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1. -Lemmas

   A dilemma is a difficult choice between two alternatives. I recently learned that there is a word for a choice between three alternatives: trilemma. But what…

2. \(SL_4/\mu_2\) and a mod \(8\) congruence

   This is a continuation of a previous post . Recall that we wanted to prove the following claim: Claim. Let be a representation of such that no irreducible…

3. 12 minutes of monodromy

   Here’s a video of a (12 minute!) talk I gave on Friday about some of my recent work, mostly from this paper of mine . The talk is aimed at a general…

4. A "minimal" proof of the fundamental theorem of algebra

   When I was in graduate school, I came up with what I think is a nice proof of the fundamental theorem of algebra. At the time, I wrote it up here somewhat…

5. A non-prorepresentable deformation functor

   I've been teaching a topics course on deformation theory this semester; so far we've covered quite a few interesting things -- the Tian-Todorov theorem and…

6. A quick comment on recent RH news

   I recently commented for this article in Gizmodo on Atiyah’s supposed proof of the Riemann Hypothesis. In the article I assert there is an internal…

7. A short story about prompt engineering

   The idea for this (very short, and somewhat silly) story popped into my head a couple of weeks ago. Please enjoy. Toast , or, The Golems “It’s just not so…

8. A tiling puzzle

   Here are four magic triominoes: Each is made out of three squares, two red and one blue or two blue and one red, alternating in color. These squares have the…

9. About

   Biography, research interests, and professional background of mathematician Daniel Litt.

10. ADDING

    Archived information, schedule, and participants for the ADDING workshop at the University of Georgia, April 30–May 1, 2022.

11. AG Seminar 2022-2023

    Archived schedule for the University of Toronto Algebraic Geometry Seminar in 2022–2023.

12. AGONIZE

    Archived schedule and videos from the AGONIZE online arithmetic geometry conference, March 25, 2020.

13. AGONIZE

    This post announces the first ever AGONIZE conference ( A rithmetic G eometry is ON line I n Z oom, E veryone)! The conference will take place Wednesday…

14. Algebra II

    Math 1101 Algebra II course page at the University of Toronto, Winter 2025.

15. Algebraic Geometry

    This course will cover Chapter III of Hartshorne’s Algebraic Geometry.

16. An NSERC Proposal

    I try to make a habit of posting my grant proposals here after the application period has passed, both because I hope people might find them to be useful…

17. Are Shimura Varieties \(K(\pi, 1)\)'s?

    Let be the moduli space of principally polarized Abelian varieties of dimension . The complex-analytic space (stack) associated to is a ; that is, its only…

18. Arithmetic and Representations of Fundamental Groups

    I gave a talk at the IPAM conference “ Braids, Resolvent Degree, and Hilbert’s 13th Problem ” this past Thursday. The conference was really inspiring — I…

19. arXiv in trouble?

    Since June 15, 2025 there have been 8 papers posted to arXiv with the phrase “Hodge conjecture” in the title or abstract. By my count 6 of them (75%!) are…

20. BIOPSY

    Archived guidelines and meeting information for the BIOPSY arithmetic geometry problem seminar, Summer 2020.

21. Biospheres

    This is Biosphere 1: And this is Biosphere 2:

22. C.S. Lewis on Commutative Algebra

    Read the whole essay here . Sorry for the pause in blogging -- I should start up again soon.

23. CCAM

    Archived materials from the Fall 2021 CCAM learning seminar on Catalan’s conjecture and Mihăilescu’s proof.

24. Commutative Algebra

    Archived homework and course information for Commutative Algebra at the University of Georgia, Spring 2022.

25. Constructive Criticism

    Here is a classical example of a non-constructive proof. Thm 1. There exist irrational numbers such that is rational. Proof. If is rational, then we may take…

26. Contact

    Email and office contact information for Daniel Litt at the University of Toronto.

27. CRAG

    Archived schedules and resources for the CRAG classic papers seminar in arithmetic and algebraic geometry, 2020–2021.

28. Curves & Surfaces

    Archived course information and resources for Curves and Surfaces at the University of Toronto, Winter 2024.

29. Department tea, and revised office hours tomorrow.

    A historical April 2020 announcement about virtual UGA department teas and office hours.

30. Donate to MathOverflow

    I just noticed that MathOverflow is soliciting donations at this link , or click here to donate directly. If you haven't donated yet, please consider it --…

31. Étale cohomology

    Archived course materials, lecture notes, and videos for Étale Cohomology and the Weil Conjectures, Fall 2020.

32. Expository Notes

    Expository notes and articles by Daniel Litt on algebraic geometry, number theory, topology, and related subjects.

33. Fall 2017 – Topics in Algebraic Geometry – Deformation Theory

    Archived syllabus and schedule for a Columbia University topics course in deformation theory, Fall 2017.

34. Families of Curves Wanted

    An interesting problem Let be a large positive integer. Recently I've been looking for a family of curves with the following properties: is flat and proper of…

35. Geometricity and Galois actions on fundamental groups

    A couple months ago I went to a fantastic conference on Arithmetic Topology at PIMS . The video from my talk is now up: enjoy ! I spend the first few minutes…

36. Grant Materials

    I was recently funded by the NSF Algebra and Number Theory grant DMS-2001196. Since other people may find it useful, I figured I would post my proposal here .…

37. Graph Theory and \(\mathfrak{sl}_2\)

    How many unlabeled graphs are there with vertices and edges? (More below the fold.)

38. Guest Post: Ordinals and Hydras, by Brian Lawrence

    A few days ago, the hydra game came up in discussion with Brian Lawrence; we'd both run into a somewhat mystifying analysis of the game via ordinals. Brian…

39. Hire me!

    I'm currently on the market for tenure-track jobs in mathematics. The application process is somewhat formal -- I think it's hard, in a research statement, to…

40. Hodge theory

    Archived course information and schedule for Hodge Theory at the University of Toronto, Fall 2022.

41. Holding the p-adics in the palm of your hand (with thanks to Matt Kukla)

    A few years ago I made a picture of the 3-adic numbers in answer to a MathOverflow question (using the free 3d modeling and rendering software Blender , which…

42. I'm a Numberphile!

    The popular YouTube channel Numberphile has just released a video featuring yours truly — filming this with Brady Haran was a real pleasure! A couple of quick…

43. Integral House

    I'm teaching Calculus III at Columbia this semester, and am kind of amazed at the exploitative prices charged for Stewart's Calculus, 8th Edition, "Early…

44. Jie Liu on projective space

    Exciting news! Jie Liu has proven a conjecture of mine -- thereby resolving an old conjecture of Sommese. I'll briefly explain his result in this post.

45. Krashen the party

    I'm at UGA for the week, in between SWAG and TAAAG . Today Danny Krashen gave a great talk on this paper of Auel, First, and Williams. The paper is one of the…

46. Man After Man

    One of my favorite books growing up was Dougal Dixon 's Man after man: an anthropology of the future , which imagines the development and speciation of…

47. MAT138H1

    Archived course materials for MAT138H1, Introduction to Proofs, at the University of Toronto in Fall 2022.

48. Math 1100 - Algebra

    Archived syllabus, assignments, and schedule for MAT1100 Algebra I at the University of Toronto, Fall 2023.

49. Math 2250

    Archived syllabus, homework, and course resources for Math 2250 at the University of Georgia, Fall 2019.

50. Mathematics in the Library of Babel

    Mathematics isn't only about saying true things. It's about asking the right questions, being confused, stumbling about, getting distracted, being wrong…

51. More Tate curves, more problems

    I’m giving an expository lecture on the Tate curve and non-archimedean geometry next Tuesday, November 6, as one of the preparatory lectures for Peter…

52. More Tautological Classes?

    Still at UGA -- I just saw a great talk by Jason van Zelm (a student of Nicola Pagani who apparently does not have a webpage), constructing non-tautological…

53. Morita Theory, Tannaka Duality, and Approximate Tannaka Duality

    Let be a ring -- it is well-known that the category of (left) -modules does not determine . For example, the functor is an equivalenc…

54. Mumford at the Met

    I was at the Met yesterday, where by chance I ran across the Concinnitas Project . (Pictures below the fold.)

55. My Hero

    This is a picture of Alexander Grothendieck, taken near the end of his life: I took this picture of a page in a book that was just lying around in Oberwolfach…

56. Non-Mathematical Writing

    Non-mathematical essays, fiction, and other prose by Daniel Litt.

57. Office Hours

    A March 2020 announcement of temporary virtual office hours for the UGA arithmetic geometry community.

58. Open Questions

    Open research questions and mathematical problems collected by Daniel Litt.

59. ProblemsILike.com

    Announcing a new project: problemsilike.com , a website collecting open problems that I, personally, like, with comments on their context, difficulty, and…

60. Publications and Preprints

    Papers and preprints by Daniel Litt, with citations and abstracts.

61. Rational Points

    Archived course information and schedule for Rational Points at the University of Georgia, Fall 2021.

62. Rationalia, USA

    In June 2016, Neil deGrasse Tyson proposed (not entirely seriously, as this series of tweets should make obvious) the creation of a new country: Rationalia…

63. Real Fano Surface Visualization

    An interactive three-dimensional mesh visualization of the real Fano surface.

64. Reflections on AGONIZE and online conferences

    Videos are now up for AGONIZE. I’ve committed to organizing another one of these — stay tuned for more info. Since this was one of the first math conferences…

65. Representation Theory

    Math 445 Representation Theory course page at the University of Toronto.

66. Representation Theory

    Math 445 Representation Theory course page at the University of Toronto, Winter 2026.

67. Rigid Local Systems

    Archived schedule and references for the Rigid Local Systems learning seminar, Winter 2023.

68. Sawin on Severi's Conjecture

    One of my favorite questions is: for which is the moduli space of -pointed genus curves unirational/uniruled? Will Sawin has just posted a beautiful paper on…

69. Scissors integration

    On Twitter Sarah Griffith made the following wonderful observation: Maybe this doesn't seem strange to anyone else, but I just realized I find it very strange…

70. SeZoom

    Archived schedule and notes from the SeZoom learning seminar on Serre's work, Winter 2021.

71. Single-author Paper Reviews, Audits, and Errata

    Refine reviews, mathematical audits, and errata for eight single-author published papers.

72. Some low-hanging fruit

    Today is the #ShutdownSTEM strike , a day when non-black members of the academy strike in solidarity with the black lives matter movement, and take action to…

73. Starting a blog?

    I'm thinking of starting a blog. Let's see how this goes.

74. SWAG

    I'm currently at SWAG , the awesomely named Summer Workshop in Algebraic Geometry at Georgia. Jonathan Wise gave a really amazing talk today about logarithmic…

75. TAAAG

    Still at UGA, at the very enjoyable but weirdly named conference TAAAG . The conference featured a very interesting talk by Padmavathi Srinivasan , as well as…

76. Talk Notes and Slides

    Selected talk notes, slides, videos, and older mathematical writing by Daniel Litt.

77. Teaching, Seminars, and Service

    Archived course pages, seminar materials, mentorship, and service activities by Daniel Litt.

78. Tensor powers of faithful representations

    Let be a finite group and a faithful representation, with a finite-dimensional complex vector space. The following is well-known: Theorem 1. Let be any…

79. The Boston-Markin Conjecture for Three-Manifolds

    A couple of months ago I was in Oberwolfach, where Tomer Schlank told me about the following conjecture: Conjecture. ( Boston-Markin ) Let be a finite group.…

80. The End of Mathematics

    I'm currently returning to Toronto from a summit on the future of mathematics, at OpenAI. Sebastian Bubeck asked me to talk a bit about the future we'd all…

81. The geometry of the Sylow theorems

    Today I want to explain some algebro-geometric manifestations of the Sylow theorems. This blog post is an expansion of a Twitter Thread I wrote a few months…

82. The Lost World

    I. Opening the Airlock While I was in Arizona last week (running a study group for this year's Arizona Winter School on perfectoid spaces), I took the…

83. The parity of zero, the primality of two, and other mysteries

    From time to time, I try to speak or write about mathematics for general (non-mathematical) audiences. If you've done this, you know it's pretty hard -- in…

84. The Typographical Equivalent of a Knife Fight

    I've been thinking recently about typefaces -- the four to eight readers of this blog may have noticed that the font used in the body text of these posts has…

85. Tiling puzzle: solution

    My last post was a little tiling puzzle: you can read it here . In this post I want to quickly give the solution. Represent a red tile by and a blue tile by…

86. Uniformization over finite fields

    I just asked this question on MathOverflow. It's basically idle curiosity, but I've now been idly curious about this for several years, so I figured I might…

87. Varieties with infinitely generated automorphism group

    John Lesieutre has just sent me an exciting new preprint in which he constructs a smooth projective variety such that is discrete, and is not finitely…

88. Villani for Parliament!

    The (relatively new) French party En Marche! (from which the winning presidential candidate, Macron, hails) has nominated spider-brooch wearing mathematician…

89. WAGON

    For those of you who haven’t yet, you should register for WAGON ! Poster below — it’s going to be great.

90. WAGON: Lessons learned

    This past weekend was the first-ever WAGON conference (Western Algebraic Geometry ONline), which was meant as the online iteration of the Western Algebraic…

91. Weapons of Math Destruction

    I've just finished reading Cathy O'Neil's book Weapons of Math Destruction , which I highly recommend. (One notable feature of the book is that the skull and…

92. What I've been thinking about recently

    I wrote a MathOverflow answer just now which also happens to be a pretty good summary of some of the open questions I’ve been thinking about recently. Take a…

93. What's wrong with the world?

    In 1910, G.K. Chesterton (one of my favorite authors -- I highly recommend The Man Who Was Thursday and the Father Brown mysteries) diagnosed all the world's…

94. ZaZoom

    Archived schedule and references for the ZaZoom unlikely intersections seminar, Fall 2020.