seminars:arit
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| **PLACE and TIME**: This semester the seminar meets primarily on Tuesdays at 4:15 p.m, with possible special lectures on Mondays at 3:30 or other days and times. The in-house talks will be in-person, while visitors outside of Binghamton area will be by Zoom: [[https://binghamton.zoom.us/j/98485937832|Zoom link]]\\ | **PLACE and TIME**: This semester the seminar meets primarily on Tuesdays at 4:15 p.m, with possible special lectures on Mondays at 3:30 or other days and times. The in-house talks will be in-person, while visitors outside of Binghamton area will be by Zoom: [[https://binghamton.zoom.us/j/98485937832|Zoom link]]\\ | ||
| - | **ORGANIZERS**: \\ **Regular Faculy:** [[:people:borisov:|Alexander Borisov]], [[:people:mazur:|Marcin Mazur]], [[:people:adrian:|Adrian Vasiu]], \\ **Post-Docs:** [[:people:sailun:|Sailun Zhan]]. | + | **ORGANIZERS**: \\ **Regular Faculy:** [[:people:borisov:|Alexander Borisov]], [[:people:mazur:|Marcin Mazur]], [[:people:adrian:|Adrian Vasiu]]. \\ **Post-Docs:** |
| - | **Current Ph.D. students:** [[:people:grads:lamoureux:|Andrew Lamoureux]], [[:people:grads:loverro:|Micah Loverro]], [[:people:grads:sengupta:|Sayak Sengupta]], [[:people:grads:hari:|Hari Asokan]], [[:people:grads:mithunp:|Mithun Padinhare Veettil]]. | + | **Current Ph.D. students:** [[:people:grads:sengupta:|Sayak Sengupta]], [[:people:grads:hari:|Hari Asokan]], [[:people:grads:mithunp:|Mithun Padinhare Veettil]]. |
| **Graduated Ph.D. students** (in number theory and related topics): [[:people:grads:snopce:|Ilir Snopce]] (Dec. 2009), [[:people:grads:xiao:|Xiao Xiao]] (May 2011), [[:people:grads:jinghao:|Jinghao Li]] (May 2015), [[:people:grads:ding:|Ding Ding]] (Dec. 2015), | **Graduated Ph.D. students** (in number theory and related topics): [[:people:grads:snopce:|Ilir Snopce]] (Dec. 2009), [[:people:grads:xiao:|Xiao Xiao]] (May 2011), [[:people:grads:jinghao:|Jinghao Li]] (May 2015), [[:people:grads:ding:|Ding Ding]] (Dec. 2015), | ||
| - | [[:people:grads:milano:|Patrick Milano]] (May 2018), [[:people:grads:zhou:|Changwei Zhou]] (May 2019). | + | [[:people:grads:milano:|Patrick Milano]] (May 2018), [[:people:grads:zhou:|Changwei Zhou]] (May 2019), Patrick Carney (May 2023), [[:people:grads:lamoureux:|Sarah Lamoureux]] (Sep. 2023). |
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| - | **SEMINAR ANNOUNCEMENTS**: To receive announcements of seminar talks by email, please join our [[http://www1.math.binghamton.edu/mailman/listinfo/Arithmetic_sem|mailing list]]. | + | **SEMINAR ANNOUNCEMENTS**: To receive announcements of seminar talks by email, please join our [[http://www1.math.binghamton.edu/mailman/listinfo/Arithmeticsem|mailing list]]. |
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| * **March 19** \\ **//Speaker//**: Shane Chern (Dalhousie) \\ **//Title//**: The Seo-Yee conjecture: Nonmodular infinite products, seaweed algebras, and integer partitions \\ **//Abstract//**: In this talk, I will present my recent work on the Seo-Yee conjecture, which claims the nonnegativity of coefficients in the expansion of a q-series infinite product. The Seo-Yee conjecture arises from the study of seaweed algebras (a special type of Lie algebra), and is closely tied with the enumeration of the index statistic of integer partitions. Our proof of the Seo-Yee conjecture is built upon the asymptotic analysis for a generic family of nonmodular infinite products near each root of unity. \\ | * **March 19** \\ **//Speaker//**: Shane Chern (Dalhousie) \\ **//Title//**: The Seo-Yee conjecture: Nonmodular infinite products, seaweed algebras, and integer partitions \\ **//Abstract//**: In this talk, I will present my recent work on the Seo-Yee conjecture, which claims the nonnegativity of coefficients in the expansion of a q-series infinite product. The Seo-Yee conjecture arises from the study of seaweed algebras (a special type of Lie algebra), and is closely tied with the enumeration of the index statistic of integer partitions. Our proof of the Seo-Yee conjecture is built upon the asymptotic analysis for a generic family of nonmodular infinite products near each root of unity. \\ | ||
| - | * **March 26** \\ **//Speaker//**: TBA \\ **//Title//**: TBA \\ **//Abstract//**: TBA \\ | + | * **March 26** \\ **//Speaker//**: Alexander Borisov (Binghamton) \\ **//Title//**: On irreducibility of higher derivatives of polynomials x^n+...+x+1 \\ **//Abstract//**: In our 1999 joint paper with Filaseta, Lam, and Trifonov we proved, among other results, that for every fixed positive integer k the k-th derivatives of the polynomials in the title are irreducible over the rationals for a density one set of natural n. The proof relies on understanding the "location" of the roots of these derivatives in complex numbers and in p-adic complex numbers for primes dividing (n+1)n...(n+1-k). I will explain the main ideas of the proof while trying to avoid the rather formidable technical details.\\ |
| - | * **April 2** \\ **//Speaker//**: TBA \\ **//Title//**: TBA \\ **//Abstract//**: TBA \\ | + | * **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** \\ **//Speaker//**: TBA \\ **//Title//**: TBA \\ **//Abstract//**: TBA \\ | + | * **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 16** \\ **//Speaker//**: TBA \\ **//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 \\ |
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| - | * **April 30** \\ **//Speaker//**: TBA \\ **//Title//**: TBA \\ **//Abstract//**: TBA \\ | + | |
seminars/arit.1709510400.txt · Last modified: 2024/03/03 19:00 by borisov