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BEGIN:VEVENT
SUMMARY:Bruce Berndt
DTSTART:20210416T140000Z
DTEND:20210416T150000Z
DTSTAMP:20260404T111006Z
UID:KoelnNumberTheory/1
DESCRIPTION:Title: Balanced Derivatives\, Identities\, and Bounds for Trigon
ometric Sums and Bessel Series\nby Bruce Berndt as part of Cologne Num
ber Theory Seminars\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/KoelnNumberTheory/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Scott Ahlgren
DTSTART:20210430T140000Z
DTEND:20210430T150000Z
DTSTAMP:20260404T111006Z
UID:KoelnNumberTheory/2
DESCRIPTION:Title: Congruences for the partition function\nby Scott Ahlg
ren as part of Cologne Number Theory Seminars\n\n\nAbstract\nThe arithmeti
c properties of the ordinary partition function have been the topic of int
ensive study for many years. Much of the interest (and the difficulty) in
this problem arises from the fact that values of the partition function ar
e given by the coefficients of a weakly holomorphic modular form of half i
ntegral weight. I’ll describe some new work with Olivia Beckwith and Mar
tin Raum and some new work with Patrick Allen and Shiang Tang which goes a
long way towards explaining exactly when congruences for the partition fu
nction can occur. The main tools are techniques from the theory of modular
forms\, Galois representations\, and analytic number theory.\n
LOCATION:https://stable.researchseminars.org/talk/KoelnNumberTheory/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Danylo Radchenko
DTSTART:20210507T140000Z
DTEND:20210507T150000Z
DTSTAMP:20260404T111006Z
UID:KoelnNumberTheory/3
DESCRIPTION:Title: Fourier interpolation from zeros of the Riemann zeta func
tion\nby Danylo Radchenko as part of Cologne Number Theory Seminars\n\
n\nAbstract\nI will talk about a recent result that shows that any suffici
ently nice even analytic function can be recovered from its values at the
nontrivial zeros of $\\zeta(1/2+is)$ and the values of its Fourier transfo
rm at logarithms of integers. The proof uses an explicit linear interpolat
ion formula\, whose construction involves modular integrals for the theta
group. The talk is based on a joint work with Andriy Bondarenko and Kristi
an Seip.\n
LOCATION:https://stable.researchseminars.org/talk/KoelnNumberTheory/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:George Andrews
DTSTART:20210514T140000Z
DTEND:20210514T150000Z
DTSTAMP:20260404T111006Z
UID:KoelnNumberTheory/4
DESCRIPTION:Title: How Ramanujan May Have Discovered of the Mock Theta Funct
ions\nby George Andrews as part of Cologne Number Theory Seminars\n\nA
bstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/KoelnNumberTheory/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jan Manschot
DTSTART:20210521T140000Z
DTEND:20210521T150000Z
DTSTAMP:20260404T111006Z
UID:KoelnNumberTheory/5
DESCRIPTION:Title: Modularity in Topological Field Theory\nby Jan Mansch
ot as part of Cologne Number Theory Seminars\n\n\nAbstract\nPartition func
tions of topological quantum field theories are of interest in both physic
s and mathematics. A remarkable phenomenon is that these partition functio
ns can often be expressed in terms of modular forms thanks to physical dua
lities 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 explicit evaluation of the partition function of the topologically twi
st of this theory on a smooth\, compact 4-manifold gives rise to bi-modula
r forms\, mock modular forms and generalizations. Based on joint work with
G. W. Moore.\n
LOCATION:https://stable.researchseminars.org/talk/KoelnNumberTheory/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Frank Garvan
DTSTART:20210604T140000Z
DTEND:20210604T150000Z
DTSTAMP:20260404T111006Z
UID:KoelnNumberTheory/7
DESCRIPTION:Title: The Unimodal Sequence Conjectures\nby Frank Garvan as
part of Cologne Number Theory Seminars\n\n\nAbstract\nIn 2012 Bryson\, On
o\, Pitman and Rhoades showed how the generating functions\nfor certain st
rongly unimodal sequences are related to quantum modular\nand mock modular
forms. They proved some parity results and conjectured\nsome mod 4 congru
ences for the coefficients of these generating functions.\nIn 2016 Kim\, L
im and Lovejoy obtained similar results for odd-balanced\nunimodal sequenc
es and made similar mod 4 conjectures. In 2017\nthe speaker made some simi
lar conjectures for the Andrews spt-function.\n\nIn this talk we sketch th
e proof of one of these conjectures.\nThe proof involves connecting the Hu
rwitz class number function\nwith one of Ramanujan's mock theta functions.
\n\nIf time permits we describe the necessary ingredients for approaching\
nthe other conjectures.\n\nThis is joint work with Rong Chen.\n
LOCATION:https://stable.researchseminars.org/talk/KoelnNumberTheory/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sameer Murthy
DTSTART:20210611T140000Z
DTEND:20210611T150000Z
DTSTAMP:20260404T111006Z
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\nTh
e AdS/CFT correspondence predicts that the microstates of supersymmetric b
lack holes 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 certain integral over unitary matrices. I will present analytical and nu
merical analyses of this matrix integral which show that the asymptotic gr
owth of states at large charge agrees with that of the dual black hole mic
rostates. 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 b
y rational points\, one of which is identified with the black hole. The de
formation is closely related to the Bloch-Wigner elliptic dilogarithm\, a
function introduced by number theorists.\n
LOCATION:https://stable.researchseminars.org/talk/KoelnNumberTheory/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Riad Masri
DTSTART:20210625T140000Z
DTEND:20210625T150000Z
DTSTAMP:20260404T111006Z
UID:KoelnNumberTheory/9
DESCRIPTION:Title: Equidistribution of Fourier coefficients of weak Maass fo
rms\nby Riad Masri as part of Cologne Number Theory Seminars\n\n\nAbst
ract\nIn this talk\, I will discuss joint work with Wei-Lun Tsai which sho
ws that the normalized Fourier coefficients of a generic family of weak Ma
ass forms of weight $k$ and prime level $p$ become quantitatively equidist
ributed on $[-1\,1]$ with respect to a natural probability measure as $p$
approaches infinity.\n
LOCATION:https://stable.researchseminars.org/talk/KoelnNumberTheory/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stephen Kudla
DTSTART:20210702T140000Z
DTEND:20210702T150000Z
DTSTAMP:20260404T111006Z
UID:KoelnNumberTheory/10
DESCRIPTION:Title: The case of the N-gon\nby Stephen Kudla as part of C
ologne Number Theory Seminars\n\n\nAbstract\nIn joint work with Jens Funke
\, we construct indefinite theta series for the data \nproposed in S. Alex
androv\, S. Banerjee\, J. Manschot\, and B. Pioline\, Multiple D3-instant
ons 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 \n
an inner product space of signature (m-2\,2). As in our earlier work\, th
e resulting theta series is defined\nby integrating the KM theta 2-form ov
er a surface S in D with boundary $\\gamma$. The problem of actually cons
tructing such a surface S\nis avoided by the introduction of a homotopy ar
gument. This new method provides an interpretation of the \nsubtle sign in
variant as a linking number and should be applicable in more general situa
tions.\n
LOCATION:https://stable.researchseminars.org/talk/KoelnNumberTheory/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeremy Lovejoy
DTSTART:20210709T140000Z
DTEND:20210709T150000Z
DTSTAMP:20260404T111006Z
UID:KoelnNumberTheory/11
DESCRIPTION:Title: Parity Bias in Partitions\nby Jeremy Lovejoy as part
of Cologne Number Theory Seminars\n\n\nAbstract\nBy parity bias in partit
ions\, we mean the tendency of \npartitions to have more odd parts than e
ven parts. 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 more even parts than odd \nparts and the number of partitions of n w
ith more odd parts than even \nparts\, respectively. We also discuss som
e open problems\, one of which \nconcerns a q-series with an "almost regu
lar" sign pattern\, reminiscent \nof some notorious q-series found in Ram
anujan's lost notebook. This \nis joint work with Byungchan Kim and Eunm
i Kim.\n
LOCATION:https://stable.researchseminars.org/talk/KoelnNumberTheory/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ken Ono
DTSTART:20210716T140000Z
DTEND:20210716T150000Z
DTSTAMP:20260404T111006Z
UID:KoelnNumberTheory/12
DESCRIPTION:Title: Variants of Lehmer's Conjecture on Ramanujan's tau-funct
ion\nby Ken Ono as part of Cologne Number Theory Seminars\n\n\nAbstrac
t\nIn the spirit of Lehmer's unresolved speculation on the non-vanishing o
f Ramanujan's tau-function\, it is natural to ask whether a fixed integer
is a value of $\\tau(n)$\, or is a Fourier coefficient of any given modula
r form. In joint work with J. Balakrishnan\, W. Craig\, and W.-L. Tsai\, t
he speaker has obtained the first results for such questions. This lecture
will describe the latest results on such questions.\n
LOCATION:https://stable.researchseminars.org/talk/KoelnNumberTheory/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ken Ono
DTSTART:20210906T130000Z
DTEND:20210906T140000Z
DTSTAMP:20260404T111006Z
UID:KoelnNumberTheory/13
DESCRIPTION:Title: Frobenius Trace Distributions for Gaussian hypergeometri
c varieties\nby Ken Ono as part of Cologne Number Theory Seminars\n\n\
nAbstract\nIn the 1980's\, J. Greene defined hypergeometric functions over
finite fields using Jacobi sums. The framework of his theory establishes
that these functions possess many properties that are analogous to those o
f the classical hypergeometric series studied by Gauss and Kummer. These f
unctions have played important roles in the study of Ap\\'ery-style superc
ongruences\, the Eichler-Selberg trace formula\, Galois representations\,
and zeta-functions of arithmetic varieties. We study the value distributio
n (over large finite fields) of natural families of these functions. For t
he $_2F_1$ functions\, the limiting distribution is semicircular\, whereas
the distribution for the $_3F_2$ functions is the more exotic Batman dist
ribution.\n
LOCATION:https://stable.researchseminars.org/talk/KoelnNumberTheory/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wei-Lun Tsai
DTSTART:20220128T140000Z
DTEND:20220128T150000Z
DTSTAMP:20260404T111006Z
UID:KoelnNumberTheory/14
DESCRIPTION:by Wei-Lun Tsai as part of Cologne Number Theory Seminars\n\nA
bstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/KoelnNumberTheory/14/
END:VEVENT
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