BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Bruce Berndt DTSTART:20210416T140000Z DTEND:20210416T150000Z DTSTAMP:20260422T212748Z UID:KoelnNumberTheory/1 DESCRIPTION:Title: Balanced Derivatives\, Identities\, and Bounds for Trigonometric Sums and Bessel Series\nby Bruce Berndt as part of Cologne Number The ory Seminars\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/KoelnNumberTheory/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Scott Ahlgren DTSTART:20210430T140000Z DTEND:20210430T150000Z DTSTAMP:20260422T212748Z UID:KoelnNumberTheory/2 DESCRIPTION:Title: Congruences for the partition function\nby Scott Ahlgren as part of Cologne Number Theory Seminars\n\n\nAbstract\nThe arithmetic prope rties of the ordinary partition function have been the topic of intensive study for many years. Much of the interest (and the difficulty) in this pr oblem arises from the fact that values of the partition function are given by the coefficients of a weakly holomorphic modular form of half integral weight. I’ll describe some new work with Olivia Beckwith and Martin Rau m and some new work with Patrick Allen and Shiang Tang which goes a long w ay towards explaining exactly when congruences for the partition function can occur. The main tools are techniques from the theory of modular forms\ , Galois representations\, and analytic number theory.\n LOCATION:https://researchseminars.org/talk/KoelnNumberTheory/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Danylo Radchenko DTSTART:20210507T140000Z DTEND:20210507T150000Z DTSTAMP:20260422T212748Z UID:KoelnNumberTheory/3 DESCRIPTION:Title: Fourier interpolation from zeros of the Riemann zeta function\nby Danylo Radchenko as part of Cologne Number Theory Seminars\n\n\nAbst ract\nI will talk about a recent result that shows that any sufficiently n ice even analytic function can be recovered from its values at the nontriv ial zeros of $\\zeta(1/2+is)$ and the values of its Fourier transform at l ogarithms of integers. The proof uses an explicit linear interpolation for mula\, whose construction involves modular integrals for the theta group. The talk is based on a joint work with Andriy Bondarenko and Kristian Seip .\n LOCATION:https://researchseminars.org/talk/KoelnNumberTheory/3/ END:VEVENT BEGIN:VEVENT SUMMARY:George Andrews DTSTART:20210514T140000Z DTEND:20210514T150000Z DTSTAMP:20260422T212748Z UID:KoelnNumberTheory/4 DESCRIPTION:Title: How Ramanujan May Have Discovered of the Mock Theta Functions\nby George Andrews as part of Cologne Number Theory Seminars\n\nAbstract : TBA\n LOCATION:https://researchseminars.org/talk/KoelnNumberTheory/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Jan Manschot DTSTART:20210521T140000Z DTEND:20210521T150000Z DTSTAMP:20260422T212748Z UID:KoelnNumberTheory/5 DESCRIPTION:Title: Modularity in Topological Field Theory\nby Jan Manschot as p art of Cologne Number Theory Seminars\n\n\nAbstract\nPartition functions o f topological quantum field theories are of interest in both physics and m athematics. A remarkable phenomenon is that these partition functions can often be expressed in terms of modular forms thanks to physical dualities of the theories. This talk will focus on the modularity of a theory known as $N=2^*$ super Yang-Mills with gauge group SU(2). I will explain how exp licit evaluation of the partition function of the topologically twist of t his theory on a smooth\, compact 4-manifold gives rise to bi-modular forms \, mock modular forms and generalizations. Based on joint work with G. W. Moore.\n LOCATION:https://researchseminars.org/talk/KoelnNumberTheory/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Frank Garvan DTSTART:20210604T140000Z DTEND:20210604T150000Z DTSTAMP:20260422T212748Z UID:KoelnNumberTheory/7 DESCRIPTION:Title: The Unimodal Sequence Conjectures\nby Frank Garvan as part o f Cologne Number Theory Seminars\n\n\nAbstract\nIn 2012 Bryson\, Ono\, Pit man and Rhoades showed how the generating functions\nfor certain strongly unimodal sequences are related to quantum modular\nand mock modular forms. They proved some parity results and conjectured\nsome mod 4 congruences f or the coefficients of these generating functions.\nIn 2016 Kim\, Lim and Lovejoy obtained similar results for odd-balanced\nunimodal sequences and made similar mod 4 conjectures. In 2017\nthe speaker made some similar con jectures for the Andrews spt-function.\n\nIn this talk we sketch the proof of one of these conjectures.\nThe proof involves connecting the Hurwitz c lass number function\nwith one of Ramanujan's mock theta functions.\n\nIf time permits we describe the necessary ingredients for approaching\nthe ot her conjectures.\n\nThis is joint work with Rong Chen.\n LOCATION:https://researchseminars.org/talk/KoelnNumberTheory/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Sameer Murthy DTSTART:20210611T140000Z DTEND:20210611T150000Z DTSTAMP:20260422T212748Z UID:KoelnNumberTheory/8 DESCRIPTION:Title: Microstates of supersymmetric black holes in AdS5\nby Sameer Murthy as part of Cologne Number Theory Seminars\n\n\nAbstract\nThe AdS/C FT correspondence predicts that the microstates of supersymmetric black ho les in 5-dimensional Anti de Sitter space are quantum states of the dual 4 -dimensional super Yang-Mills (SYM) theory\, which are captured by a certa in integral over unitary matrices. I will present analytical and numerical analyses of this matrix integral which show that the asymptotic growth of states at large charge agrees with that of the dual black hole microstate s. I will then show how a deformation of the matrix integral allows us to find large-N saddle-points and the resultant phase structure of SYM. There is an infinite family of large-N saddle points (phases) labelled by ratio nal points\, one of which is identified with the black hole. The deformati on is closely related to the Bloch-Wigner elliptic dilogarithm\, a functio n introduced by number theorists.\n LOCATION:https://researchseminars.org/talk/KoelnNumberTheory/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Riad Masri DTSTART:20210625T140000Z DTEND:20210625T150000Z DTSTAMP:20260422T212748Z UID:KoelnNumberTheory/9 DESCRIPTION:Title: Equidistribution of Fourier coefficients of weak Maass forms \nby Riad Masri as part of Cologne Number Theory Seminars\n\n\nAbstract\nI n this talk\, I will discuss joint work with Wei-Lun Tsai which shows that the normalized Fourier coefficients of a generic family of weak Maass for ms of weight $k$ and prime level $p$ become quantitatively equidistributed on $[-1\,1]$ with respect to a natural probability measure as $p$ approac hes infinity.\n LOCATION:https://researchseminars.org/talk/KoelnNumberTheory/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Stephen Kudla DTSTART:20210702T140000Z DTEND:20210702T150000Z DTSTAMP:20260422T212748Z UID:KoelnNumberTheory/10 DESCRIPTION:Title: The case of the N-gon\nby Stephen Kudla as part of Cologne Number Theory Seminars\n\n\nAbstract\nIn joint work with Jens Funke\, we c onstruct indefinite theta series for the data \nproposed in S. Alexandrov\ , S. Banerjee\, J. Manschot\, and B. Pioline\, Multiple D3-instantons and mock modular forms II. \nThis data can be viewed as defining an N-gon $\\ gamma$ in the symmetric space D of oriented negative 2-planes in \nan inne r product space of signature (m-2\,2). As in our earlier work\, the resul ting theta series is defined\nby integrating the KM theta 2-form over a su rface S in D with boundary $\\gamma$. The problem of actually constructin g such a surface S\nis avoided by the introduction of a homotopy argument. This new method provides an interpretation of the \nsubtle sign invariant as a linking number and should be applicable in more general situations.\ n LOCATION:https://researchseminars.org/talk/KoelnNumberTheory/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Jeremy Lovejoy DTSTART:20210709T140000Z DTEND:20210709T150000Z DTSTAMP:20260422T212748Z UID:KoelnNumberTheory/11 DESCRIPTION:Title: Parity Bias in Partitions\nby Jeremy Lovejoy as part of Col ogne Number Theory Seminars\n\n\nAbstract\nBy parity bias in partitions\, we mean the tendency of \npartitions to have more odd parts than even par ts. In this talk we \nwill discuss exact and asymptotic results for $p_ e(n)$ and $p_o(n)$\, which \ndenote the number of partitions of n with mo re even parts than odd \nparts and the number of partitions of n with mor e odd parts than even \nparts\, respectively. We also discuss some open problems\, one of which \nconcerns a q-series with an "almost regular" si gn pattern\, reminiscent \nof some notorious q-series found in Ramanujan' s lost notebook. This \nis joint work with Byungchan Kim and Eunmi Kim.\ n LOCATION:https://researchseminars.org/talk/KoelnNumberTheory/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Ken Ono DTSTART:20210716T140000Z DTEND:20210716T150000Z DTSTAMP:20260422T212748Z UID:KoelnNumberTheory/12 DESCRIPTION:Title: Variants of Lehmer's Conjecture on Ramanujan's tau-function \nby Ken Ono as part of Cologne Number Theory Seminars\n\n\nAbstract\nIn t he spirit of Lehmer's unresolved speculation on the non-vanishing of Raman ujan's tau-function\, it is natural to ask whether a fixed integer is a va lue of $\\tau(n)$\, or is a Fourier coefficient of any given modular form. In joint work with J. Balakrishnan\, W. Craig\, and W.-L. Tsai\, the spea ker has obtained the first results for such questions. This lecture will d escribe the latest results on such questions.\n LOCATION:https://researchseminars.org/talk/KoelnNumberTheory/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Ken Ono DTSTART:20210906T130000Z DTEND:20210906T140000Z DTSTAMP:20260422T212748Z UID:KoelnNumberTheory/13 DESCRIPTION:Title: Frobenius Trace Distributions for Gaussian hypergeometric varie ties\nby Ken Ono as part of Cologne Number Theory Seminars\n\n\nAbstra ct\nIn the 1980's\, J. Greene defined hypergeometric functions over finite fields using Jacobi sums. The framework of his theory establishes that th ese functions possess many properties that are analogous to those of the c lassical hypergeometric series studied by Gauss and Kummer. These function s have played important roles in the study of Ap\\'ery-style supercongruen ces\, the Eichler-Selberg trace formula\, Galois representations\, and zet a-functions of arithmetic varieties. We study the value distribution (over large finite fields) of natural families of these functions. For the $_2F _1$ functions\, the limiting distribution is semicircular\, whereas the di stribution for the $_3F_2$ functions is the more exotic Batman distributio n.\n LOCATION:https://researchseminars.org/talk/KoelnNumberTheory/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Wei-Lun Tsai DTSTART:20220128T140000Z DTEND:20220128T150000Z DTSTAMP:20260422T212748Z UID:KoelnNumberTheory/14 DESCRIPTION:by Wei-Lun Tsai as part of Cologne Number Theory Seminars\n\nA bstract: TBA\n LOCATION:https://researchseminars.org/talk/KoelnNumberTheory/14/ END:VEVENT END:VCALENDAR