Daniel Litt

@littmath.bsky.social

5716 Followers 284 Following

Assistant professor (of mathematics) at the University of Toronto. Algebraic geometry, number theory, forever distracted and confused, etc. He/him.

Let 𝑓 :𝑋 →𝑆 be a smooth proper morphism of smooth, connected complex algebraic varieties, and fix 𝑠 ∈𝑆. Let 𝕍 be a complex local system on 𝑋, and suppose that 𝕍|𝑋𝑠 is of geometric origin. Is it true that the restriction of 𝕍 to every fiber of 𝑓 is of geometric origin?
A wart on the palm of a hand, with “Will you marry me” written on it.
Let 𝑋 be a smooth projective variety over a perfect field 𝑘 of characteristic 𝑝 >0. Let ℰ be an ample vector bundle on 𝑋 and 𝒢 a coherent sheaf on 𝑋. Let 𝐹 :𝑋 →𝑋 be the absolute Frobenius morphism. Is it necessarily the case that for all 𝑖 ≥rk⁡(ℰ), we have 𝐻𝑖⁡(𝑋,(𝐹𝑛)∗⁢ℰ⊗𝒢)=0 for 𝑛 sufficiently large?
Conjecture 1.1.1 of "Algebraicity and integrality of solutions to differential equations."
A del Pezzo surface (I think of degree 2?)
Serre's question: do there exist motives with exceptional Galois group?
A wiggling Fano surface on the Fermat cubic
The E6 root system
The finite Dynkin diagrams
E6-local systems from cubic threefolds Thomas Krämer, Daniel Litt, Marco Maculan We produce infinitely many local systems on (level covers of) the moduli space of smooth cubic threefolds, with algebraic monodromy group equal to the exceptional group E6. These local systems arise in the middle cohomology of abelian étale covers of the Fano scheme parametrizing lines in the universal cubic threefold.
MATHEMATICS IN THE LIBRARY OF BABEL February 21, 2026 Mathematics isn't only about saying true things. It's about asking the right questions, being confused, stumbling about, getting distracted, being wrong, recognizing when you're wrong, being stuck. Mostly being stuck. It's about clinging to a giant edifice and feeling it out until you understand some tiny piece of it. It's about finding meaning in and intuition for the texture of an object which, at first, can only be apprehended by bashing your skull into it until it imprints on your forehead. Then trying to convey some of that insight to someone else, and watching as they find their own way to it. I started trying to get LLMs to do math in July 2020, through the game "AI Dungeon," one of the earliest applications powered by GPT-3. I first got GPT-3 to produce a correct proof (of Fermat's Little Theorem) in April 2022. At the time I did not think they would become useful for math research in the near term.
4-month moving average of new MO questions, steep decline in 2025
New MathOverflow questions each month since the site's beginning; soft decline starting in 2021 and then steep decline in 2025
Montreal biosphere
pancakes smothered in maple syrup
Subway station garbage bags dancing upside-down in the wind
Woody Guthrie with his "This machine kills fascists" guitar.
Ellipsoid
Some pictures from the paper.
Density of integral points in the Betti moduli of quasi-projective varieties Simone Coccia, Daniel Litt Let Y be a smooth quasi-projective complex variety equipped with a simple normal crossings compactification. We show that integral points are potentially dense in the (relative) character varieties parametrizing SL2-local systems on Y with fixed algebraic integer traces along the boundary components. The proof proceeds by using work of Corlette-Simpson to reduce to the case of Riemann surfaces, where we produce an integral point with Zariski-dense orbit under the mapping class group.
Let 𝐸 be a non-CM elliptic curve over ℚ . Elkies famously showed there are infinitely many primes 𝑝 at which 𝐸 has supersingular reduction. One may reinterpret this as follows: there are infinitely many primes 𝑝 modulo which the invariant differential 𝑑𝑥𝑦 is locally exact. I am curious about the following: Let 𝑎,𝑏∈ℚ be rational numbers. Are there infinitely many primes 𝑝 modulo which the differential 𝜔=𝑎𝑑𝑥𝑦+𝑏𝑥𝑑𝑥𝑦 is locally exact?
46% chance of AI utopia by 2100
2% chance of dyson sphere by 2030
Robert Francis Prevost was born in Chicago on 14 September 1955, the son of Louis Marius Prevost and Mildred Martínez.[4] His father, who was a United States Navy veteran of World War II and school administrator,[5] was of French and Italian descent, and his mother of Spanish descent.[6] As a child, Prevost served as an altar boy at St. Mary of the Assumption Church on the far South Side of Chicago.[7] He completed his secondary studies at the minor seminary of the Order of St. Augustine in 1973. Prevost earned a Bachelor of Science degree in mathematics at Villanova University in 1977.[8]
Google search for “cocomelon etymology”
The Schlesinger system
The same globally bounded hypergeometric function from before. It's an elliptic integral!
A globally bounded hypergeometric function
Gotthold Eisenstein
A general differential equation
Lazarus Fuchs
A general differential equation
17-gon constructed by compass and straightedge
A Forgotten Grave? If one enters the Jerusalem Cemetery from Blücherplatz, passes through the main entrance all the way to the end, then goes about thirty paces to the right around a cluster of family burial sites, and then another twenty paces to the right, one arrives—so a friend of our paper informs us—at a decaying grave. The iron plaque, once set into a stone and bearing the inscription, had long since fallen off and was lying behind the grave. Acquaintances of the deceased’s parents have, with great effort, raised the stone and plaque back up onto the grave. This plaque bears the following inscription: Ferd. Gotthold Maxim. Eisenstein, Doctor of Philosophy, Lecturer at the University, Member of the Academy of Sciences in Berlin, Göttingen, and other learned societies. Born on April 16, 1823, died on October 11, 1852. “He lives on for his parents and for science.” When one sees the condition of this grave, those last words seem like sheer mockery. Yet who was the deceased—still under thirty years of age? We learn this from the following article in the Spenersche Zeitung of October 13, 1852, which reads: “The Academy of Sciences lost its youngest member, Dr. Eisenstein, day before yesterday through his death. He had reached only thirty years of age, yet he was one of the leading mathematicians not only of Germany but of the entire civilized world!!! After Jacoby’s death, he was probably the only scholar who treated that specialized field of science—number theory—in its full scope, in the broadest…”
The cemetery at Blücherplatz
Gotthold Eisenstein
Traveler finds Ozymandias's shattered statue in desert; once-mighty power lost forever to drifting sands.
Geometric local systems on very general curves and isomonodromy, JAMS
Tweet of a Quanta article about me, followed by a response that reads “that nerd need to see the real world”
an unbelievable mess of notation from a paper i'm writing
Graph of a real affine cubic surface with one compact component
notes on hyperelliptic involutions with "What is he cooking?" written in red text
Headline: New publisher Spines aims to ‘disrupt’ industry by using AI to publish 8000 books in 2025 alone
Trolley program with trolley programmer saying he is not responsible for the outcome
DOGE ad on Xitter
The joker
Glass of Ottawa’s best lager; not sure if the bartender meant to damn it with faint praise
Two recurrence relations.
Taylor expansion of hypergeometric functions
Elliptic integral for lambda family