Emily Riehl
@emilyriehl
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category theorist, working mathematician
Joined June 2011
I am proud today to join the editorial board of a new diamond open access journal in logic: . Zeitschrift für Mathematische Logik.und Grundlagen der Mathematik. The website includes an open letter from the editorial board with the following text:.
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In perhaps my most difficult writing challenge to date, I attempted to give a non-technical tour of how category theory and ∞-category provide a bird's-eye view of mathematics, to appear in the October issue of @sciam:.
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With the help of a wonderful team @WIRED, I recently had the chance to try to explain how mathematicians think about infinity at five levels of increasing complexity. You can see our conversations at the link below:.
To infinity and. beyond? While the concept of infinity may seem mysterious, mathematicians have developed processes to reason the strange properties of infinity. Mathematician @emilyriehl has been challenged to explain infinity in 5 levels; from child to expert.
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In May of 2019, at the end the 2nd year of my PhD, I set a 10 year goal to spend 10^4 hours thinking about categorical homotopy theory. By my imperfect accounting, I made it just in time to celebrate the very welcome news that I'll get to stay @JHUmath for the foreseeable future.
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Here's a vivid illustration of how small a role arithmetic plays in mathematics. I've been using #LaTeX for 18 years and just today realized that I have no clue what LaTeX code produces the division symbol "÷".
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Mathematicians wear chalk on top of everything: hands, pants, face, keyboard.
Today I was asked what scientist wear. The answer: Filth. Field-specific filth. Geologists and paleontologists wear dirt on top of denim.Biologists wear varied ichors on top of white cotton coats.Physicists wear coffee on top of khaki slacks. Tag in with your field and filth.
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We - @carloangiuli, @dan2christensen, @EscardoMartin, Chris Kapulkin, @admitscut, @EgbertRijke, and myself - are delighted to announce the HoTTEST Summer School, which will take place online everywhere in the world during the months of July and August 2022.
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By popular demand, I'm planning to repeat a talk "∞-category theory for undergraduates" originally prepared for the Berkeley Logic Colloquium at a time more friendly to other parts of the world.
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By popular demand, I'm planning to repeat a talk "∞-category theory for undergraduates" originally prepared for the Berkeley Logic Colloquium on Friday May 8 from 2:30-4pm UTC. Slides are available here:.
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I have no idea who this is but this is great:.
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I'm honored to have been asked by @writesRCrowell to answer a few questions about higher category theory for @QuantaMagazine:.
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I always choose "Dr" when filling out forms because I'd prefer not to highlight my marital status every time I'm asked for my name.
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Yesterday I finally had occasion to use one of those @duolingo phrases that had always felt totally impractical: with a botched version of "Soy mujer" the bathroom attendant understood that I was where I'd intended to be. #HappyPrideMonth.
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It's wonderful that this is available free online.
We are happy to share that “Topology: A Categorical Approach” is now available! It's a graduate-level textbook on basic topology from the perspective of category theory, and is also available free online via MIT Press:
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It's nice for me and for @doverpubs when folks buy the book, but I'd much much rather have folks read the book (or parts of it). So it's a high priority of mine to ensure that it will always be freely available.
A few weeks ago I downloaded the pdf of this book and read through the first chapter. Loved it, so I decided to buy a hard copy that just came in the mail :). Don’t know if I would have bought it without first having free access, so big thanks to @emilyriehl for that!
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@plt_abbie @sarah_zrf @alittledelta Happy to reply to anyone but it helps if you @ me. Y'all are way too fast and I'm perpetually behind. But anyway happy to confirm. For the second edition I'll be sure to tell Dover that my target audience is the furries on math twitter 😽.
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In her new book "x+y: a mathematician's manifesto for rethinking gender" published by @basicbooks, @DrEugeniaCheng divulges, with my blessing, a personal confession I made to her, and now I feel like I should elaborate.
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This just in: Tom Leinster's terrific book "Basic Category Theory" has hit the arXiv #CategoryTheory.
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At a publisher's request, I'm forced to cut my bibliography from 48 citations down to 20. Apologizing to everyone in advance.
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For the record, I always do this when teaching abstract algebra bc literally every other theorem we cover is due to a man. Everyone should get to have heroes (and she's absolute one of mine).
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#AGITTOC statement of values from Ravi Vakil on the importance of doing the exercises: a hard fought (possibly incomplete) solution > the "right" solution. Corollary: if you can't solve the exercise don't look it up. Instead be content to let it continue to bother you.
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I'm happy to report I've finally accomplished my writing goal for the summer - only eight weeks late!. They're still very rough, so use at your own risk, but the first draft of these appendices are finally in place (comments & suggestions very welcome):.
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Today at 2pm EDT/6pm UTC I'll be giving a tutorial talk entitled "The Yoneda lemma in the category of matrices" as part of Applied Category Theory 2020 Tutorial Day: . Spoilers follow.
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IMO the best mathOVERFLOW answer ever:.
"The product of mathematics is clarity and understanding. Not theorems, by themselves."
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It was really kind of @DrDeidraCrews to take the time to come surprise me this morning. I'm hugely honored to be recognized alongside her.
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Do you know that the free group on 26 letters modulo homophones in English is trivial? (Cf "Homophonic quotients of free groups.").
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20 years ago today I aspirationally signed a poster saying I was "out and proud" at a table in front of the science center staffed by my @RadcliffeRugby crush. The following day, I started coming out by telling two friends from my home town. Happy #NationalComingOutDay to all🏳️🌈🏳️⚧️.
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This week I'll be giving a 3-lecture series @uclamath to be live-streamed on Zoom and recorded for posterity. The lectures will take place at 3pm PDT (=10pm UTC). More details can be found here:.
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Me too :(.
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I'm super excited to share a billing with @accommodatingly next week in "The Multiplicity Turn: Theories of Identity from Poetry to Mathematics", moderated by @JSEllenberg and Marisa Galvez.
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I've heard that a number of you were sad to miss the talk, which wasn't recorded. If there's sufficient interest, I'd be happy to give it again, perhaps over a somewhat longer period (say 90 minutes), so the Q&A could happen along the way.
Hi @emilyriehl I'm bummed I have to miss your talk today; it would be awesome if you can ask them to record it! I understand if that's not possible, but it'd be wonderful to get to watch.
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Today @ 3:45-4:20pm in @DrEugeniaCheng's "Category Theory for All" session @maanow #MAAthFest we'll prove a x (b + c) = a x b + a x c via a roundabout method that takes us on a tour through several deep ideas including categorification, universal properties, and the Yoneda lemma.
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Communicating Mathematics is a 4-day workshop for mathematicians at all career stages who are interested in exploring how we share our research and interests with fellow mathematicians, students, and the public:.
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Hi 👋.
Meet @emilyriehl—assistant professor @JHUmath, category theorist #HomotopyTheory #WomenInSTEM #GoHop
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This year I'll be celebrating International Women in Mathematics day at the wonderful @Perimeter Institute making the point that one of my favorite mathematics papers could have been even better if the authors had considered women's perspectives in their investigations.
Date night, anyone? This Wednesday, @JohnsHopkins mathematician @emilyriehl delves into the stable marriage problem. What could be more romantic?
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"It is not the job of underrepresented minorities to educate others on systemic issues we did not create. Just as everyone in this room is capable of taking an abstract mathematics research paper and work to understand that, they too can learn from literature on these topics.”.
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So what's the point? As @DrEugeniaCheng notes, there are myriad ways that the mathematics profession needs to improve to become more inclusive. But I also believe that there are decisive contributions each of us can make as individuals to change the rooms we find ourselves in.
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Do logicians have a name for the "currying" tautology: that for propositions A, B, and C, if A and B implies C, then A implies that B implies C?. ((A x B) → C) → (A → (B →C)).
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Stumbled across this gem by @johncarlosbaez in @NautilusMag, or "how a math professor learned to stop worrying and love algebraic geometry":.
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Thinking about replacing my laptop (2015 MacBook air) with a Dell XPS running Ubuntu. Relevant computer skills: I can navigate directories from the terminal and commit to and pull from my git repositories. Merging is a challenge bc I cannot exit vim. Am I going to regret this?.
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“all of what goes on between humans appears in the mathematics community, perhaps toned down quite a bit, but it’s not a world of pure brains, people behaving rationally & unemotionally.” - A Groundbreaking Mathematician on the Gender Politics of Her Field
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Thanks to @Bibli_CIRM for making these lectures available to all:.
🎬 Logic and higher structures.Mini course : Emily Riehl (Johns Hopkins University) On the ∞-topos semantics of homotopy type theory.#math #course #conference #video @_CIRM .
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I'm hiring a postdoctoral fellow in homotopy type theory! More details can be found at the link below and please feel free to reach out with questions:.
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Later this week, I'll be giving a talk "∞-category theory for undergraduates" in the Berkeley Logic Colloquium:. (H/t to @PraphullaK who suggested I advertise it here.).
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But I do feel like my performative question-asking changes something imperceptible in the atmosphere of the mathematical spaces I inhabit. I like to imagine that the difference is that it's easier for others to find their voice as well. But who knows.
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It just occurred to me that the category of matrices is enriched over itself, which feels very weird. A priori it seems like the enriched category of matrices is forgetting a ton of information, but somehow it's not.
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If you ain’t down with fractals, I feel bad for you, son.I’ve got 99 problems, and 99 smaller problems inside of each one.
If you ain’t down with fractals, I feel bad for you, son.I’ve got 99 problems, and 99 smaller problems inside of each one.
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That day I vowed that I'd vocalize the questions that occurred to me during talks. Not so much for myself (though it is nice to have your questions answered in real time) but so that no one else who was in a room with me would sit through a talk where only the men asked questions.
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Help me be a hero for my classes tomorrow. Where can I find this filter?!?.
“I’m here live, I’m not a cat,” says lawyer after Zoom filter mishap. “I can see that,” responds judge
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Since y'all persuaded me to record, a video is now available as well:. Thanks to everyone who attended, and especially those who asked questions, either on film or in the chat.
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I'm one of one thousand women of STEM with Wikipedia pages created by David Eppstein. I'm surprised and delighted to hear about the initiative he's undertaken over the past several years. Congratulations on this milestone and thanks! (h/t @joshuagrochow).
David Eppstein has created over 1,000 Wikipedia pages for women in math, computer science, and related fields -- some of them are described in his recent post:
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I'm happy to see @QuantaMagazine take on the community effort towards the infinity-categorification of equality.
A community of mathematicians say the equal sign is too rigid to capture many mathematical complexities. They're replacing equality with a new mathematics of equivalence.
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Brouwer's fixed point theorem IRL!.
Doesn’t this mean there’s a point in the puddle that is touching the actual point it represents?.
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Showed this to my partner who asked "how does @AlbertEinstein have a verified account?" ¯\_(ツ)_/¯.
Mathematician Emily Riehl of @JohnsHopkins University hopes to make infinity category theory — a never-ending tower of equivalences — accessible to more mathematicians.
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If you want to follow along from home, two versions of the slides are available:. - a leisurely version ( with a page break between the questions and their answers or . - a condensed version ( with the answers given immediately.
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I'm so here for this 🏳️⚧️.
the transgender to category theory pipeline.
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Solidarity statements are totally insufficient gesture in the face of overwhelming historic and ongoing injustices. But when I remember how I felt while attending a mathematics workshop in the wake of the Pulse shooting, I feel it's better to say something than to stay silent:.
We, the members of the JHU Math Dept., are horrified by the brutal killing of George Floyd by police in Minnesota, and by the state violence against Black Americans that has been this country's legacy since 1619. We kneel with the students of color who are studying with us today.
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Steve Mitchell, who algebraic topology lost this week, wrote the world's most inspiring mathematical autobiography:.
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😍 ask me as many as you'd like to @BarbaraFantechi.
I'll be busy for a few days, because I have nonmaths stuff to do (nothing bad! just life!). But I am looking forward to a sabbatical full of maths. And especially to reading (as much as I can manage of) this book; I hope I won't ask @emilyriehl too many questions.
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A week ago, I attempted to explain a new theorem proven with @DomVerity — that there is a formal language for ∞-category theory and all statements written in this language are invariant under change of model — to a general audience @JohnsHopkins: .
President's Frontier Award Lecture by @JohnsHopkins Prof. Emily Riehl
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In fact all the category theory texts you recommend are free online: kudos to Tom, Brendan, and David for making that happen!.
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A close friend just told me I was the first (only?) female math professor she ever had. She took my course in categorical homotopy theory as a *postdoc*.
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This is something I remember Mike Shulman saying in a topology seminar talk when we were both grad students. As always, he makes an excellent point!.
"A perpetual challenge in [category theory, or in many areas of abstract] mathematics, is to find the right level of generality, which is often not the maximal level of generality." --@emilyriehl and @DomVerity .
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Today!.
Today on "Meet a Mathematician," I'll be chatting with Emily Riehl @emilyriehl. Join us at 4pm ET on Zoom to learn about her work in category theory, hear the story of her Rubik's cube collection , and learn what violas have to do with math. Register at
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I told Egbert that the only way to avoid finding mistakes in your writing is to never read anything you've written. Now he's sharing this story with the entire conference CIRM in one of the single most impressive acts of bravery I've seen in mathematics:.
While preparing the second talk of my lecture series at CIRM, I discovered a mistake in a result that I wanted to present. This mistake was in my thesis, is mentioned in a paper of mine, and in my book (which thankfully isn’t yet submitted to the publisher). Not fun.
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This is absolutely delightful:. Inna is one of my favorite people, absolutely hilarious, and the most charismatic mathematician I know. There is so much wisdom here. (And kudos to Maria Yakerson for the new YouTube channel on math-life balance.).
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We did something about this! There will be gender neutral bathrooms at the #JMM2019 in Baltimore thanks to a collaborative effort of the @JointMath organizing committee and the @amermathsoc director of education and diversity Helen Grundman. I'll tell you how to find them:.
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"And yet, as a female mathematician who also grappled with the exact environment that she describes so well, I realize she’s put her finger on something that I hadn’t been able to articulate before, and her new notation helps. I've been by turns a mathematics professor, . .
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This is phenomenal: @math3ma presents a beautiful categorical proof of the Brouwer Fixed Point theorem in non-technical language. "Category theory opens up portals (functors) between a myriad of mathematical worlds." I 💜 it.
We love @tweetsauce’s video “Fixed Points,” and it made us wonder about Brouwer’s Fixed Point Theorem. WHY is it true? Tai-Danae (@math3ma) uses a mathematical portal to give the proof! New episode!
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In case it couldn’t be made more obvious that @GovLarryHogan does not stand with Baltimore. I’m voting @BenJealous.
The intersection of North & Charles in Baltimore (2016 compared with 2018)
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Fantastic news today: the good folks over at the journal "Theory and Applications of Categories" (TAC) have just announced a new series entitled "TAC Expositions".
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For me it was the whole first page of results. I'm like, doesn't anyone else care about this?!?.
tfw when you google the answer to a math question and 3 of the first 4 hits are things you wrote.
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One of the most personally challenging presentations in a workshop on #NormsInMath was Denis Hirschfeldt's "Turning coffee into unions: mathematicians and collective bargaining" and now you can read the whole thing here:.
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On the subject of giving credit where due in abstract algebra, it's Sunzi's remainder theorem:.
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{|}.
I am sorry to confirm the passing of my colleague John Conway. An incomparable mathematician, a pleasant neighbor, and an excellent coffee acquaintance. His passing was sudden (fever started only Wednesday morning). Part of coronavirus's hard toll in New Jersey.
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Ran four blocks alongside the shuttle and made it. The kind driver who waited for me and complimented my fitness has really turned my morning around 🙏.
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I like this book so much I use when I teach out undergraduate honors abstract algebra course 🙀.
in other news, i am reading Aluffi's "Algebra: Chapter 0" and all I have to say is that it's a masterpiece.
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Today from 11:30-12:30 EDT, I'll speak about "The synthetic theory of ∞-categories vs the synthetic theory of ∞-categories" at the Vladimir Voevodsky Memorial Conference @the_IAS and you can follow along:. slides: live stream:
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That's the best compliment anyone has paid me in a long while 💜 Looking forward to seeing you @mathmoves in a couple weeks.
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and I want to work with other people who also want to work in congressive environments. It feels like progress to be able to say this without reference to gender." - @mathbabedotorg reviewing @DrEugeniaCheng's new book "x+y" for @nytimesbooks:.
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