Department of Mathematics and Statistics

Department of Mathematics and Statistics
Department of Mathematics and Statistics
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Number Theory Seminar

Number Theory - Riley Becker

Wednesday, May 16th, 2018

Time: 2:30-3:20p.m.  Place: Jeffery Hall 422

Speaker: Riley Becker

Title: The Size of Sets with the Property D(n).

Abstract: Let $n$ be a nonzero integer, and suppose $A$ is a set of distinct positive integers for which $ab+n$ is a perfect square for each pair of distinct $a$ and $b$ in $A$. Using a discussion of Andrej Dujella, we will find an upper bound on the size of such a set.

Strength in Numbers: Graduate Workshop in Number Theory

Strength In Numbers Poster

Strength in Numbers: A Graduate Workshop in Number Theory and Related Areas

Dates: Friday, May 11th and Saturday, May 12th, 2018

Venue: Jeffery Hall, Queen's University

This is a two-day workshop aimed primarily at graduate students. Participation is open to all. There are five plenary talks by experts and many contributed talks by graduate students on a topic of their choice. Schedules and abstracts of the talks are attached with this email.

A novel feature of this workshop is a presentation by Prof. Erin Maloney, a psychologist specializing in math anxiety and related areas. The invited speakers will also lead a panel discussion regarding professional development on Saturday. Questions can be submitted here - https://docs.google.com/forms/d/e/1FAIpQLSdedZpevw4t8mDHlctq1Nmbmz3hX6v6IC-pyeBmV79jlWLM2g/viewform?usp=sf_link

More information about the workshop can also be found on the website: https://sites.google.com/view/strengthinnumbers2018/home

This workshop is sponsored by the Fields institute, the Number Theory Foundation and the department of Mathematics and Statistics, Queen's.

We hope to see you there!
Sincerely,
The organizing committee
Neha Prabhu, Siddhi Pathak and Vaidehee Thatte

Number Theory - Seoyoung Kim (Brown University)

Thursday, May 10th, 2018

Time: 2:30-3:20p.m.  Place: Jeffery Hall 422

Speaker: Seoyoung Kim (Brown University)

Title: The density of the terms in an elliptic divisibility sequence having a fixed G.C.D. with their indices.

Abstract: Let $\D=(D_{n})_{n\geq 1}$ be an elliptic divisibility sequence associated to the pair $(E,P)$. For a fixed integer $k$, we define $\A_{E,k}=\{n\geq 1 : \gcd(n,D_{n})=k\}$. We give an explicit structural description of $\A_{E,k}$. Also, we explain when $\A_{E,k}$ has positive asymptotic density using bounds related to the distribution of trace of Frobenius of $E$. Furthermore, with preconditions, we obtain an explicit density for $\A_{E,k}$ using the M\"obius function. The precondition holds when $E$ is a finitely anomalous elliptic curve.

Number Theory - M. Ram Murty (Queen's University)

Wednesday, May 2nd, 2018

Time: 4:00-5:30p.m.  Place: Jeffery Hall 422

Speaker: M. Ram Murty (Queen's University)

Title: SPECIAL VALUES OF MODULAR $L$-SERIES.

Abstract: We will discuss the Rankin-Selberg method as well as the analytic continuation of Eisenstein series that allows us to evaluate special values of modular $L$-series at critical point (in the sense of Deligne).

Number Theory - Neha Prabhu (Queen's University)

Wednesday, April 4th, 2018

Time: 2:15 p.m.  Place: Jeffery Hall 319

Speaker: Neha Prabhu (Queen's University)

Title: Moments of the error term in the Sato-Tate law for elliptic curves.

Abstract: The Sato-Tate theorem for elliptic curves was proved by L. Clozel, M. Harris, N. Shepherd-Barron and R. Taylor in a series of papers from 2008-2010. Since the Sato-Tate law is an asymptotic statement, one is naturally interested in studying the nature of the error terms. In this talk, I shall describe some results relating to moments of the error term when we consider averages over certain families of elliptic curves. This is joint work with Stephan Baier.

Number Theory - Siddhi Pathak (Queen's University)

Wednesday, March 28th, 2018

Time: 2:15 p.m.  Place: Jeffery Hall 319

Speaker: Siddhi Pathak (Queen's University)

Title: On the primitivity of Dirichlet characters.

Abstract: A Dirichlet character modulo q is said to be imprimitive if it is induced from a lower level. A characterization of the primitivity of characters is the separability of the Gauss sum ( Fourier transform of $\chi$ ), i.e., $G_q(n, \bar{chi}) = \chi(n) G_q(1, \bar{ \chi } )$ for all n. In this talk, we discuss a paper of R. Daielda and N. Jones in which they introduce another way of extending primitive Dirichlet characters so that the above separability property holds even for imprimitive characters.

Number Theory - Francois Seguin (Queen's University)

Wednesday, March 21st, 2018

Time: 2:15 p.m.  Place: Jeffery Hall 319

Speaker: François Séguin (Queen's University)

Title: Frequency of primes dividing n and $\Phi_n$.

Abstract: In a previous talk, we have seen that at most one prime Pn, can divide both an integer n and the nth cyclotomic polynomial evaluated at some integer a. During this talk, we will use methods in Dirichlet series to investigate how often Pn actually divides the nth cyclotomic polynomial $\Phi_n$.

Number Theory - Arpita Kar (Queen's University)

Wednesday, March 14th, 2018

Time: 2:15 p.m.  Place: Jeffery Hall 319

Speaker: Arpita Kar (Queen's University)

Title: On the normal number of prime factors of Ramanujan Tau function.

Abstract: We will discuss various results concerning $\omega(\tau(p))$, $omega(\tau(n))$, $\omega(\tau(p+1))$ where $\tau$ denotes Ramanujan Tau function and $\omega(n)$ denotes the number of prime factors of $n$ counted without multiplicity. This is work in progress with Prof. Ram Murty.

Number Theory - M. Ram Murty (Queen's University)

Wednesday, March 7th, 2018

Time: 2:15 p.m.  Place: Jeffery Hall 319

Speaker: M. Ram Murty (Queen's University)

Title: The Central Limit Theorem in algebra and Number Theory.

Abstract: The central limit theorem is certainly one of the pinnacles of 20th century mathematics that has transformed human civilization extending its influence outside mathematics and now touching every other scientific discipline and beyond. I will give a short historical survey and then highlight how the central limit theorem has inspired the development of probabilistic number theory and probabilistic group theory. At the end, I will report on some old work with Kumar Murty and recent joint work with Arpita Kar and Neha Prabhu regarding arithmetical aspects of Fourier coefficients of modular forms.

Number Theory - Francois Seguin (Queen's University)

Wednesday, February 28th, 2018

Time: 2:15 p.m.  Place: Jeffery Hall 319

Speaker: François Séguin (Queen's University)

Title: Prime divisors of sparse values of cyclotomic polynomials.

Abstract: We will be presenting a result about the largest prime divisors of cyclotomic polynomials evaluated at a specific integer. We will also see how this ties in to problems we previously encountered.

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