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BEGIN:VEVENT
SUMMARY:Dennis Stanton (University of Minnesota)
DTSTART;VALUE=DATE-TIME:20200818T160000Z
DTEND;VALUE=DATE-TIME:20200818T170000Z
DTSTAMP;VALUE=DATE-TIME:20230925T221238Z
UID:VandyNumberTheory/1
DESCRIPTION:Title: Historical remarks and recent conjectures for integer partitions
\nby Dennis Stanton (University of Minnesota) as part of Vanderbilt Nu
mber Theory Seminar\n\n\nAbstract\nI will concentrate on two areas:\n\n(1)
ranks\, cranks\, and the Ramanujan congruences for $p(n)$\,\n\n(2) the Ro
gers-Ramanujan identities and MacMahon’s combinatorial versions.\n\nSeve
ral open questions will be presented.\n
LOCATION:https://researchseminars.org/talk/VandyNumberTheory/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicolas Allen Smoot (RISC)
DTSTART;VALUE=DATE-TIME:20200908T160000Z
DTEND;VALUE=DATE-TIME:20200908T170000Z
DTSTAMP;VALUE=DATE-TIME:20230925T221238Z
UID:VandyNumberTheory/2
DESCRIPTION:Title: Partition congruences and the localization method\nby Nicola
s Allen Smoot (RISC) as part of Vanderbilt Number Theory Seminar\n\n\nAbst
ract\nA notable problem in partition theory is the study of infinite famil
ies of partition congruences modulo powers of a prime. It has recently be
en discovered that there exist congruence families\, associated with a mod
ular curve of genus 0\, for which the traditional methods of proof fail.
One such congruence family is related to the spt analogue of the omega moc
k theta function. We recently gave a proof of this congruence family by a
new method\, based on the manipulation of a localized polynomial ring\, r
ather than by studying $ \\mathbb{Z}[X] $ via the more classical methods.
We will give a brief outline of this method\, its surprisingly unique cha
racteristics\, and its potential for future work.\n
LOCATION:https://researchseminars.org/talk/VandyNumberTheory/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Walter Bridges (LSU)
DTSTART;VALUE=DATE-TIME:20200915T160000Z
DTEND;VALUE=DATE-TIME:20200915T170000Z
DTSTAMP;VALUE=DATE-TIME:20230925T221238Z
UID:VandyNumberTheory/3
DESCRIPTION:Title: Statistics for Partitions and Unimodal Sequences\nby Walter
Bridges (LSU) as part of Vanderbilt Number Theory Seminar\n\n\nAbstract\nT
he study of the asymptotic distribution of statistics for partitions lies
at a crossroads of classical methods and the more recent probabilistic fra
mework of Fristedt and others. We discuss two results---one that uses the
probabilistic machinery and one that calls for a more direct ``elementary
'' method.\n\nWe first review Fristedt's conditioning device and\, followi
ng Romik\, implement a similar construction to give an asymptotic formula
for distinct parts partitions of $n$ with largest part bounded by $t\\sqrt
{n}$. We discuss the intuitive advantages of this approach over a classic
al circle method/saddle-point method proof.\n\nWe then turn to unimodal se
quences\, a generalization of partitions where parts are allowed to increa
se and then decrease. We use an elementary approach to prove limit shapes
for the diagrams of strongly\, semi-strict and unrestricted unimodal sequ
ences. We also recover a limit shape for overpartitions via a simple tran
sfer.\n
LOCATION:https://researchseminars.org/talk/VandyNumberTheory/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gene Kopp (University of Bristol)
DTSTART;VALUE=DATE-TIME:20200922T160000Z
DTEND;VALUE=DATE-TIME:20200922T170000Z
DTSTAMP;VALUE=DATE-TIME:20230925T221238Z
UID:VandyNumberTheory/4
DESCRIPTION:Title: Indefinite zeta functions\nby Gene Kopp (University of Brist
ol) as part of Vanderbilt Number Theory Seminar\n\n\nAbstract\nIndefinite
theta functions were introduced by Sander Zwegers in his thesis\, in which
they are used to generalize and explain the remarkable properties of Rama
nujan’s mock theta functions. In this talk\, we will discuss the Mellin
transforms of indefinite theta functions\, which we call indefinite zeta f
unctions. Indefinite zeta functions satisfy a functional equation and live
in a continuous parameter space. Special points in this parameter space y
ield arithmetically interesting zeta functions\, such as certain differenc
es of ray class zeta functions of real quadratic fields. Generally\, howev
er\, indefinite zeta functions are not Dirichlet series but have a series
expansion involving hypergeometric functions. We prove a Kronecker limit f
ormula in dimension 2 for indefinite zeta functions as s=0\, which special
izes to a new analytic formula for Stark class invariants.\n
LOCATION:https://researchseminars.org/talk/VandyNumberTheory/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hannah Burson (University of Minnesota)
DTSTART;VALUE=DATE-TIME:20200929T160000Z
DTEND;VALUE=DATE-TIME:20200929T170000Z
DTSTAMP;VALUE=DATE-TIME:20230925T221238Z
UID:VandyNumberTheory/5
DESCRIPTION:Title: Mock theta functions\, false theta functions\, and weighted odd
Ferrers diagrams.\nby Hannah Burson (University of Minnesota) as part
of Vanderbilt Number Theory Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/VandyNumberTheory/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikos Diamantis (University of Nottingham)
DTSTART;VALUE=DATE-TIME:20201006T160000Z
DTEND;VALUE=DATE-TIME:20201006T170000Z
DTSTAMP;VALUE=DATE-TIME:20230925T221238Z
UID:VandyNumberTheory/6
DESCRIPTION:Title: Modular iterated integrals associated with cusp forms.\nby N
ikos Diamantis (University of Nottingham) as part of Vanderbilt Number The
ory Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/VandyNumberTheory/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeremy Rouse (Wake Forest University)
DTSTART;VALUE=DATE-TIME:20201013T160000Z
DTEND;VALUE=DATE-TIME:20201013T170000Z
DTSTAMP;VALUE=DATE-TIME:20230925T221238Z
UID:VandyNumberTheory/7
DESCRIPTION:Title: Integers represented by positive-definite quadratic forms and Pe
tersson inner products.\nby Jeremy Rouse (Wake Forest University) as p
art of Vanderbilt Number Theory Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/VandyNumberTheory/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Schneider (University of Georgia)
DTSTART;VALUE=DATE-TIME:20201027T160000Z
DTEND;VALUE=DATE-TIME:20201027T170000Z
DTSTAMP;VALUE=DATE-TIME:20230925T221238Z
UID:VandyNumberTheory/8
DESCRIPTION:Title: A multiplicative theory of (additive) partitions.\nby Robert
Schneider (University of Georgia) as part of Vanderbilt Number Theory Sem
inar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/VandyNumberTheory/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Madeline Locus Dawsey (University of Texas at Tyler)
DTSTART;VALUE=DATE-TIME:20201103T170000Z
DTEND;VALUE=DATE-TIME:20201103T180000Z
DTSTAMP;VALUE=DATE-TIME:20230925T221238Z
UID:VandyNumberTheory/9
DESCRIPTION:Title: Modular Forms and Ramsey Theory.\nby Madeline Locus Dawsey (
University of Texas at Tyler) as part of Vanderbilt Number Theory Seminar\
n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/VandyNumberTheory/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:William Craig (University of Virginia)
DTSTART;VALUE=DATE-TIME:20201109T160000Z
DTEND;VALUE=DATE-TIME:20201109T170000Z
DTSTAMP;VALUE=DATE-TIME:20230925T221238Z
UID:VandyNumberTheory/10
DESCRIPTION:Title: Variants of Lehmer’s Conjecture.\nby William Craig (Unive
rsity of Virginia) as part of Vanderbilt Number Theory Seminar\n\nAbstract
: TBA\n
LOCATION:https://researchseminars.org/talk/VandyNumberTheory/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Osburn (University College Dublin)
DTSTART;VALUE=DATE-TIME:20201117T170000Z
DTEND;VALUE=DATE-TIME:20201117T180000Z
DTSTAMP;VALUE=DATE-TIME:20230925T221238Z
UID:VandyNumberTheory/11
DESCRIPTION:Title: Generalized Fishburn numbers and torus knots.\nby Robert Os
burn (University College Dublin) as part of Vanderbilt Number Theory Semin
ar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/VandyNumberTheory/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ankush Goswami (RISC)
DTSTART;VALUE=DATE-TIME:20201124T170000Z
DTEND;VALUE=DATE-TIME:20201124T180000Z
DTSTAMP;VALUE=DATE-TIME:20230925T221238Z
UID:VandyNumberTheory/12
DESCRIPTION:Title: Arithmeticity and quantum modularity for generalized Kontsevich
-Zagier strange series.\nby Ankush Goswami (RISC) as part of Vanderbil
t Number Theory Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/VandyNumberTheory/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lola Thompson (Utrecht University)
DTSTART;VALUE=DATE-TIME:20201201T170000Z
DTEND;VALUE=DATE-TIME:20201201T180000Z
DTSTAMP;VALUE=DATE-TIME:20230925T221238Z
UID:VandyNumberTheory/13
DESCRIPTION:Title: Counting quaternion algebras\, with applications to spectral ge
ometry.\nby Lola Thompson (Utrecht University) as part of Vanderbilt N
umber Theory Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/VandyNumberTheory/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amanda Folsom (Amherst College)
DTSTART;VALUE=DATE-TIME:20201208T170000Z
DTEND;VALUE=DATE-TIME:20201208T180000Z
DTSTAMP;VALUE=DATE-TIME:20230925T221238Z
UID:VandyNumberTheory/14
DESCRIPTION:Title: Eisenstein series\, cotangent-zeta sums\, knots\, and quantum m
odular forms.\nby Amanda Folsom (Amherst College) as part of Vanderbil
t Number Theory Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/VandyNumberTheory/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jesse Thorner (University of Illinois)
DTSTART;VALUE=DATE-TIME:20210203T170000Z
DTEND;VALUE=DATE-TIME:20210203T180000Z
DTSTAMP;VALUE=DATE-TIME:20230925T221238Z
UID:VandyNumberTheory/15
DESCRIPTION:Title: An approximate form of Artin’s holomorphy conjecture and nonv
anishing of Artin L-functions.\nby Jesse Thorner (University of Illino
is) as part of Vanderbilt Number Theory Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/VandyNumberTheory/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sarah Peluse (Princeton/IAS)
DTSTART;VALUE=DATE-TIME:20210210T170000Z
DTEND;VALUE=DATE-TIME:20210210T180000Z
DTSTAMP;VALUE=DATE-TIME:20230925T221238Z
UID:VandyNumberTheory/16
DESCRIPTION:Title: Modular zeros in the character table of the symmetric group.\nby Sarah Peluse (Princeton/IAS) as part of Vanderbilt Number Theory Sem
inar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/VandyNumberTheory/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joshua Males (University of Cologne)
DTSTART;VALUE=DATE-TIME:20210217T170000Z
DTEND;VALUE=DATE-TIME:20210217T180000Z
DTSTAMP;VALUE=DATE-TIME:20230925T221238Z
UID:VandyNumberTheory/17
DESCRIPTION:by Joshua Males (University of Cologne) as part of Vanderbilt
Number Theory Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/VandyNumberTheory/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kathrin Bringmann (University of Cologne)
DTSTART;VALUE=DATE-TIME:20210224T160000Z
DTEND;VALUE=DATE-TIME:20210224T170000Z
DTSTAMP;VALUE=DATE-TIME:20230925T221238Z
UID:VandyNumberTheory/18
DESCRIPTION:by Kathrin Bringmann (University of Cologne) as part of Vander
bilt Number Theory Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/VandyNumberTheory/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jan-Willem Van Ittersum (Utrecht University)
DTSTART;VALUE=DATE-TIME:20210317T160000Z
DTEND;VALUE=DATE-TIME:20210317T170000Z
DTSTAMP;VALUE=DATE-TIME:20230925T221238Z
UID:VandyNumberTheory/19
DESCRIPTION:Title: Partitions and quasimodular forms: variations on the Bloch-Okou
nkov theorem\nby Jan-Willem Van Ittersum (Utrecht University) as part
of Vanderbilt Number Theory Seminar\n\n\nAbstract\nPartitions of integers
and (quasi)modular forms are related in many ways. We discuss a connection
made by a certain normalized generating series of functions f on partitio
ns\, called the q-bracket of f. There are many families of functions on pa
rtitions\, such as (i) the shifted symmetric functions\, (ii) their p-adic
generalizations\, (iii) the weighted t-hook functions and (iv) symmetric
functions on partitions\, for which the corresponding q-brackets are quasi
modular forms. We explain how these four examples can be traced back to th
e generating series of shifted symmetric functions. The main technical too
l for doing so is the study of the Taylor coefficients of strictly meromor
phic quasi-Jacobi forms around rational lattice points.\n
LOCATION:https://researchseminars.org/talk/VandyNumberTheory/19/
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