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. [Permanent link] CARMA SEMINAR Speaker: Prof Wadim Zudilin, CARMA, The University of Newcastle Title: SSP report Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Dates: Wed, 15th Mar 2017 - Wed, 15th Mar 2017 [Permanent link] 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. [Permanent link] CARMA OANT SEMINAR Speaker: Prof Wadim Zudilin, CARMA, The University of Newcastle Title: Legendre polynomials squared Location: Room V206, Mathematics Building (Callaghan Campus) The University of Newcastle Access Grid Venue: UNewcastle [ENQUIRIES] Time and Date: 3:00 pm, Mon, 29th Oct 2012 Abstract: We discuss how the title is related to π. [Permanent link] 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. [Permanent link] 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. [Permanent link] 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. [Permanent link] 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. [Permanent link]