April 15 (Thu), 2021, 10:00--11:00, online

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Title:
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Robba-valued cohomology
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Speaker:
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Koji Shimizu (UC Berkeley)

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Abstract:
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Rigid cohomology is a good p-adic cohomology theory for algebraic varieties in characteristic p. In this talk, I will explain a relevant idea by Monsky and Washnitzer and then discuss my ongoing attempt to define a p-adic cohomology theory for rigid analytic varieties over a local field of characteristic p.

April 01 (Thu), 2021, 17:00--18:00, online

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Title:
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On Euler systems for adjoint modular Galois representations
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Speaker:
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Eric Urban (Columbia University)

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Abstract:
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The purpose of this talk is to illustrate a new method to construct Euler systems based on the study of congruences between modular forms of arbitrary weights and level and their corresponding deformations of Galois representations. We will focus on the case of adjoint modular Galois representations attached to an ordinary eigenform and connect our construction to a conjecture for the Fitting ideal of the equivariant congruence module attached to the abelian base changes of that moduar form.

March 05 (Fri), 2021, 10:30--11:30, online

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Title:
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Some analytic quantities having arithmetic information on elliptic curves
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Speaker:
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Masato Kurihara (Keio University)

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Abstract:
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I will discuss some analytic quantities constructed from modular symbols for a rational elliptic curve, which have some interesting arithmetic information on the Mordell-Weil group and related subjects.

February 04 (Thu), 2021, 10:00--11:00, online

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Title:
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Slopes of modular forms and the ghost conjecture
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Speaker:
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Robert Pollack (Boston University)

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Abstract:
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Modular forms are mathematical objects born in complex analysis but in fact have become central objects in number theory. In particular, special modular forms, called eigenforms, have Fourier coefficients which are algebraic integers and these integers contain loads of number theoretic data. In this talk, we will focus on one slice of this data, namely, the highest power of p dividing the pth Fourier coefficient (called the slope of the form). Through many numerical examples, we will discuss the properties of these slopes and ultimately state the so-called "ghost conjecture" which predicts them in a combinatorial way.