NTS ABSTRACTSpring2023
Jan 26
| MSRI/SLMath workshop |
| Introductory Workshop: Algebraic Cycles, L-Values, and Euler Systems |
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NTS of the week is cancelled as most of the number theory group are attending the MSRI/SLMath Introductory Workshop: Algebraic Cycles, L-Values, and Euler Systems, see https://www.msri.org/workshops/979. |
Feb 02
| Asvin Gothandaraman |
| A p-adic Chebotarev density theorem and functional equation |
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We (Asvin G, Yifan Wei and John Yin) define a notion of splitting density for "nice" generically finite maps over p-adic fields and show that these densities satisfy a functional equation. As a consequence, we prove a conjecture about factorization probabilities of Bhargava, Cremona, Fisher, Gajovic.
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Feb 09
| MSRI/SLMath workshop |
| Introductory workshop: Diophantine Geometry |
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NTS of the week is cancelled as most of the number theory group are attending the MSRI/SLMath introductory workshop on Diophantine Geometry, see https://www.msri.org/workshops/977. |
March 02
| Naser Talebizadeh Sardari |
| Limiting distributions of conjugate algebraic integers |
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Let $\Sigma \subset \mathbb{C}$ be a compact subset of the complex plane, and $\mu$ be a probability distribution on $\Sigma$. We give necessary and sufficient conditions for $\mu$ to be the weak* limit of a sequence of uniform probability measures on a complete set of conjugate algebraic integers lying eventually in any open set containing $\Sigma$. Given $n\geq 0$, any probability measure $\mu$ satisfying our necessary conditions, and any open set $D$ containing $\Sigma$, we develop and implement a polynomial time algorithm in $n$ that returns an integral monic irreducible polynomial of degree $n$ such that all of its roots are inside $D$ and their root distributions converge weakly to $\mu$ as $n\to \infty$. We also prove our theorem for $\Sigma\subset \mathbb{R}$ and open sets inside $\mathbb{R}$ that recovers Smith's main theorem~\cite{Smith} as special case. Given any finite field $\mathbb{F}_q$ and any integer $n$, our algorithm returns infinitely many abelian varieties over $\mathbb{F}_q$ which are not isogenous to the Jacobian of any curve over $\mathbb{F}_{q^n}$. |
March 16
| MSRI/SLMath workshop |
| Shimura Varieties and L functions |
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NTS of the week is cancelled as most of the number theory group are attending the MSRI/SLMath workshop on Shimura Varieties and L functions, see https://www.msri.org/workshops/1032. |
April 27
| MSRI/SLMath workshop |
| Degeneracy of Algebraic Points |
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NTS of the week is cancelled as most of the number theory group are attending the MSRI/SLMath workshop on Degeneracy of Algebraic Points, see https://www.msri.org/workshops/1040. |