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BEGIN:VEVENT
SUMMARY:Regis de la Bretèche (Paris Diderot University)
DTSTART:20210525T140000Z
DTEND:20210525T150000Z
DTSTAMP:20260404T111326Z
UID:HIMnumbertheory/1
DESCRIPTION:Title: Higher moments of primes in arithmetic progressions\nb
y Regis de la Bretèche (Paris Diderot University) as part of HIM Number T
heory Seminar\n\n\nAbstract\nSince the work of Barban\, Davenport and Hal
berstam\, the variances of primes in arithmetic\nprogressions have been wi
dely studied and continue to be an active topic\nof research. However\, mu
ch less is known about higher moments. Hooley\nestablished a bound on the
third moment in progressions\, which was later\nsharpened by Vaughan for a
variant involving a major arcs approximation.\nLittle is known for moment
s of order four or higher\, other than the\nconjecture of Hooley. In this
talk I will discuss recent joint work\nwith Daniel Fiorilli on weighted m
oments of moments in progressions.\n
LOCATION:https://stable.researchseminars.org/talk/HIMnumbertheory/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paul Nelson (ETH Zurich)
DTSTART:20210531T140000Z
DTEND:20210531T150000Z
DTSTAMP:20260404T111326Z
UID:HIMnumbertheory/2
DESCRIPTION:Title: The orbit method\, microlocal analysis and applications to
L-functions\nby Paul Nelson (ETH Zurich) as part of HIM Number Theory
Seminar\n\n\nAbstract\nI will describe how the orbit method can be develop
ed in a quantitative form\, along the lines of microlocal analysis\, and a
pplied to local problems in representation theory and global problems conc
erning automorphic forms. The local applications include asymptotic expan
sions of relative characters. The global applications include moment esti
mates and 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://stable.researchseminars.org/talk/HIMnumbertheory/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maryna Viazovska (EPFL)
DTSTART:20210621T123000Z
DTEND:20210621T133000Z
DTSTAMP:20260404T111326Z
UID:HIMnumbertheory/3
DESCRIPTION:Title: Fourier interpolation\nby Maryna Viazovska (EPFL) as pa
rt of HIM Number Theory Seminar\n\n\nAbstract\nThis lecture is about Fouri
er uniqueness and Fourier interpolation pairs. Suppose that we have two su
bsets X and Y of the Euclidean space. Can we reconstruct a function f from
its restriction 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 pr
ogress on explicit constructions and existence results for Fourier interpo
lation pairs and corresponding interpolation formulas.\n
LOCATION:https://stable.researchseminars.org/talk/HIMnumbertheory/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yiannis Sakellaridis (John Hopkins University)
DTSTART:20210621T140000Z
DTEND:20210621T150000Z
DTSTAMP:20260404T111326Z
UID:HIMnumbertheory/4
DESCRIPTION:Title: Plancherel formula\, intersection complexes\, and local L-f
unctions\nby Yiannis Sakellaridis (John Hopkins University) as part of
HIM Number Theory Seminar\n\n\nAbstract\nIn the theory of automorphic for
ms\, L-functions (and their special values) are usually realized by variou
s types of period integrals. It is now understood that the local L-factors
associated to a period represent a Plancherel density for a homogeneous s
pace. I will start by reviewing the conjectural relationship between local
Plancherel formulas and local L-factors. Then\, I will talk about joint w
ork with Jonathan Wang\, which shows that\, on certain singular spaces\, t
he test function whose Plancherel density is an L-factor is related to an
intersection cohomology complex. The talk will be fairly elementary\, e.g.
\, I will not assume knowledge of intersection cohomology.\n
LOCATION:https://stable.researchseminars.org/talk/HIMnumbertheory/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Claudia Alfes (Bielefeld)
DTSTART:20210628T153000Z
DTEND:20210628T163000Z
DTSTAMP:20260404T111326Z
UID:HIMnumbertheory/5
DESCRIPTION:Title: Traces of CM values and geodesic cycle integrals of modular
functions\nby Claudia Alfes (Bielefeld) as part of HIM Number Theory
Seminar\n\n\nAbstract\nIn this talk we give an introduction to the study o
f generating series of the traces of CM values and geodesic cycle integral
s of different modular functions. \nFirst we define modular forms and harm
onic Maass forms. Then we briefly discuss the theory of theta lifts that g
ives a conceptual framework for such generating series.\nWe end with some
applications of the theory: It can be used to obtain results on the vanish
ing on the central derivative of the $L$-series of elliptic curves and to
obtain rationality results for cycle integrals of certain meromorphic func
tions.\n
LOCATION:https://stable.researchseminars.org/talk/HIMnumbertheory/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maryna Viazovska (EPFL)
DTSTART:20210628T123000Z
DTEND:20210628T133000Z
DTSTAMP:20260404T111326Z
UID:HIMnumbertheory/6
DESCRIPTION:Title: Fourier interpolation\nby Maryna Viazovska (EPFL) as pa
rt of HIM Number Theory Seminar\n\n\nAbstract\nThis lecture is about Four
ier uniqueness and Fourier interpolation pairs. Suppose that we have two s
ubsets $X$ and $Y$ of the Euclidean space. Can we reconstruct a function f
from its restriction to the set $X$ and the restriction of its Fourier t
ransform to the set $Y$? We are interested in the pairs $(X\,Y)$ such tha
t the answer to the question above is affirmative. I will give an overview
of recent progress on explicit constructions and existence results for Fo
urier interpolation pairs and corresponding interpolation formulas.\n
LOCATION:https://stable.researchseminars.org/talk/HIMnumbertheory/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:James Maynard (University of Oxford)
DTSTART:20210705T140000Z
DTEND:20210705T150000Z
DTSTAMP:20260404T111326Z
UID:HIMnumbertheory/7
DESCRIPTION:Title: Half-isolated zeros and zero-density estimates\nby Jame
s Maynard (University of Oxford) as part of HIM Number Theory Seminar\n\n\
nAbstract\nWe introduce a new zero-detecting method which is sensitive to
the vertical distribution of zeros of the zeta function. This allows us to
show that there are few 'half-isolated' zeros\, and allows us to improve
the classical zero density result to $N(\\sigma\,T)\\ll T^{24(1-\\sigma)/1
1+o(1)}$ if we assume that the zeros of the zeta function are restricted t
o finitely many vertical lines (and so gives new results about primes in s
hort intervals under this assumption). This relies on a new variant of the
Turan power sum method\, which might be of independent interest to harmon
ic analysts. This is joint work with Kyle Pratt.\n
LOCATION:https://stable.researchseminars.org/talk/HIMnumbertheory/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sarah Peluse (Princeton/IAS)
DTSTART:20210719T140000Z
DTEND:20210719T150000Z
DTSTAMP:20260404T111326Z
UID:HIMnumbertheory/8
DESCRIPTION:Title: Bounds for subsets of F_p^n x F_p^n without L’s\nby S
arah Peluse (Princeton/IAS) as part of HIM Number Theory Seminar\n\n\nAbst
ract\nI will discuss the difficult problem of proving reasonable bounds in
the multidimensional generalization of Szemerédi’s theorem\, and descr
ibe a proof for such bounds for sets lacking nontrivial configurations of
the form $(x\,y)\, (x\,y+z)\, (x\,y+2z)\, (x+z\,y)$ in the finite field mo
del setting.\n
LOCATION:https://stable.researchseminars.org/talk/HIMnumbertheory/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexandra Florea (UC Irvine)
DTSTART:20210726T153000Z
DTEND:20210726T163000Z
DTSTAMP:20260404T111326Z
UID:HIMnumbertheory/9
DESCRIPTION:Title: The Ratios Conjecture over function fields\nby Alexandr
a Florea (UC Irvine) as part of HIM Number Theory Seminar\n\n\nAbstract\nI
will talk about some recent joint work with H. Bui and J. Keating where w
e study the Ratios Conjecture for the family of quadratic L-functions over
function fields. I will also discuss the closely related problem of obtai
ning upper bounds for negative moments of L-functions\, which allows us to
obtain partial results towards the Ratios Conjecture in the case of one o
ver one\, two over two and three over three L-functions.\n
LOCATION:https://stable.researchseminars.org/talk/HIMnumbertheory/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ian Petrow (UCL)
DTSTART:20210802T140000Z
DTEND:20210802T150000Z
DTSTAMP:20260404T111326Z
UID:HIMnumbertheory/10
DESCRIPTION:Title: Relative trace formulas for GL(2) and analytic number theo
ry\nby Ian Petrow (UCL) as part of HIM Number Theory Seminar\n\n\nAbst
ract\nThe Petersson/Kuznetsov formula is a classical tool in analytic numb
er theory with striking applications in the analytic theory of L-functions
. It is the primitive example of a relative trace formula\, and acts as a
spectral summation device tying together some basic families of automorphi
c forms. In this talk I will discuss some of these families\, and how vary
ing the test function in the relative trace formula can pick out other fam
ilies of automorphic forms of interest. Along these lines I will describe
some past joint work with M.P. Young\, some work of Y. Hu\, and some curre
nt/future work joint between all three of us\n
LOCATION:https://stable.researchseminars.org/talk/HIMnumbertheory/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rachel Greenfeld (UCLA)
DTSTART:20210809T153000Z
DTEND:20210809T163000Z
DTSTAMP:20260404T111326Z
UID:HIMnumbertheory/11
DESCRIPTION:Title: Decidability and periodicity of translational tilings\
nby Rachel Greenfeld (UCLA) as part of HIM Number Theory Seminar\n\n\nAbst
ract\nLet $G$ be a finitely generated abelian group\, and $F_1\,...\,F_J$
be finite subsets of $G$. We say that $F_1\,...\,F_J$ tile $G$ by translat
ions\, if $G$ can be covered by translated copies of $F_1\,...\,F_J$\, wit
hout any 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 they admit a periodic tiling? A well known argument of Hao Wang ('61)\
, shows that these two questions are closely related. In the talk\, we wil
l discuss this relation\, and present some results\, old and new\, about t
he decidability and periodicity of translational tilings\, in the case of
a single tile ($J=1$) as well as in the case of a multi-tileset ($J>1$).\n
LOCATION:https://stable.researchseminars.org/talk/HIMnumbertheory/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Will Sawin (Columbia University)
DTSTART:20210816T140000Z
DTEND:20210816T150000Z
DTSTAMP:20260404T111326Z
UID:HIMnumbertheory/12
DESCRIPTION:Title: Sums in progressions to squarefree moduli among polynomial
s over a finite field\nby Will Sawin (Columbia University) as part of
HIM Number Theory Seminar\n\n\nAbstract\nThere are many problems about cou
nting special types of numbers (primes or other numbers with special facto
rizations) in arithmetic progressions\, or summing arithmetic functions in
arithmetic progressions. These all have analogues polynomials over a fini
te field. Recently I proved\, by a geometric method\, strong bounds for th
ese analogues (approaching level of distribution 1 and square-root cancell
ation as the size of the finite field goes to infinity). I will explain ho
w these bounds relate to those obtained from a simpler approach using the
Riemann hypothesis (i.e. by using Fourier analysis on the multiplicative g
roup) and how we can deduce\, using a classical probability-theoretic meth
od\, a result that applies to every factorization type at once.\n
LOCATION:https://stable.researchseminars.org/talk/HIMnumbertheory/12/
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