cahilfil https://cahilfil.xyz/home/ home /home/ cahilfil's playground false hi 🌺 this is cahilfil. welcome to my playground. cahilfil 2025 3 10 https://cahilfil.xyz/now/ now /now/ top of my mind although i know enough about complexity theory to know that i like it, fortunately there is a lot more to learn. i'm currently exploring areas such as pseudorandomness, catalytic computing, meta-complexity etc. more concretely, i'm reading: bipartite matching is in catalytic logspace np-hardness of learning programs and partial mcsp on one-way functions and kolmogorov complexity when connectivity is hard, random walks are easy with non-determinism regularity, boosting, and efficiently simulating every high-entropy distribution watching: frontiers in complexity theory meta-complexity boot camp taking courses:algebra listening to: chassol https://cahilfil.xyz/notes/ notes /notes/ notes to navigate through all the notes (or trees in forester lingo), you can press Ctrl+K. i'll be adding some starting points here as the notes start taking shape. https://cahilfil.xyz/starting-points/ starting-points /starting-points/ starting points some notes i'm currently working on: expander codes, some obstacles toward moser-tardos in catalytic logspace. https://cahilfil.xyz/questions/ questions /questions/ questions 2026 2 4 https://cahilfil.xyz/QVQGF/ QVQGF /QVQGF/ how can we bound the list size for XOR codes beyond the johnson bound? question question-QVQGF status: open time: 14h 54m https://cahilfil.xyz/related-question-QVQGF/related-question-QVQGF/related-question-QVQGF/related to-dos 2026225https://cahilfil.xyz/TCPK/TCPK/TCPK/read new proofs of the green-tao-ziegler dense model theorem: an expositionto-dotodo-TCPK status: incomplete time: 0m 2026225https://cahilfil.xyz/U08N/U08N/U08N/read regularity, boosting, and efficiently simulating every high-entropy distributionto-dotodo-U08N status: incomplete time: 2h 42m 2026121https://cahilfil.xyz/NRO8/NRO8/NRO8/read chapter 12 of expander graphs and their applicationsto-dotodo-NRO8 status: incomplete time: 3h 31m 2026 1 20 https://cahilfil.xyz/QP4OX/ QP4OX /QP4OX/ how does a constructive proof of the general lovasz local lemma look like in the catalytic setting? question question-QP4OX status: open time: 2h 30m https://cahilfil.xyz/related-question-QP4OX/related-question-QP4OX/related-question-QP4OX/related to-dos 2026119https://cahilfil.xyz/OXND/OXND/OXND/read https://timroughgarden.org/s14/l/l8.pdfto-dotodo-OXND status: incomplete time: 1h 20m 2026119https://cahilfil.xyz/GDOP/GDOP/GDOP/read a constructive proof of the general lovasz local lemmato-dotodo-GDOP status: incomplete time: 0m depends on:2026119https://cahilfil.xyz/OXND/OXND/OXND/read https://timroughgarden.org/s14/l/l8.pdfto-dotodo-OXND status: incomplete time: 1h 20m https://cahilfil.xyz/planning/ planning /planning/ planning the plan is simple: every day, i take some stuff from the backlog and make progress. easy. https://cahilfil.xyz/logs/ logs /logs/ logs here is a directory of my research logs. https://cahilfil.xyz/2026/ 2026 /2026/ https://cahilfil.xyz/2026-01/ 2026-01 /2026-01/ https://cahilfil.xyz/2026-01-06/ 2026-01-06 /2026-01-06/ january 6, 2026 log today was a light day. after last year's unsuccessful attempt, i tried to revamp cahilfil's playground for ~3 hours. new forester release definitely didn't help. i am still a believer (in the cause of doing research in public). i don't enjoy the dance of excuses, but one of the reasons it didn't work last year was that it introduced too much friction on top of the actual work i was doing. now that my coursework load has decreased and that i am more familiar with both my research and forester, and most importantly now that i have a working github action to deploy this website, i feel it's worth giving a second shot. if it doesn't work this year either, i'm quite sure it would be due to my incompetence, so don't get discouraged to create your own playgrounds. https://cahilfil.xyz/2026-01-07/ 2026-01-07 /2026-01-07/ january 7, 2026 log same as yesterday. worked a couple hours on cahilfil's playground. https://cahilfil.xyz/2026-01-13/ 2026-01-13 /2026-01-13/ january 13, 2026 log finish first chapter of analysis of boolean functions -- 1h 26m https://cahilfil.xyz/2026-01-14/ 2026-01-14 /2026-01-14/ january 14, 2026 log read a dense model theorem for the boolean slice -- 1h 24m https://cahilfil.xyz/2026-01-15/ 2026-01-15 /2026-01-15/ january 15, 2026 log i talked with chatty for ~2 hours to "make progress" over some research questions i've been thinking about catalytic space, namely whether it's possible to characterize the power of catalytic space through some sort of interactive proof system. https://cahilfil.xyz/2026-01-16/ 2026-01-16 /2026-01-16/ january 16, 2026 log same as yesterday. https://cahilfil.xyz/2026-01-17/ 2026-01-17 /2026-01-17/ january 17, 2026 log again, same thing as january 15, 2026. https://cahilfil.xyz/2026-01-18/ 2026-01-18 /2026-01-18/ january 18, 2026 log inspired by bipartite matching is in catalytic logspace etc., i wanted to explore some other techniques that can be potentially derandomized in the catalytic space setting, chatty suggested i should look at a constructive proof of the general lovasz local lemma. at a first glance, it seemed promising, so i spent a couple hours on understanding the algorithm for k-SAT and trying to design a CL algorithm. https://cahilfil.xyz/2026-01-19/ 2026-01-19 /2026-01-19/ january 19, 2026 log how does a constructive proof of the general lovasz local lemma look like in the catalytic setting? -- 1h 30m read https://timroughgarden.org/s14/l/l8.pdf -- 1h 20m read a dense model theorem for the boolean slice -- 22m meeting -- 1h 00m https://cahilfil.xyz/2026-01-20/ 2026-01-20 /2026-01-20/ january 20, 2026 log how does a constructive proof of the general lovasz local lemma look like in the catalytic setting? -- 1h 00m read chapter 12 of expander graphs and their applications -- 16m https://cahilfil.xyz/2026-01-21/ 2026-01-21 /2026-01-21/ january 21, 2026 log read chapter 12 of expander graphs and their applications -- 3h 15m meeting -- 1h 30m https://cahilfil.xyz/2026-01-23/ 2026-01-23 /2026-01-23/ january 23, 2026 log how can we bound the list size for XOR codes beyond the johnson bound? -- 3h 00m meeting -- 1h 00m https://cahilfil.xyz/2026-01-25/ 2026-01-25 /2026-01-25/ january 25, 2026 log how can we bound the list size for XOR codes beyond the johnson bound? -- 1h 00m https://cahilfil.xyz/2026-01-26/ 2026-01-26 /2026-01-26/ january 26, 2026 log how can we bound the list size for XOR codes beyond the johnson bound? -- 2h 00m https://cahilfil.xyz/2026-01-27/ 2026-01-27 /2026-01-27/ january 27, 2026 log how can we bound the list size for XOR codes beyond the johnson bound? -- 1h 00m https://cahilfil.xyz/2026-01-28/ 2026-01-28 /2026-01-28/ january 28, 2026 log how can we bound the list size for XOR codes beyond the johnson bound? -- 3h 00m meeting -- 1h 00m https://cahilfil.xyz/2026-02/ 2026-02 /2026-02/ https://cahilfil.xyz/2026-02-02/ 2026-02-02 /2026-02-02/ february 2, 2026 log how can we bound the list size for XOR codes beyond the johnson bound? -- 1h 00m meeting -- 2h 00m https://cahilfil.xyz/2026-02-03/ 2026-02-03 /2026-02-03/ february 3, 2026 log read chapter 2 of analysis of boolean functions -- 30m https://cahilfil.xyz/2026-02-26/ 2026-02-26 /2026-02-26/ february 26, 2026 log read regularity, boosting, and efficiently simulating every high-entropy distribution -- 2h 42m https://cahilfil.xyz/2026-03/ 2026-03 /2026-03/ https://cahilfil.xyz/2026-03-09/ 2026-03-09 /2026-03-09/ march 9, 2026 log how can we bound the list size for XOR codes beyond the johnson bound? -- 3m https://cahilfil.xyz/2026-03-10/ 2026-03-10 /2026-03-10/ march 10, 2026 log how can we bound the list size for XOR codes beyond the johnson bound? -- 2h 51m https://cahilfil.xyz/2026-03-11/ 2026-03-11 /2026-03-11/ march 11, 2026 log how can we bound the list size for XOR codes beyond the johnson bound? -- 1h 00m https://cahilfil.xyz/backlog/ backlog /backlog/ backlog 2026 2 25 https://cahilfil.xyz/TCPK/ TCPK /TCPK/ read new proofs of the green-tao-ziegler dense model theorem: an exposition to-do todo-TCPK status: incomplete time: 0m 2026 2 25 https://cahilfil.xyz/U08N/ U08N /U08N/ read regularity, boosting, and efficiently simulating every high-entropy distribution to-do todo-U08N status: incomplete time: 2h 42m 2026 2 4 https://cahilfil.xyz/SX9T/ SX9T /SX9T/ read chapter 2 of analysis of boolean functions to-do todo-SX9T status: incomplete time: 30m 2026 1 21 https://cahilfil.xyz/NRO8/ NRO8 /NRO8/ read chapter 12 of expander graphs and their applications to-do todo-NRO8 status: incomplete time: 3h 31m 2026 1 19 https://cahilfil.xyz/XV3G/ XV3G /XV3G/ read derandomizing isolation in catalytic logspace to-do todo-XV3G status: incomplete time: 0m 2026 1 19 https://cahilfil.xyz/Z5AG/ Z5AG /Z5AG/ read the structure of in-place space-bounded computation to-do todo-Z5AG status: incomplete time: 0m 2026 1 19 https://cahilfil.xyz/OXND/ OXND /OXND/ read https://timroughgarden.org/s14/l/l8.pdf to-do todo-OXND status: incomplete time: 1h 20m 2026 1 19 https://cahilfil.xyz/GDOP/ GDOP /GDOP/ read a constructive proof of the general lovasz local lemma to-do todo-GDOP status: incomplete time: 0m depends on:2026119https://cahilfil.xyz/OXND/OXND/OXND/read https://timroughgarden.org/s14/l/l8.pdfto-dotodo-OXND status: incomplete time: 1h 20m 2026 1 13 https://cahilfil.xyz/N9PC/ N9PC /N9PC/ read part 1 of higher-order fourier analysis and applications to-do todo-N9PC status: incomplete time: 0m 2026 1 7 https://cahilfil.xyz/FK4Y/ FK4Y /FK4Y/ read a dense model theorem for the boolean slice to-do todo-FK4Y status: incomplete time: 1h 46m depends on:202617https://cahilfil.xyz/3K30/3K30/3K30/finish first chapter of analysis of boolean functionsto-dotodo-3K30 status: complete time: 1h 26m https://cahilfil.xyz/completed/ completed /completed/ completed 2026 1 7 https://cahilfil.xyz/3K30/ 3K30 /3K30/ finish first chapter of analysis of boolean functions to-do todo-3K30 status: complete time: 1h 26m References Context Backlinks https://cahilfil.xyz/2026-01-06/ 2026-01-06 /2026-01-06/ january 6, 2026 log today was a light day. after last year's unsuccessful attempt, i tried to revamp cahilfil's playground for ~3 hours. new forester release definitely didn't help. i am still a believer (in the cause of doing research in public). i don't enjoy the dance of excuses, but one of the reasons it didn't work last year was that it introduced too much friction on top of the actual work i was doing. now that my coursework load has decreased and that i am more familiar with both my research and forester, and most importantly now that i have a working github action to deploy this website, i feel it's worth giving a second shot. if it doesn't work this year either, i'm quite sure it would be due to my incompetence, so don't get discouraged to create your own playgrounds. https://cahilfil.xyz/2026-01-07/ 2026-01-07 /2026-01-07/ january 7, 2026 log same as yesterday. worked a couple hours on cahilfil's playground. Related https://cahilfil.xyz/cahilfil/ cahilfil /cahilfil/ cahilfil person https://www.cahilfil.xyz/ i'm a phd student at uc riverside working under silas richelson. i'm interested in complexity theory, and tcs in general. you can reach me at yunus.aydin@protonmail.com. and here is my PGP public key a laundry list of who i am: my actual name is yunus aydin. when translated literally from turkish, it would be "dolphin enlightened", so i found it fitting to pick the alias cahilfil, which means the ignorant elephant. back in undergrad, my initial exposure to complexity theory was through erik demaine's algorithmic lower bounds: fun with hardness proofs, which lead to my undergraduate thesis under the supervision of standa živný. once upon a time, i made a puzzle game called r v r s e. i'm into running, weightlifting, bouldering, film photography, and competitive programming. i'm not good at any of the activities above. some stats: my 5k pr is 24:21. my half pr is 02:02:00. my highest codeforces rating was 2003. i recently got back into it and planning to beat that by the end of 2025 2026. i can squat ~1.5x my bodyweight. here are some photos that i took. my favorite tv show is it's always sunny in philadelphia. my favorite band is the bad plus. in a previous life, i was a software engineer for a social networking start-up that pivoted to become a decentralized cryptocurrency exchange. i've previously lived in istanbul, oxford, london, miami, and nyc. i'm currently at riverside, and flirting with the idea of moving to los angeles. https://cahilfil.xyz/playground/ playground /playground/ playground this website is a forest made by forester. it's close to what niklas luhmann called a zettelkasten, or andy matuschak called evergreen notes. although there are differences between these objects/methods, i'm currently not too hung up on all the nuances, basically since "who has time for that?" but also because "premature optimization is the root of all evil" as knuth put it. my motivation to create these notes is essentially to become more active in the process of learning. in my experience, especially with mathematics, you kind of need to reinvent the wheel to be able to ride it. the decision to make it public is definitely more controversial, since the lack of privacy might influence what or how i write, which might potentially be less productive. however, this very tension is actually what made me decide to make it public. most of my life, my self-worth was intimately linked to being intelligent, thus the worst sin has been to be perceived as stupid, which is also quite counter-productive. i believe learning to overcome this fear will make me a better researcher (and hopefully more at peace with who i am). and i picked the word playground to refer to these notes because i'm essentially intending to play: to engage actively (and hopefully pleasurably) in the open-ended platonic word of complexity-theoretic constructs. 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