• CARMA SEMINAR
  • Speaker: Prof Wadim Zudilin, CARMA, The University of Newcastle
  • Title: Hypergeometric heritage of W.N. Bailey
  • Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 4:00 pm, Tue, 16th May 2017
  • Abstract:

    Part of my 2016 SSP included completion of a semi-historical review on the mathematics of W.N. Bailey, a familiar name in some combinatorics circles in relation with the "Bailey lemma" and "Bailey pairs." My personal encounters with the mathematician from the first half of the 20th century were somewhat different and more related to applications of special functions to number theory—the subject Bailey had never dealt with himself. One motivation for my writing was the place where I spent my SSP—details to be revealed in the talk. There will be some formulas displayed, sometimes scary, but they will serve as a background to historical achievements. Broad audience is welcome.

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  • CARMA OANT SEMINAR
  • Speaker: Prof Wadim Zudilin, CARMA, The University of Newcastle
  • Title: Mock theta functions
  • Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Access Grid Venue: CARMA [ENQUIRIES]
  • Time and Date: 3:00 pm, Tue, 3rd Sep 2013
  • Abstract:

    In his deathbed letter to G.H. Hardy, Ramanujan gave a vague definition of a mock modular function: at each root of unity its asymptotics matches the one of a modular form, though a choice of the modular function depends on the root of unity. Recently Folsom, Ono and Rhoades have proved an elegant result about the match for a general family related to Dyson’s rank (mock theta) function and the Andrews—Garvan crank (modular) function. In my talk I will outline some heuristics and elementary ingredients of the proof.

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  • CARMA NUMBER THEORY SHORT COURSE
  • Speaker: Prof Wadim Zudilin, CARMA, The University of Newcastle
  • Title: Hilbert's 7th Problem
  • Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Dates: Wed, 4th Apr 2012 - Wed, 4th Apr 2012
  • 11:00 am - 1:30 pm and 2:30 pm - 4:00 pm
  • Abstract:

    The problem posed by Hilbert in 1900 was resolved in the 1930s independently by A. Gelfond and Th. Schneider. The statement is that $a^b$ is transcendental for algebraic $a \ne 0,1$ and irrational algebraic $b$. The aim of the two 2-hour lectures is to give a proof of this result using the so-called method of interpolation determinants.

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  • CARMA COLLOQUIUM
  • Speaker: Prof Wadim Zudilin, CARMA, The University of Newcastle
  • Title: Odds of Riemann's zeta function
  • Location: Room V129, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 4:00 pm, Thu, 4th Aug 2011
  • Abstract:

    In my talk I will try to overview ideas behind (still recent) achievements on arithmetic properties of numbers $\zeta(s)=\sum_{n=1}^\infty n^{-s}$ for integral $s\ge2$, with more emphasis on odd $s$. The basic ingredients of proofs are generalized hypergeometric functions and linear independence criteria. I will also address some "most recent" results and observations in the subject, as well as connections with other problems in number theory.

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  • CARMA ANALYSIS AND NUMBER THEORY SEMINAR
  • Speaker: Prof Wadim Zudilin, CARMA, The University of Newcastle
  • Title: Ramanujan-style mathematics for Mahler measures
  • Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 3:30 pm, Wed, 13th Apr 2011
  • Abstract:

    In my talk I will review some recent progress on evaluations of Mahler measures via hypergeometric series and Dirichlet L-series. I will provide more details for the case of the Mahler measure of $1+x+1/x+y+1/y$, whose evaluation was observed by C. Deninger and conjectured by D. Boyd (1997). The main ingredients are relations between modular forms and hypergeometric series in the spirit of Ramanujan. The talk is based on joint work with Mat Rogers.

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  • CARMA ANALYSIS AND NUMBER THEORY SEMINAR
  • Speaker: Prof Wadim Zudilin, CARMA, The University of Newcastle
  • Title: Hypergeometric evaluations of lattice sums
  • Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 3:30 pm, Wed, 8th Sep 2010
  • Abstract:

    It is an expository talk about (conjectural) hypergeometric evaluations of lattice sums

    $F(a,b,c,d)=(a+b+c+d)^2\sum_{n_j=-\infty,\ j=1,2,3,4}^\infty \frac{(-1)^{n_1+n_2+n_3+n_4}}{(a(6n_1+1)^2+b(6n_2+1)^2+c(6n_3+1)^2+d(6n_4+1)^2)^2}$

    which arise as the values of L-functions of certain elliptic curves.

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