ of a finite poset $R$, we consider the permutation matrix indexing the Schubert cell containing the Cartan matrix of $R$ with respect to $σ$. This yields a bijection $\mat...
arxiv.org
July 25, 2025 at 4:35 AM
arxiv.org/abs/2507.18230
/Rowmotion and Echelonmotion/
Colin Defant, Yuhan Jiang, Rene Marczinzik, Adrien Segovia, David E Speyer, Hugh Thomas, Nathan Williams
/Rowmotion and Echelonmotion/
Colin Defant, Yuhan Jiang, Rene Marczinzik, Adrien Segovia, David E Speyer, Hugh Thomas, Nathan Williams
Reposted by Atabey Kaygun
arxiv.org/abs/2507.15060
/Morse matchings and Khovanov homology of 4-strand torus links/
Tuomas Kelomäki
/Morse matchings and Khovanov homology of 4-strand torus links/
Tuomas Kelomäki
Morse matchings and Khovanov homology of 4-strand torus links
Given a link or a tangle diagram, we define algorithmic Morse theoretic simplifications on their Khovanov homology. In contrast to Bar-Natan's scanning algorithm, the cancellations are postponed until...
arxiv.org
July 22, 2025 at 5:29 AM
arxiv.org/abs/2507.15060
/Morse matchings and Khovanov homology of 4-strand torus links/
Tuomas Kelomäki
/Morse matchings and Khovanov homology of 4-strand torus links/
Tuomas Kelomäki
Reposted by Atabey Kaygun
The first-known observations of matter–antimatter asymmetry in a decaying composite subatomic particle that belongs to the baryon class are reported from the LHCb experiment located at the Large Hadron Collider at CERN in a paper published in Nature. go.nature.com/46eNqpn ⚛️ 🧪
July 17, 2025 at 7:27 PM
The first-known observations of matter–antimatter asymmetry in a decaying composite subatomic particle that belongs to the baryon class are reported from the LHCb experiment located at the Large Hadron Collider at CERN in a paper published in Nature. go.nature.com/46eNqpn ⚛️ 🧪
Reposted by Atabey Kaygun
A simple interactive program for visualizing conformal self-maps of a sphere, or in fancy terms, the action of PSL(2,C) on the complex projective line. Read more:
www.diffgeom.com/blogs/free-o...
#MathSky #ITeachmath
www.diffgeom.com/blogs/free-o...
#MathSky #ITeachmath
July 6, 2025 at 2:55 PM
A simple interactive program for visualizing conformal self-maps of a sphere, or in fancy terms, the action of PSL(2,C) on the complex projective line. Read more:
www.diffgeom.com/blogs/free-o...
#MathSky #ITeachmath
www.diffgeom.com/blogs/free-o...
#MathSky #ITeachmath
Reposted by Atabey Kaygun
arxiv.org/abs/2506.21064
/Introduction to the Cohomology of the Flag Variety/
Sara C. Billey, Yibo Gao, Brendan Pawlowski (192 pages)
/Introduction to the Cohomology of the Flag Variety/
Sara C. Billey, Yibo Gao, Brendan Pawlowski (192 pages)
Introduction to the Cohomology of the Flag Variety
One hundred years ago, Hilbert gave a list of important open problems in mathematics. His 15th problem asked for the development of a rigorous calculus explaining Schubert's enumerative results for in...
arxiv.org
June 27, 2025 at 6:28 AM
arxiv.org/abs/2506.21064
/Introduction to the Cohomology of the Flag Variety/
Sara C. Billey, Yibo Gao, Brendan Pawlowski (192 pages)
/Introduction to the Cohomology of the Flag Variety/
Sara C. Billey, Yibo Gao, Brendan Pawlowski (192 pages)
I implemented a Lambda-Mu interpreter in #clojure: github.com/kaygun/lambd...
GitHub - kaygun/lambda-mu: A lambda-mu calculus implemented in clojure.
A lambda-mu calculus implemented in clojure. Contribute to kaygun/lambda-mu development by creating an account on GitHub.
github.com
June 20, 2025 at 9:18 PM
I implemented a Lambda-Mu interpreter in #clojure: github.com/kaygun/lambd...