SEMINARS, NUMBER THEORY
February 15, 2023 3:00 pmFermat identified the integers which are a sum of two squares, integral or rational: they are exactly those integers which have all primes congruent to 3 (mod 4) occurring to...
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SEMINARS, NUMBER THEORY
February 8, 2023 3:00 pmTitle: TBA Abstract: TBA
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SEMINARS, NUMBER THEORY
February 8, 2023 3:00 pmElliptic curves E over the rational numbers are modular: this means there is a nonconstant map from a modular curve to E. When instead the coefficients of E belong to...
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SEMINARS, NUMBER THEORY
February 1, 2023 3:00 pmTitle: TBA Abstract: TBA
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SEMINARS, NUMBER THEORY
November 30, 2022 3:00 pmLet S be a Shimura variety such that the connected components of the set of complex points S(C) are of the form D/Γ, where Γ is a torsion-free arithmetic group...
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SEMINARS, NUMBER THEORY
November 16, 2022 3:00 pmTo a connected reductive group G over a local field F we define a compact topological group π_1~(G) and an extension G(F)_∞ of G(F) by π_1~(G). From any character x of π_1~(G) of order...
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SEMINARS, NUMBER THEORY
November 9, 2022 3:00 pmAn automorphic form can appear in multiple degrees of the cohomology of arithmetic manifolds, and this happens mostly when the arithmetic manifolds are not algebraic. This phenomenon is a part...
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SEMINARS, NUMBER THEORY
November 2, 2022 3:00 pmRelative trace formulas are central tools in the study of relative functoriality. In many cases of interest, basic stability problems have not previously been addressed. In this talk, I discuss...
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SEMINARS, NUMBER THEORY
October 26, 2022 3:00 pmThe usual language of algebraic geometry is not appropriate for arithmetical geometry: addition is singular at the real prime. We developed two languages that overcome this problem: one replace s...
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SEMINARS, NUMBER THEORY
October 19, 2022 3:00 pmI will explain how various results in arithmetic statistics by Bhargava, Gross, Shankar and others on 2-Selmer groups of Jacobians of (hyper)elliptic curves can be organised and reproved using the...
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