iiinova — where your digital self keeps evolving

Gülce @gkardesd.bsky.social · 30/09/2026

I wrote especially* because they increase the production pace in ways the community is not used to; otherwise we should hold all mathematics to the same standard. I am not a Luddite: I merely appreciate that we can't carry 10,000 local steps to optimize proofs so we seek invariants that reveal more.

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Gülce @gkardesd.bsky.social · 30/09/2026

One reason machines can solve some problems humans cannot: we have the gift of a short attention span, which forces us to come up with good proofs. Recent discussion has focused on good expositions in math but I think it misses a point: a good exposition of a bad proof is still a bad proof.

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Gülce @gkardesd.bsky.social · 30/09/2026

Whether or not one uses machines and especially* if one does one owes the community not just a good exposition but a good proof. Otherwise one encourages proofs no human expert would naturally produce: locally optimized combinatorial rabbit holes which are technically successful, conceptually opaque

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Gülce @gkardesd.bsky.social · 30/09/2026

I woke up to learn that a problem I really cared about & worked on now has a chatgpt-proof, and the proof is unsightly, full of combinatorial optimizations that teach me nothing new about the structure of the problem, regardless of the human author’s fantastic exposition. I was reminded of this poem

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Gülce @gkardesd.bsky.social · 30/09/2026

Also, I learned recently that Or Meir gave a wonderfully accessible talk at Cambridge on a recent work of mine with Ben Rossman on chopping games (arxiv.org/abs/2609.01759), and brought together a few strands of top-down lower bounds.

youtube.com

Prof. Or Meir | On Top-Down Lower Bound Techniques for Constant-Depth Circuits

YouTube video by INI Seminar Room 1

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Gülce @gkardesd.bsky.social · 30/09/2026

and I love when a book ushers me into autumn; this year it’s Steinbeck’s “Journal of a Novel“, composed of letters he wrote to his editor-friend almost every morning as an exercise in self-discipline – or, in his gentler words, “getting in shape to pitch a good game.” Winsome book; do read.

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Gülce @gkardesd.bsky.social · 30/09/2026

officially entered the autumn: in the back is a photo of dear Cormac (McCarthy), whom I miss talking to in particular at the beginning of every autumn; a goldfish plant; Gaddis' and other helpful books nearby; the most well-scented candle I have ever found.

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Gülce @gkardesd.bsky.social · 30/08/2026

Sean, thank you! Looking forward to talking with you soon (desert or otherwise) for a proper catch-up on all things work. And Zizek & Carroll is easily the news of the day.

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Gülce @gkardesd.bsky.social · 29/08/2026

joint work with wonderful collaborators @joshuagrochow.bsky.social and Michael Levet!

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Gülce @gkardesd.bsky.social · 29/08/2026

New on the low-depth complexity of Group Isomorphism: the first nontrivial circuit lower bounds and quasipoly-size depth-2 1/2 upper bounds -- departing from the generator-enumerator approach underlying prior low-depth work: instead we use composition series, group extensions, & short presentations.

arxiv.org

Group Isomorphism and the Polylogarithmic-Time Hierarchy: Depth-2$\frac{1}{2}$ Circuits and Lower Bounds

In this paper, we investigate the low-depth circuit complexity of Group Isomorphism in the multiplication (Cayley) table model. We prove the first circuit lower bounds for Group Isomorphism: namely, w...

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