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  2. Jack Thorne

    https://www.dpmms.cam.ac.uk/~jat58/
    17 May 2024: On the average number of 2-Selmer elements of elliptic curves over F. ... Elliptic curves over Q. are modular. J. Eur. Math. Soc. 21 (2019), no.
  3. Publications | Department of Pure Mathematics and Mathematical…

    https://www.dpmms.cam.ac.uk/publications?page=33%2CCONCAT%280x716b767071%2C%28SELECT%20%28ELT%282383%3D2383%2C1%29%29%29%2C0x7178767871%2CFLOOR%28RAND%280%29%2A2%29%29x%20FROM%20INFORMATION_SCHEMA.PLUGINS%20GROUP%20BY%20x%29a%29%27
    4 Jul 2024: 2019). 148,. 103. (doi: 10.1090/proc/14749). Cut-off phenomenon for the axb Markov chain over a finite field. ... M Gross, B Siebert. (2019). Explicit moduli spaces for congruences of elliptic curves.
  4. MATHEMATICAL TRIPOS: PART IA Lent 2024 PROBABILITY JRNExample Sheet…

    https://www.dpmms.cam.ac.uk/study/IA/Probability/2023-2024/pex3.pdf
    11 Jan 2024: 3. Let X be a Poisson random variable of parameter λ (0, ). (a) By optimizing the estimate of Question 2(b) over β, show that, for all x λ,. ... yet appeared? (b) What is the probability that the entire culture dies out eventually?
  5. ON THE SMOOTH LOCUS OF AFFINE SCHUBERT VARIETIES GEORGIOS ...

    https://www.dpmms.cam.ac.uk/~rz240/Min_deg.pdf
    28 Jan 2024: We fix T B Ga maximal torus and Borel pair in G defined over F which are in good positionrelative to s, and let I = Gal(F/F). ... We let B Tbe the Borel subgroup defined over F determined by BH and let X(T).
  6. The density of integral quadratic forms having ak-dimensional totally …

    https://www.dpmms.cam.ac.uk/~taf1000/papers/isotropic-subspaces.pdf
    22 Jan 2024: Our main result computes these local probabilities for quadratic forms over thep-adics. ... Then Q is k-isotropic (and regular) over Qp. 4. 3 GLOBAL DENSITIES.
  7. 16 Jan 2024: has fibre V , and thus ρ(P) is a vector bundle over M. ... Let the Roman indices a, b, c,. run over the set {1,. ,
  8. Part IB - Groups, Rings, and Modules

    https://www.dpmms.cam.ac.uk/~or257/teaching/notes/GRM.pdf
    31 Jan 2024: 533.2 Direct sums and free modules. 573.3 Matrices over Euclidean domains. ... r (0R 0R) = r 0R. We now use the fact that multiplication distributes over addition.
  9. Part II Logic and Set Theory András Zsák Lent ...

    https://www.dpmms.cam.ac.uk/~az10000/2024-lent-partii-logic-and-set-notes.pdf
    29 May 2024: 2. R is a vector space over the field Q. A basis of R over Q is called a Hamelbasis. ... If B 6= A, thenfor any x A B, the extension (B,R) =. (B {x},R {(b,x) : b B}. )contradicts the maximality of (B,R).
  10. CONGRUENCES BETWEEN MODULAR FORMS JACK A. THORNE Abstract. We ...

    https://www.dpmms.cam.ac.uk/~jat58/congruences.pdf
    11 Jan 2024: The set of (isomorphism classes of) irreducible smooth GL2(Ql)-modules(over C). • ... of potentialautomorphy [Tay02], together with an ‘R = T’ theorem over a suitable base exten-sion.
  11. A WEISS–WILLIAMS THEOREM FOR SPACES OF EMBEDDINGSAND THE HOMOTOPY ...

    https://www.dpmms.cam.ac.uk/~sm2600/papers/A%20Weiss-Williams%20result%20for%20embedding%20spaces%20and%20spaces%20of%20long%20knots.pdf
    5 Jun 2024: functor F : J O(1)0 TopO(1) enriched over Top, where J. ... First let ξ and π be vector bundles over spaces B and B′, respectively, and fixsome bundle map I : ξ π.

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