Time and Place:  Friday, Jan. 28, 10:30-11:30 AM, 4325 HP Carleton

Speaker:  Kevin Hare (University of Waterloo)

Title: The Monic Integer Chebyshev Problem

Abstract:   We study the problem of finding monic integer polynomials $P$ with small supremum norm $||P||_I$
on an interval $I$.  The monic integer trasfinite diameter $t_{\mathrm{M}}(I)$ is defined as
t_{\mathrm{M}}(I) := {\inf_P ||P||_I^{1/\deg(P)},$
where the infimum is taken over all non-constant monic polynomials with integer coefficients. We
;show that if $I$ has length $l$ then $t_{\mathrm{M}}(I) = 1/2$.

We also consider the problem of determining $t_{\mathrm{M}}(I)$ when $I$ is a Farey interval.
We give some partial results, which support a conjecture of Borwein, Pinner and Pritsker concerning
this value.

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Time and Place:  Friday, Feb. 11, 10:30-11:30 AM, KED B015 University of Ottawa

Speaker:   Abdelkrim El basraoui (University of Ottawa)

Title:   Replicable functions

Abstract:   In this talk we present the notion of replicable functions and provide some examples related to
modular forms.

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Time and Place:  Friday, March 18, 10:30-11:30 AM, 4325 HP Carleton

Speaker:   Paul Mezo (Carleton University)

Title: Langlands reciprocity

Abstract:   We begin by describing the conjecture of Langlands reciprocity in the context of earlier
reciprocity laws in number theory. Afterwards we present some ideas which may help in
proving this conjecture.

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Time and Place:  Monday, March 28, 4:30-5:30 PM, 4325 HP Carleton

Speaker: Piroska Lakatos (Debrecen University)

Title: On zeroes of self-inversible polynomials

Abstract: Click here

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Time and Place:  Friday, Apr. 1, 10:30-11:30 AM, 4351 HP Carleton

Speaker: Ram Murty (Queen's University)

Title: Dirichlet series and hyperelliptic curves

Abstract: We will attach Dirichlet series to hyperelliptic and superelliptic curves to study the variation
of rational points of twists of such curves. This is joint work with Jung-Jo Lee.

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