seminars:arit
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| * **April 9** 4:00-6:00 pm Special Event: PhD Defense \\ **//Speaker//**: Sayak Sengupta (Binghamton) \\ **//Title//**: Iteration of Polynomials over Integers \\ **//Abstract//**: For a polynomial $u=u(x)$ over $\mathbb Z$ and $r\in\mathbb Z$, we consider the orbit of $u$ at $r$, denoted and defined by $\mathcal{O}_u(r):=\{u(r),u(u(r)),\ldots\}$. There are two main questions that we plan to answer: (1) what are the polynomials $u$ for which $0\in \mathcal{O}_u(r)$, and (2) what are the integer polynomials $u$ that satisfies the condition that for each prime number $p$ there is some iteration $m_p$ of $u$ such that $p|u^{(m_p)}(r)$? In this talk we will provide partial answer to (1), and a complete answer to (2). \\ | * **April 9** 4:00-6:00 pm Special Event: PhD Defense \\ **//Speaker//**: Sayak Sengupta (Binghamton) \\ **//Title//**: Iteration of Polynomials over Integers \\ **//Abstract//**: For a polynomial $u=u(x)$ over $\mathbb Z$ and $r\in\mathbb Z$, we consider the orbit of $u$ at $r$, denoted and defined by $\mathcal{O}_u(r):=\{u(r),u(u(r)),\ldots\}$. There are two main questions that we plan to answer: (1) what are the polynomials $u$ for which $0\in \mathcal{O}_u(r)$, and (2) what are the integer polynomials $u$ that satisfies the condition that for each prime number $p$ there is some iteration $m_p$ of $u$ such that $p|u^{(m_p)}(r)$? In this talk we will provide partial answer to (1), and a complete answer to (2). \\ | ||
| - | * **April 16** \\ **//Speaker//**: Alexander Borisov (Binghamton) \\ **//Title//**: On the Nyman-Beurling -Baez-Duarte criterion for the Riemann Hypothesis \\ **//Abstract//**: I will talk about an attractive criterion for the Riemann Hypothesis, originally due to Nyman and Beurling in 1950s and strengthened by Baez-Duarte in early 2000s. The talk will be partially based on my 2005 paper https://people.math.binghamton.edu/borisov/documents/papers/quot-fact-rh.pdf and will also include some more recent unpublished considerations. \\ | + | * **April 16** \\ **//Speaker//**: Alexander Borisov (Binghamton) \\ **//Title//**: On the Nyman-Beurling-Baez-Duarte criterion for the Riemann Hypothesis \\ **//Abstract//**: I will talk about an attractive criterion for the Riemann Hypothesis, originally due to Nyman and Beurling in early 1950s and strengthened by Baez-Duarte in early 2000s. The talk will be partially based on my 2005 paper https://people.math.binghamton.edu/borisov/documents/papers/quot-fact-rh.pdf and will also include some more recent unpublished considerations. \\ |
| - | * **April 30** Special event: Comprehensive for Mithun Veettil (tentative)\\ **//Speaker//**: Mithun Veettil \\ **//Title//**: TBA \\ **//Abstract//**: TBA \\ | + | * **April 29 (Monday)** 4:00-6:00 pm Special event: Admission to candidacy \\ **//Speaker//**: Mithun Veettil (Binghamton) \\ **//Talk 1//** (4:00-4:55)\\ **//Title//**: Hilbert's Irreducibility Theorem \\ **//Abstract//**: Hilbert's irreducibility theorem deals with the following problem: Let $f(t,x)$ be an irreducible polynomial in $K[t,x]$. Then for which field $K$ is it true that there are infinitely many specializations $t\mapsto t_0\in K$ such that $f(t_0,x)$ is irreducible in $K[x]$? Surprisingly, it turns out that $\mathbb{Q}$ and function fields have this property. \\ **//Talk 2//** (5:00-5:55)\\ **//Title//**: Golomb Topology on a Domain \\ **//Abstract//**: Golomb topology on a domain is a generalization of arithmetic topology on $\mathbb{Z}^+,$ appearing in Furstenberg's proof of the infinitude of primes. This paves way for the otherwise rare examples of countably infinite connected Hausdorff spaces. Following this, I shall conclude with a homeomorphism problem of Golomb topology on Dedekind domains. This talk is based on the 2019 paper by Pete Clark, Noah Lebowitz-Lockard, and Paul Pollack http://alpha.math.uga.edu/~pete/CLLP_November_30_2017.pdf \\ |
seminars/arit.1713101913.txt · Last modified: 2024/04/14 09:38 by borisov