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BEGIN:VEVENT
SUMMARY:Regis de la Bretèche (Paris Diderot University)
DTSTART:20210525T140000Z
DTEND:20210525T150000Z
DTSTAMP:20260422T225839Z
UID:HIMnumbertheory/1
DESCRIPTION:Title: Higher moments of primes in arithmetic progressions\nby Regis
de la Bretèche (Paris Diderot University) as part of HIM Number Theory S
eminar\n\n\nAbstract\nSince the work of Barban\, Davenport and Halberstam
\, the variances of primes in arithmetic\nprogressions have been widely st
udied and continue to be an active topic\nof research. However\, much less
is known about higher moments. Hooley\nestablished a bound on the third m
oment in progressions\, which was later\nsharpened by Vaughan for a varian
t involving a major arcs approximation.\nLittle is known for moments of or
der four or higher\, other than the\nconjecture of Hooley. In this talk I
will discuss recent joint work\nwith Daniel Fiorilli on weighted moments
of moments in progressions.\n
LOCATION:https://researchseminars.org/talk/HIMnumbertheory/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paul Nelson (ETH Zurich)
DTSTART:20210531T140000Z
DTEND:20210531T150000Z
DTSTAMP:20260422T225839Z
UID:HIMnumbertheory/2
DESCRIPTION:Title: The orbit method\, microlocal analysis and applications to L-funct
ions\nby Paul Nelson (ETH Zurich) as part of HIM Number Theory Seminar
\n\n\nAbstract\nI will describe how the orbit method can be developed in a
quantitative form\, along the lines of microlocal analysis\, and applied
to local problems in representation theory and global problems concerning
automorphic forms. The local applications include asymptotic expansions o
f relative characters. The global applications include moment estimates a
nd subconvex bounds for L-functions. These results are the subject of two
papers\, the first joint with Akshay Venkatesh: \n\nhttps://arxiv.org/abs
/1805.07750\nhttps://arxiv.org/abs/2012.02187\n
LOCATION:https://researchseminars.org/talk/HIMnumbertheory/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maryna Viazovska (EPFL)
DTSTART:20210621T123000Z
DTEND:20210621T133000Z
DTSTAMP:20260422T225839Z
UID:HIMnumbertheory/3
DESCRIPTION:Title: Fourier interpolation\nby Maryna Viazovska (EPFL) as part of H
IM Number Theory Seminar\n\n\nAbstract\nThis lecture is about Fourier uniq
ueness and Fourier interpolation pairs. Suppose that we have two subsets X
and Y of the Euclidean space. Can we reconstruct a function f from its re
striction to the set X and the restriction of its Fourier transform to the
set Y? We are interested in the pairs (X\,Y) such that the answer to the
question above is affirmative. I will give an overview of recent progress
on explicit constructions and existence results for Fourier interpolation
pairs and corresponding interpolation formulas.\n
LOCATION:https://researchseminars.org/talk/HIMnumbertheory/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yiannis Sakellaridis (John Hopkins University)
DTSTART:20210621T140000Z
DTEND:20210621T150000Z
DTSTAMP:20260422T225839Z
UID:HIMnumbertheory/4
DESCRIPTION:Title: Plancherel formula\, intersection complexes\, and local L-function
s\nby Yiannis Sakellaridis (John Hopkins University) as part of HIM Nu
mber Theory Seminar\n\n\nAbstract\nIn the theory of automorphic forms\, L-
functions (and their special values) are usually realized by various types
of period integrals. It is now understood that the local L-factors associ
ated to a period represent a Plancherel density for a homogeneous space. I
will start by reviewing the conjectural relationship between local Planch
erel formulas and local L-factors. Then\, I will talk about joint work wit
h Jonathan Wang\, which shows that\, on certain singular spaces\, the test
function whose Plancherel density is an L-factor is related to an interse
ction cohomology complex. The talk will be fairly elementary\, e.g.\, I wi
ll not assume knowledge of intersection cohomology.\n
LOCATION:https://researchseminars.org/talk/HIMnumbertheory/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Claudia Alfes (Bielefeld)
DTSTART:20210628T153000Z
DTEND:20210628T163000Z
DTSTAMP:20260422T225839Z
UID:HIMnumbertheory/5
DESCRIPTION:Title: Traces of CM values and geodesic cycle integrals of modular functi
ons\nby Claudia Alfes (Bielefeld) as part of HIM Number Theory Seminar
\n\n\nAbstract\nIn this talk we give an introduction to the study of gener
ating series of the traces of CM values and geodesic cycle integrals of di
fferent modular functions. \nFirst we define modular forms and harmonic Ma
ass forms. Then we briefly discuss the theory of theta lifts that gives a
conceptual framework for such generating series.\nWe end with some applica
tions of the theory: It can be used to obtain results on the vanishing on
the central derivative of the $L$-series of elliptic curves and to obtain
rationality results for cycle integrals of certain meromorphic functions.\
n
LOCATION:https://researchseminars.org/talk/HIMnumbertheory/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maryna Viazovska (EPFL)
DTSTART:20210628T123000Z
DTEND:20210628T133000Z
DTSTAMP:20260422T225839Z
UID:HIMnumbertheory/6
DESCRIPTION:Title: Fourier interpolation\nby Maryna Viazovska (EPFL) as part of H
IM Number Theory Seminar\n\n\nAbstract\nThis lecture is about Fourier uni
queness and Fourier interpolation pairs. Suppose that we have two subsets
$X$ and $Y$ of the Euclidean space. Can we reconstruct a function f from i
ts restriction to the set $X$ and the restriction of its Fourier transfor
m to the set $Y$? We are interested in the pairs $(X\,Y)$ such that the a
nswer to the question above is affirmative. I will give an overview of rec
ent progress on explicit constructions and existence results for Fourier i
nterpolation pairs and corresponding interpolation formulas.\n
LOCATION:https://researchseminars.org/talk/HIMnumbertheory/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:James Maynard (University of Oxford)
DTSTART:20210705T140000Z
DTEND:20210705T150000Z
DTSTAMP:20260422T225839Z
UID:HIMnumbertheory/7
DESCRIPTION:Title: Half-isolated zeros and zero-density estimates\nby James Mayna
rd (University of Oxford) as part of HIM Number Theory Seminar\n\n\nAbstra
ct\nWe introduce a new zero-detecting method which is sensitive to the ver
tical distribution of zeros of the zeta function. This allows us to show t
hat there are few 'half-isolated' zeros\, and allows us to improve the cla
ssical zero density result to $N(\\sigma\,T)\\ll T^{24(1-\\sigma)/11+o(1)}
$ if we assume that the zeros of the zeta function are restricted to finit
ely many vertical lines (and so gives new results about primes in short in
tervals under this assumption). This relies on a new variant of the Turan
power sum method\, which might be of independent interest to harmonic anal
ysts. This is joint work with Kyle Pratt.\n
LOCATION:https://researchseminars.org/talk/HIMnumbertheory/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sarah Peluse (Princeton/IAS)
DTSTART:20210719T140000Z
DTEND:20210719T150000Z
DTSTAMP:20260422T225839Z
UID:HIMnumbertheory/8
DESCRIPTION:Title: Bounds for subsets of F_p^n x F_p^n without L’s\nby Sarah Pe
luse (Princeton/IAS) as part of HIM Number Theory Seminar\n\n\nAbstract\nI
will discuss the difficult problem of proving reasonable bounds in the mu
ltidimensional generalization of Szemerédi’s theorem\, and describe a p
roof for such bounds for sets lacking nontrivial configurations of the for
m $(x\,y)\, (x\,y+z)\, (x\,y+2z)\, (x+z\,y)$ in the finite field model set
ting.\n
LOCATION:https://researchseminars.org/talk/HIMnumbertheory/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexandra Florea (UC Irvine)
DTSTART:20210726T153000Z
DTEND:20210726T163000Z
DTSTAMP:20260422T225839Z
UID:HIMnumbertheory/9
DESCRIPTION:Title: The Ratios Conjecture over function fields\nby Alexandra Flore
a (UC Irvine) as part of HIM Number Theory Seminar\n\n\nAbstract\nI will t
alk about some recent joint work with H. Bui and J. Keating where we study
the Ratios Conjecture for the family of quadratic L-functions over functi
on fields. I will also discuss the closely related problem of obtaining up
per bounds for negative moments of L-functions\, which allows us to obtain
partial results towards the Ratios Conjecture in the case of one over one
\, two over two and three over three L-functions.\n
LOCATION:https://researchseminars.org/talk/HIMnumbertheory/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ian Petrow (UCL)
DTSTART:20210802T140000Z
DTEND:20210802T150000Z
DTSTAMP:20260422T225839Z
UID:HIMnumbertheory/10
DESCRIPTION:Title: Relative trace formulas for GL(2) and analytic number theory\
nby Ian Petrow (UCL) as part of HIM Number Theory Seminar\n\n\nAbstract\nT
he Petersson/Kuznetsov formula is a classical tool in analytic number theo
ry with striking applications in the analytic theory of L-functions. It is
the primitive example of a relative trace formula\, and acts as a spectra
l summation device tying together some basic families of automorphic forms
. In this talk I will discuss some of these families\, and how varying the
test function in the relative trace formula can pick out other families o
f automorphic forms of interest. Along these lines I will describe some pa
st joint work with M.P. Young\, some work of Y. Hu\, and some current/futu
re work joint between all three of us\n
LOCATION:https://researchseminars.org/talk/HIMnumbertheory/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rachel Greenfeld (UCLA)
DTSTART:20210809T153000Z
DTEND:20210809T163000Z
DTSTAMP:20260422T225839Z
UID:HIMnumbertheory/11
DESCRIPTION:Title: Decidability and periodicity of translational tilings\nby Rac
hel Greenfeld (UCLA) as part of HIM Number Theory Seminar\n\n\nAbstract\nL
et $G$ be a finitely generated abelian group\, and $F_1\,...\,F_J$ be fini
te subsets of $G$. We say that $F_1\,...\,F_J$ tile $G$ by translations\,
if $G$ can be covered by translated copies of $F_1\,...\,F_J$\, without an
y overlaps. Given some finite sets $F_1\,...\,F_J$ in $G$\, can we decide
whether they admit a tiling of $G$? Suppose that they do tile $G$\, do the
y admit a periodic tiling? A well known argument of Hao Wang ('61)\, shows
that these two questions are closely related. In the talk\, we will discu
ss this relation\, and present some results\, old and new\, about the deci
dability and periodicity of translational tilings\, in the case of a singl
e tile ($J=1$) as well as in the case of a multi-tileset ($J>1$).\n
LOCATION:https://researchseminars.org/talk/HIMnumbertheory/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Will Sawin (Columbia University)
DTSTART:20210816T140000Z
DTEND:20210816T150000Z
DTSTAMP:20260422T225839Z
UID:HIMnumbertheory/12
DESCRIPTION:Title: Sums in progressions to squarefree moduli among polynomials over
a finite field\nby Will Sawin (Columbia University) as part of HIM Num
ber Theory Seminar\n\n\nAbstract\nThere are many problems about counting s
pecial types of numbers (primes or other numbers with special factorizatio
ns) in arithmetic progressions\, or summing arithmetic functions in arithm
etic progressions. These all have analogues polynomials over a finite fiel
d. Recently I proved\, by a geometric method\, strong bounds for these ana
logues (approaching level of distribution 1 and square-root cancellation a
s the size of the finite field goes to infinity). I will explain how these
bounds relate to those obtained from a simpler approach using the Riemann
hypothesis (i.e. by using Fourier analysis on the multiplicative group) a
nd how we can deduce\, using a classical probability-theoretic method\, a
result that applies to every factorization type at once.\n
LOCATION:https://researchseminars.org/talk/HIMnumbertheory/12/
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