July 24 (Fri), 2020, 14:00--15:00, Room 1424

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Title:
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On certain multiple Dirichlet series
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Speaker:
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Lee, Eun Hye (Stony Brook University)

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Abstract:
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In this talk, I will be talking about the analytic properties of multiple Dirichlet series defined using the space of binary cubic forms. First I will construct the double zeta function from the 2 (out of 4) relative invariants of the binary cubic forms, and then I will prove its meromorphic continuation to the whole $\mathbb{C}^2$ via a functional equation and as time permits, show where the poles are. This work is joint work with Ramin Takloo-Bighash.

July 06 (Mon), 2020, 14:00--15:00, Room 8309

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Title:
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On the number of abelian varieties over finite fields
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Speaker:
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Jungin Lee (POSTECH)

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Abstract:
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Let B(q, g) be the number of isomorphism classes of abelian varieties of dimension g over a finite field F_q. Since the number B(q, g) is known to be finite, it is natural to consider its asymptotic behavior. In this talk, we will provide a lower bound and an upper bound of B(p, g) as g->∞ for a fixed prime p. We will also investigate the number of simple isogeny classes of abelian varieties over F_q of dimension g.

February 20 (Thu), 2020, 16:00--17:00, Room 1424

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Title:
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On Galois covers of the projective line and their specializations
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Speaker:
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Francois Legrand (TU Dresden)

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Abstract:
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Studying Galois covers of the projective line and their specializations is a central topic in inverse Galois theory, due to their connection with the inverse Galois problem. In this talk, we shall present two applications to diophantine geometry and the theory of modular forms. Firstly, we shall explain how deriving many curves over $\mathbb{Q}$ failing the Hasse principle, under the abc-conjecture. Secondly, we shall construct infinitely many non-liftable Hecke eigenforms of weight one over $\overline{\mathbb{F}_p}$ with pairwise non-isomorphic projective Galois representations, for $p \in \{3,5,7,11\}$. This talk is based on joint works with Joachim K\"onig, and with Sara Arias-de-Reyna and Gabor Wiese.