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BEGIN:VEVENT
SUMMARY:Bruce Berndt
DTSTART;VALUE=DATE-TIME:20210416T140000Z
DTEND;VALUE=DATE-TIME:20210416T150000Z
DTSTAMP;VALUE=DATE-TIME:20231130T083109Z
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;VALUE=DATE-TIME:20210430T140000Z
DTEND;VALUE=DATE-TIME:20210430T150000Z
DTSTAMP;VALUE=DATE-TIME:20231130T083109Z
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;VALUE=DATE-TIME:20210507T140000Z
DTEND;VALUE=DATE-TIME:20210507T150000Z
DTSTAMP;VALUE=DATE-TIME:20231130T083109Z
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;VALUE=DATE-TIME:20210514T140000Z
DTEND;VALUE=DATE-TIME:20210514T150000Z
DTSTAMP;VALUE=DATE-TIME:20231130T083109Z
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;VALUE=DATE-TIME:20210521T140000Z
DTEND;VALUE=DATE-TIME:20210521T150000Z
DTSTAMP;VALUE=DATE-TIME:20231130T083109Z
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;VALUE=DATE-TIME:20210604T140000Z
DTEND;VALUE=DATE-TIME:20210604T150000Z
DTSTAMP;VALUE=DATE-TIME:20231130T083109Z
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;VALUE=DATE-TIME:20210611T140000Z
DTEND;VALUE=DATE-TIME:20210611T150000Z
DTSTAMP;VALUE=DATE-TIME:20231130T083109Z
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;VALUE=DATE-TIME:20210625T140000Z
DTEND;VALUE=DATE-TIME:20210625T150000Z
DTSTAMP;VALUE=DATE-TIME:20231130T083109Z
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;VALUE=DATE-TIME:20210702T140000Z
DTEND;VALUE=DATE-TIME:20210702T150000Z
DTSTAMP;VALUE=DATE-TIME:20231130T083109Z
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;VALUE=DATE-TIME:20210709T140000Z
DTEND;VALUE=DATE-TIME:20210709T150000Z
DTSTAMP;VALUE=DATE-TIME:20231130T083109Z
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;VALUE=DATE-TIME:20210716T140000Z
DTEND;VALUE=DATE-TIME:20210716T150000Z
DTSTAMP;VALUE=DATE-TIME:20231130T083109Z
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;VALUE=DATE-TIME:20210906T130000Z
DTEND;VALUE=DATE-TIME:20210906T140000Z
DTSTAMP;VALUE=DATE-TIME:20231130T083109Z
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;VALUE=DATE-TIME:20220128T140000Z
DTEND;VALUE=DATE-TIME:20220128T150000Z
DTSTAMP;VALUE=DATE-TIME:20231130T083109Z
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/
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