SEMINARS, NUMBER THEORY
October 12, 2022 3:00 pmWe study them, in particular showing on a smooth complex quasi-projective variety the existence of ℓℓ-adic absolutely irreducible local systems for all ℓℓ the moment there is a complex irreducible...
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SEMINARS, NUMBER THEORY
October 5, 2022 3:00 pmThe Langlands program predicts a relationship between automorphic representations of a reductive group G and Galois representations valued in its L-group. For general G over a global function field, the...
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SEMINARS, NUMBER THEORY
September 14, 2022 3:00 pmMany of the quantities appearing in the conjecture of Birch and Swinnerton-Dyer look suspiciously like squares. Motivated by this and related examples, we may ask if the central value of...
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SEMINARS, NUMBER THEORY
May 4, 2022 3:00 pmI will give an introduction to Oliver Lorscheid’s theory of ordered blueprints – one of the more successful approaches to “the field of one element” – and sketch its relationship...
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SEMINARS, NUMBER THEORY
April 27, 2022 3:00 pmThe ghost conjecture predicts slopes of modular forms whose residual representation is locally reducible. In this talk, we'll examine locally irreducible representations and discuss recent progress on formulating a conjecture in this case. ...
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SEMINARS, NUMBER THEORY
April 13, 2022 3:00 pmAbout 2 years ago, I have given a new construction of the Euler system of cyclotomic units via Eisenstein congruences in which the p-adic Langlands correspondence for GL_2(\Q_p) plays a...
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SEMINARS, NUMBER THEORY
April 6, 2022 3:00 pmLet C be an algebraic curve over a number field. Faltings's theorem on rational points on subvarieties of abelian varieties implies that all algebraic points on C arise in algebraic...
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SEMINARS, NUMBER THEORY
March 30, 2022 3:00 pmThe unbounded denominators conjecture, first raised by Atkin and Swinnerton-Dyer, asserts that a modular form for a finite index subgroup of SL_2(Z) whose Fourier coefficients have bounded denominators must be...
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SEMINARS, NUMBER THEORY
March 23, 2022 3:00 pmCohen and Lenstra gave a conjectural distribution for the class group of a random quadratic number field. Since the class group is the Galois group of the maximum abelian unramified...
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SEMINARS, NUMBER THEORY
March 9, 2022 3:00 pmFor a smooth projective curve $C/\mathbb{Q}$, how many field extensions of $\mathbb{Q}$ -- of given degree and bounded discriminant --- arise from adjoining a point of $C(\overline{\mathbb{Q}})$? Can we further count the number...
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