Department of Mathematics and Computer Science Number Theory and Combinatorics Seminar Fall 2022 For more information, contact Félix Baril Boudreau or Bobby Miraftab . Talks are usually at noon on Monday in room M1040 (Markin Hall). All times are Mountain Time. The live access zoom link is available here and on researchseminars.org, and also sent to our mailing list.
 The next talk: Sep 26 at noon in M1040 Dang-Khoa Nguyen (University of Calgary) Height gaps for coefficients of D-finite power series A power series $f(x_1,\ldots,x_m)\in \mathbb{C}[[x_1,\ldots,x_m]]$ is said to be D-finite if all the partial derivatives of $f$ span a finite dimensional vector space over the field $\mathbb{C}(x_1,\ldots,x_m)$. For the univariate series $f(x)=\sum a_nx^n$, this is equivalent to the condition that the sequence $(a_n)$ is P-recursive meaning a non-trivial linear recurrence relation of the form: $$P_d(n)a_{n+d}+\cdots+P_0(n)a_n=0$$ where the $P_i$'s are polynomials. In this talk, we consider D-finite power series with algebraic coefficients and discuss the growth of the Weil height of these coefficients. This is from a joint work with Jason Bell and Umberto Zannier in 2019 and a more recent work in June 2022.
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 Date Speaker Title Sep 12 everyone Organizational meeting and problem session at noon in M1040 (University of Lethbridge) Please bring your favourite (math) problems. Anyone with a problem to share will be given about 5 minutes to present it. We will also choose most of the speakers for the rest of the semester. no seminar on September 19    (University Holiday) Sep 26 Dang-Khoa Nguyen Height gaps for coefficients of D-finite power series at noon in M1040 (University of Calgary) A power series $f(x_1,\ldots,x_m)\in \mathbb{C}[[x_1,\ldots,x_m]]$ is said to be D-finite if all the partial derivatives of $f$ span a finite dimensional vector space over the field $\mathbb{C}(x_1,\ldots,x_m)$. For the univariate series $f(x)=\sum a_nx^n$, this is equivalent to the condition that the sequence $(a_n)$ is P-recursive meaning a non-trivial linear recurrence relation of the form: $$P_d(n)a_{n+d}+\cdots+P_0(n)a_n=0$$ where the $P_i$'s are polynomials. In this talk, we consider D-finite power series with algebraic coefficients and discuss the growth of the Weil height of these coefficients. This is from a joint work with Jason Bell and Umberto Zannier in 2019 and a more recent work in June 2022. Oct 3 Debanjana Kundu Title TBA at noon in M1040 (University of British Columbia) Abstract TBA no seminar on October 10    (Thanksgiving) Oct 17 Elchin Hasanalizade Title TBA at noon in M1040 (University of Lethbridge) Abstract TBA Oct 24 Speaker TBA Title TBA at noon in M1040 (University of Lethbridge) Abstract TBA Oct 31 Hugo Chapdelaine Title TBA at noon via zoom (Université Laval) Abstract TBA no seminar on November 7    (Reading Week) Nov 14 Julie Desjardins Title TBA at noon via zoom (University of Toronto) Abstract TBA Nov 21 Solaleh Bolvardizadeh Title TBA at noon in M1040 (University of Lethbridge) Abstract TBA Nov 28 Mathieu Dutour Title TBA at noon in M1040 (University of Alberta) Abstract TBA Dec 5 Alexandra Florea Title TBA at noon via zoom (University of California - Irvine) Abstract TBA
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