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BEGIN:VEVENT
SUMMARY:Arvind Ayyer (IISc\, Bangalore)
DTSTART;VALUE=DATE-TIME:20200618T103000Z
DTEND;VALUE=DATE-TIME:20200618T113000Z
DTSTAMP;VALUE=DATE-TIME:20201026T205624Z
UID:SF-and-nt/1
DESCRIPTION:Title: The Monopole-Dimer Model\nby Arvind Ayyer (IISc\, Banga
lore) as part of Special Functions and Number Theory seminar\n\nAbstract:
TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hjalmar Rosengren (Chalmers University of Technology and the Unive
rsity of Gothenburg)
DTSTART;VALUE=DATE-TIME:20200702T092500Z
DTEND;VALUE=DATE-TIME:20200702T103000Z
DTSTAMP;VALUE=DATE-TIME:20201026T205624Z
UID:SF-and-nt/2
DESCRIPTION:Title: On the Kanade-Russell identities\nby Hjalmar Rosengren
(Chalmers University of Technology and the University of Gothenburg) as pa
rt of Special Functions and Number Theory seminar\n\n\nAbstract\nKanade an
d Russell conjectured several Rogers-Ramanujan-type identities for triple
series. Some of these conjectures are related to characters of affine Lie
algebras\, and they can all be interpreted combinatorially in terms of par
titions. Many of these conjectures were settled by Bringmann\, Jennings-Sh
affer and Mahlburg. We describe a new approach to the Kanade-Russell ident
ities\, which leads to new proofs of five previously known identities\, as
well as four identities that were still open. For the new cases\, we need
quadratic transformations for q-orthogonal polynomials.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ali Uncu (RICAM\, Austrian Academy of Sciences)
DTSTART;VALUE=DATE-TIME:20200716T093000Z
DTEND;VALUE=DATE-TIME:20200716T103000Z
DTSTAMP;VALUE=DATE-TIME:20201026T205624Z
UID:SF-and-nt/3
DESCRIPTION:Title: The Mathematica package qFunctions for q-series and par
tition theory applications\nby Ali Uncu (RICAM\, Austrian Academy of Scien
ces) as part of Special Functions and Number Theory seminar\n\n\nAbstract\
nIn this talk\, I will demonstrate the new Mathematica package qFunctions
while providing relevant mathematical context. This implementation has sym
bolic tools to automate some tedious and error-prone calculations and it a
lso includes some other functionality for experimentation. We plan to high
light the four main tool-sets included in the qFunctions package:\n\n(1) T
he q-difference equation (or recurrence) guesser and some formal manipulat
ion tools\,\n(2) the treatment of the method of weighted words and automat
ically finding and uncoupling recurrences\,\n\n(3) a method on the cylindr
ical partitions to establish sum-product identities\,\n(4) fitting polynom
ials with suggested well-known objects to guess closed formulas.\n\nThis t
alk is based on joint work with Jakob Ablinger (RISC).\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alok Shukla (Ahmedabad University)
DTSTART;VALUE=DATE-TIME:20200730T102500Z
DTEND;VALUE=DATE-TIME:20200730T113000Z
DTSTAMP;VALUE=DATE-TIME:20201026T205624Z
UID:SF-and-nt/4
DESCRIPTION:Title: Tiling proofs of Jacobi triple product and Rogers-Raman
ujan identities\nby Alok Shukla (Ahmedabad University) as part of Special
Functions and Number Theory seminar\n\n\nAbstract\nThe Jacobi triple produ
ct identity and Rogers-Ramanujan identities are among the most famous q-se
ries identities. We will present elementary combinatorial "tiling proofs"
of these results. The talk should be accessible to a general mathematical
audience.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fatma Cicek (IIT\, Gandhinagar)
DTSTART;VALUE=DATE-TIME:20200813T103000Z
DTEND;VALUE=DATE-TIME:20200813T113000Z
DTSTAMP;VALUE=DATE-TIME:20201026T205624Z
UID:SF-and-nt/5
DESCRIPTION:Title: On the logarithm of the Riemann zeta-function near the
nontrivial zeros\nby Fatma Cicek (IIT\, Gandhinagar) as part of Special Fu
nctions and Number Theory seminar\n\n\nAbstract\nSelberg's central limit t
heorem is one of the most significant probabilistic results in analytic nu
mber theory. Roughly\, it states that the logarithm of the Riemann zeta-fu
nction on and near the critical line has an approximate two-dimensional Ga
ussian distribution.\n\nIn this talk\, we will talk about our recent resul
t which states that the distribution of the logarithm of the Riemann zeta-
function near the sequence of the nontrivial zeros has a similar central l
imit theorem. Our results are conditional on the Riemann Hypothesis and/or
suitable zero-spacing hypotheses. They also have suitable generalizations
to Dirichlet $L$-functions.\n
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BEGIN:VEVENT
SUMMARY:Amritanshu Prasad (IMSc\, Chennai)
DTSTART;VALUE=DATE-TIME:20200827T103000Z
DTEND;VALUE=DATE-TIME:20200827T113000Z
DTSTAMP;VALUE=DATE-TIME:20201026T205624Z
UID:SF-and-nt/6
DESCRIPTION:Title: Character Polynomials and their Moments\nby Amritanshu
Prasad (IMSc\, Chennai) as part of Special Functions and Number Theory sem
inar\n\n\nAbstract\nA polynomial in a sequence of variables can be regarde
d as a class \nfunction on every symmetric group when the $i$th variable i
s interpreted as \nthe number of $i$-cycles. Many nice families of represe
ntations of symmetric \ngroups have characters represented by such polynom
ials.\n\nWe introduce two families linear functionals of this space of pol
ynomials -- moments and signed moments. For each $n$\, the moment of a pol
ynomial at $n$ \ngives the average value of the corresponding class functi
on on the $n$th \nsymmetric group\, while the signed moment gives the aver
age of its \nproduct by the sign character. These linear functionals are e
asy to \ncompute in terms of binomial bases of the space of polynomials.\n
\nWe use them to explore some questions in the representation theory of \n
symmetric groups and general linear groups. These explorations lead to \ni
nteresting expressions involving multipartite partition functions and \nso
me peculiar variants.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Apoorva Khare (IISc.\, Bangalore)
DTSTART;VALUE=DATE-TIME:20200910T103000Z
DTEND;VALUE=DATE-TIME:20200910T113000Z
DTSTAMP;VALUE=DATE-TIME:20201026T205624Z
UID:SF-and-nt/7
DESCRIPTION:Title: An introduction to total positivity\nby Apoorva Khare (
IISc.\, Bangalore) as part of Special Functions and Number Theory seminar\
n\n\nAbstract\nI will give a gentle introduction to total positivity and t
he theory of Polya frequency (PF) functions. This includes their spectral
properties\, basic examples including via convolution\, and a few proofs t
o show how the main ingredients fit together. Many classical results (and
one Hypothesis) from before 1955 feature in this journey. I will end by de
scribing how PF functions connect to the Laguerre-Polya class and hence Po
lya-Schur multipliers\, and mention 21st century incarnations of the latte
r.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Apoorva Khare (IISc.\, Bangalore)
DTSTART;VALUE=DATE-TIME:20200924T103000Z
DTEND;VALUE=DATE-TIME:20200924T113000Z
DTSTAMP;VALUE=DATE-TIME:20201026T205624Z
UID:SF-and-nt/8
DESCRIPTION:Title: Totally positive matrices\, Polya frequency sequences\,
and Schur polynomials\nby Apoorva Khare (IISc.\, Bangalore) as part of Sp
ecial Functions and Number Theory seminar\n\n\nAbstract\nI will discuss to
tally positive/non-negative matrices and kernels\, including Polya frequen
cy (PF) functions and sequences. This includes examples\, history\, and ba
sic results on total positivity\, variation diminution\, sign non-reversal
\, and generating functions of PF sequences (with some proofs). I will end
with applications of total positivity to old and new phenomena involving
Schur polynomials.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Debashis Ghoshal (School of Physical Sciences\, JNU)
DTSTART;VALUE=DATE-TIME:20201008T103000Z
DTEND;VALUE=DATE-TIME:20201008T113000Z
DTSTAMP;VALUE=DATE-TIME:20201026T205624Z
UID:SF-and-nt/9
DESCRIPTION:Title: Two-dimensional gauge theories\, intersection numbers a
nd special functions\nby Debashis Ghoshal (School of Physical Sciences\, J
NU) as part of Special Functions and Number Theory seminar\n\n\nAbstract\n
The partition function of two dimensional Yang-Mills theory contains a wea
lth of information about the moduli space of connections on surfaces. We s
tudy this problem on a special class of surfaces of infinite genus\, which
are constructed recursively. While the results are suggestive of an under
lying geometrical structure\, we use it as a prop to efficiently compute r
esults for finite genus surfaces. Riemann zeta function\, confluent hyperg
eometric function and its truncations show up in explicit computations for
the gauge group SU(2). Much of the corresponding results are open for oth
er groups.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Schlosser (Universitat Wien)
DTSTART;VALUE=DATE-TIME:20201022T103000Z
DTEND;VALUE=DATE-TIME:20201022T113000Z
DTSTAMP;VALUE=DATE-TIME:20201026T205624Z
UID:SF-and-nt/10
DESCRIPTION:Title: Basic hypergeometric proofs of two quadruple equidistri
butions of Euler--Stirling statistics on ascent sequences\nby Michael Schl
osser (Universitat Wien) as part of Special Functions and Number Theory se
minar\n\n\nAbstract\nIn my talk\, I will present new applications of basic
\nhypergeometric series to specific problems in enumerative\ncombinatorics
. The combinatorial problems we are interested in\nconcern multiply refine
d equidistributions on ascent sequences.\n(I will gently explain these not
ions in my talk!)\nUsing bijections we are able to suitably decompose some
\nquadruple distributions we are interested in and obtain\nfunctional equa
tions and ultimately generating functions\nfrom them\, in the form of expl
icit basic hypergeometric series\,\nThe problem of proving equidistributio
ns then reduces to\napplying suitable transformations of basic hypergeomet
ric series.\nThe situation in our case however is tricky (caused by the\nf
act how the power series variable $r$ appears in the base\n$q=1-r$ of the
respective basic hypergeometric series\; so being\ninterested in the gener
ating function in $r$ as a Maclaurin\nseries\, we are thus interested in t
he analytic expansion of\nthe nonterminating basic hypergeometric series i
n base $q$\naround the point $q=1$)\, as none of the known transformations
\nappear to directly work to settle our problems\; we require\nthe derivat
ion of new identities.\nSpecifically\, we use the classical Sears transfor
mation and\napply some analytic tools to establish a new non-terminating\n
${}_4\\phi_3$ transformation formula of base $q$\, valid as\nan identity i
n a neighborhood around $q=1$. We use special\ncases of this formula to de
duce two different quadruple\nequidistribution results involving Euler--St
irling statistics\non ascent sequences. One of them concerns a symmetric\
nequidistribution\, the other confirms a bi-symmetric\nequidistribution th
at was recently conjectured in a paper\n(published in JCTA) by Shishuo Fu\
, Emma Yu Jin\, Zhicong Lin\,\nSherry H.F. Yan\, and Robin D.B. Zhou. Thi
s is joint work\nwith Emma Yu Jin. For full results (and further ones)\, s
ee\nhttps://arxiv.org/abs/2010.01435\n
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