BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Jon Keating (University of Oxford)
DTSTART:20210118T160000Z
DTEND:20210118T170000Z
DTSTAMP:20260404T131148Z
UID:IML_NT/1
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/IML_N
 T/1/">Joint Moments</a>\nby Jon Keating (University of Oxford) as part of 
 IML Number Theory semester (spring 2021)\n\n\nAbstract\nI will discuss the
  joint moments of the Riemann zeta-function and its\nderivative\, and the 
 corresponding joint moments of the characteristic\npolynomials of random u
 nitary matrices and their derivatives.\n
LOCATION:https://stable.researchseminars.org/talk/IML_NT/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emmanuel Kowalski (ETH)
DTSTART:20210125T160000Z
DTEND:20210125T170000Z
DTSTAMP:20260404T131148Z
UID:IML_NT/2
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/IML_N
 T/2/">The shapes of exponential sums</a>\nby Emmanuel Kowalski (ETH) as pa
 rt of IML Number Theory semester (spring 2021)\n\n\nAbstract\nWe will surv
 ey the functional limit theorems for partial sums of\nexponential sums ove
 r finite fields\, starting from the case of\nKloosterman paths\, covering 
 recent developments as well as\napplications and open problems.\n
LOCATION:https://stable.researchseminars.org/talk/IML_NT/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Valentin Blomer (Universität Bonn)
DTSTART:20210210T171500Z
DTEND:20210210T181500Z
DTSTAMP:20260404T131148Z
UID:IML_NT/3
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/IML_N
 T/3/">Uniform Titchmarsh divisor problems</a>\nby Valentin Blomer (Univers
 ität Bonn) as part of IML Number Theory semester (spring 2021)\n\n\nAbstr
 act\nThe classical Titchmarsh divisor problem asks for the asymptotic\neva
 luation of the divisor function over shifted primes. It is\nintimately rel
 ated with primes in long arithmetic progressions. Modern\nmethods can prod
 uce strong error terms for fixed shifts\, but no\nprogress since the 1960s
  has been made on the dual problem of summing\nd(n-p) for p < n or the rel
 ated problem of Hooley and Linnik of\nrepresenting a number a sum of a pri
 me and two squares. I will survey\napproaches and techniques towards the T
 itchmarsh divisor problem and\nits variations\, and present new results ob
 tained in joint work with\nEdgar Assing and Junxian Li. The methods involv
 e a blend of classical\nanalytic number theory\, automorphic forms and alg
 ebraic geometry.\n
LOCATION:https://stable.researchseminars.org/talk/IML_NT/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Fiorilli (Université Paris-Sud)
DTSTART:20210208T160000Z
DTEND:20210208T164500Z
DTSTAMP:20260404T131148Z
UID:IML_NT/4
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/IML_N
 T/4/">Higher moments of primes in intervals and in arithmetic progressions
 \, I</a>\nby Daniel Fiorilli (Université Paris-Sud) as part of IML Number
  Theory semester (spring 2021)\n\n\nAbstract\nSince the work of Selberg an
 d of Barban\, Davenport and Halberstam\, the variances of primes in interv
 als and in arithmetic progressions have been widely studied and continue t
 o be an active topic of research. However\, much less is known about highe
 r moments. Hooley established a bound on the third moment in progressions\
 , which was later sharpened by Vaughan for a variant involving a major arc
 s approximation. Little is known for moments of order four or higher\, oth
 er than the conjecture of Hooley and the conditional result of Montgomery-
 Soundararajan. In this talk I will discuss recent joint work with Régis d
 e la Bretèche on weighted moments in intervals and on weighted moments of
  moments in progressions. In particular we will show how to deduce sharp u
 nconditional omega results on all weighted even moments in certain ranges.
 \n
LOCATION:https://stable.researchseminars.org/talk/IML_NT/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Régis de la Bretèche (Université Paris Diderot\, Paris 7)
DTSTART:20210208T170000Z
DTEND:20210208T174500Z
DTSTAMP:20260404T131148Z
UID:IML_NT/5
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/IML_N
 T/5/">Higher moments of primes in intervals and in arithmetic progressions
 \, II</a>\nby Régis de la Bretèche (Université Paris Diderot\, Paris 7)
  as part of IML Number Theory semester (spring 2021)\n\n\nAbstract\nThis i
 s the second part of the talk of Daniel Fiorilli. We will explain the proo
 fs of our theorem about the moments of moments of primes in arithmetic pro
 gressions.\n
LOCATION:https://stable.researchseminars.org/talk/IML_NT/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joni Teravainen (University of Oxford)
DTSTART:20210215T160000Z
DTEND:20210215T170000Z
DTSTAMP:20260404T131148Z
UID:IML_NT/6
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/IML_N
 T/6/">Sums of two almost twin primes</a>\nby Joni Teravainen (University o
 f Oxford) as part of IML Number Theory semester (spring 2021)\n\n\nAbstrac
 t\nIn 1975\, Montgomery and Vaughan proved that the number of\nexceptions 
 to the binary Goldbach problem is power-saving. I will\ndiscuss work where
  we obtain a nearly power-saving exceptional set for\nnumbers that are not
  the sum of two "almost twin primes". This is\njoint work with Lasse Grimm
 elt.\n
LOCATION:https://stable.researchseminars.org/talk/IML_NT/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sacha Mangerel (University of Montreal)
DTSTART:20210217T171500Z
DTEND:20210217T181500Z
DTSTAMP:20260404T131148Z
UID:IML_NT/7
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/IML_N
 T/7/">Discrepancy Problems for Multiplicative Functions over F_q[t]</a>\nb
 y Sacha Mangerel (University of Montreal) as part of IML Number Theory sem
 ester (spring 2021)\n\n\nAbstract\nAn equivalent form of the famous Erdos 
 Discrepancy Problem\, proved by\nTao building on the work of the Polymath5
  project\, states that any\ncompletely multiplicative function taking valu
 es on the unit circle has\nunbounded partial sums. It was observed in the 
 course of the Polymath5\nproject that the same is not true if one consider
 s the most natural\ntranslation of this problem to the ring F_q[t] of poly
 nomials over a\nfinite field.\n\nWe will discuss recent joint work with O.
  Klurman and J. Teräväinen\ndemonstrating that the function field discre
 pancy problem depends\nheavily on the way the elements of the sums are ord
 ered\, in contrast to\nthe integer setting. In particular\, we will introd
 uce three different\nnotions of discrepancy\, and discuss the problem of c
 lassifying those\ncompletely multiplicative functions that have uniformly 
 bounded partial\nsums with respect to each of these notions.  We will also
  address the\nproblem of bounding the minimal rate of growth of unbounded 
 partial\nsums\, which is the subject of some speculation in the integer se
 tting.\n
LOCATION:https://stable.researchseminars.org/talk/IML_NT/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Steve Lester (King's College)
DTSTART:20210303T171500Z
DTEND:20210303T181500Z
DTSTAMP:20260404T131148Z
UID:IML_NT/8
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/IML_N
 T/8/">Lattice points on hyperbolic circles</a>\nby Steve Lester (King's Co
 llege) as part of IML Number Theory semester (spring 2021)\n\n\nAbstract\n
 The hyperbolic lattice point problem is to determine the\nnumber of transl
 ates of a given point in the complex upper half-plane by\nelements of a di
 screte subgroup of PSL_2(R) that lie within a hyperbolic\ncircle. This may
  be viewed as a non-Euclidean analogue of the Gauss\ncircle problem. In th
 is talk I will give an overview of some results on\nthe hyperbolic lattice
  point problem and will also present some recent\nwork concerning the angu
 lar distribution of lattice points lying on\nhyperbolic circles. This is j
 oint with Dimitrios Chatzakos\, Pär\nKurlberg\, and Igor Wigman.\n
LOCATION:https://stable.researchseminars.org/talk/IML_NT/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sandro Bettin & Sary Drappeau (University of Genova & Université 
 d'Aix-Marseille)
DTSTART:20210301T160000Z
DTEND:20210301T170000Z
DTSTAMP:20260404T131148Z
UID:IML_NT/9
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/IML_N
 T/9/">The distribution of the Estermann function and other quantum modular
  forms</a>\nby Sandro Bettin & Sary Drappeau (University of Genova & Unive
 rsité d'Aix-Marseille) as part of IML Number Theory semester (spring 2021
 )\n\n\nAbstract\nFor a rational a/q\, the Estermann function is defined as
  the additive twist of the\nthe square of the Riemann zeta-function\,\n\nD
 (s\,a/q) = \\sum_{n>0} d(n) e^{2\\pi i n a/q} n^{-s}.\n\nIt satisfies a fu
 nctional equation which encodes Voronoi's summation formula. \n\nIt is nat
 ural to ask how the central values D(1/2\,a/q) are distributed as the\nrat
 ional a/q varies.  In contrast with the case of multiplicative twists of\n
 L-functions\, D(s\,a/q) does not have an Euler product and thus the usual\
 nmachinery does not apply. However\, we are able to employ the fact that D
 \n(1/2\,a/q) is a quantum modular form (there is a certain relation betwee
 n the\nvalues at a/q and q/a) to show\, using dynamical systems methods\, 
 that D\n(1/2\,a/q) is asymptotically distributed as a Gaussian random vari
 able.\n
LOCATION:https://stable.researchseminars.org/talk/IML_NT/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sarah Peluse (Princeton/IAS)
DTSTART:20210310T171500Z
DTEND:20210310T181500Z
DTSTAMP:20260404T131148Z
UID:IML_NT/10
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/IML_N
 T/10/">Modular zeros in the character table of the symmetric group</a>\nby
  Sarah Peluse (Princeton/IAS) as part of IML Number Theory semester (sprin
 g 2021)\n\n\nAbstract\nIn 2017\, Miller conjectured\, based on computation
 al evidence\, that for\nany fixed prime $p$ the density of entries in the 
 character table of $S_n$ that\nare divisible by $p$ goes to $1$ as $n$ goe
 s to infinity. I’ll describe a proof of\nthis conjecture\, which is join
 t work with K. Soundararajan. I will also discuss the\n(still open) proble
 m of determining the asymptotic density of zeros in the\ncharacter table o
 f $S_n$\, where it is not even clear from computational data\nwhat one sho
 uld expect.\n
LOCATION:https://stable.researchseminars.org/talk/IML_NT/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kaisa Matomäki (University of Turku)
DTSTART:20210308T160000Z
DTEND:20210308T170000Z
DTSTAMP:20260404T131148Z
UID:IML_NT/11
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/IML_N
 T/11/">Moments of Dirichlet $L$-functions</a>\nby Kaisa Matomäki (Univers
 ity of Turku) as part of IML Number Theory semester (spring 2021)\n\n\nAbs
 tract\nI will discuss my on-going joint work with Vorrapan Chandee\, Xiann
 an\nLi\, and Maksym Radziwill on moments of Dirichlet $L$-functions. I wil
 l\nmostly concentrate on our result giving an asymptotic formula for the\n
 eighth moment of Dirichlet L-functions averaged over primitive\ncharacters
  modulo $q$\, over all moduli $q \\leq Q$ and with a short\naverage on t
 he critical line. Previously this result was known only\nconditionally on 
 the Generalized Riemann Hypothesis by work of Chandee\nand Li whereas a co
 rresponding unconditional result for the sixth\nmoment was known by work o
 f Conrey\, Iwaniec and Soundararajan..\n
LOCATION:https://stable.researchseminars.org/talk/IML_NT/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aled Walker (Cambridge)
DTSTART:20210315T160000Z
DTEND:20210315T170000Z
DTSTAMP:20260404T131148Z
UID:IML_NT/12
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/IML_N
 T/12/">Poissonian gap distributions of dilated sequences</a>\nby Aled Walk
 er (Cambridge) as part of IML Number Theory semester (spring 2021)\n\n\nAb
 stract\nIn the late 1990s\, Rudnick and Sarnak conjectured that the gap\nd
 istribution of the sequence of dilated squares modulo 1\, at least for a\n
 generic dilate\, should agree with the gap distribution of a set of\nunifo
 rmly distributed random points modulo 1.  This conjecture is still\ncomple
 tely open. Nonetheless\, the conjecture has stimulated a great deal\nof wo
 rk\, studying these gap distributions of dilated squares and dilates\nof o
 ther sequences\, particularly focussed on the associated correlation\nfunc
 tions. Recently\, connections were discovered to certain notions from\nadd
 itive combinatorics and sum-product theory. In this talk I will\ndiscuss s
 ome of the work I've been involved with on pair correlations\nand triple c
 orrelations related to these problems\, studying dilates of\nthe primes\, 
 the squares\, and of generic sequences -- sometimes jointly\nwith various 
 subsets of Thomas Bloom\, Sam Chow\, Ayla Gafni\, and Niclas\nTechnau.\n
LOCATION:https://stable.researchseminars.org/talk/IML_NT/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anders Södergren (Chalmers)
DTSTART:20210317T171500Z
DTEND:20210317T181500Z
DTSTAMP:20260404T131148Z
UID:IML_NT/13
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/IML_N
 T/13/">Can a random lattice and its dual be independent?</a>\nby Anders S
 ödergren (Chalmers) as part of IML Number Theory semester (spring 2021)\n
 \n\nAbstract\nIn this talk I will discuss Rogers' mean value formula in\nt
 he space of unimodular lattices as well as a recent generalization of\nRog
 ers' formula. In particular\, I will describe a formula for mean\nvalues o
 f products of Siegel transforms with arguments taken from both\na lattice 
 and its dual lattice. The main application is a result on\nthe joint distr
 ibution of the vector lengths in a random lattice and\nits dual lattice in
  the limit as the dimension of the lattices tends\nto infinity\, and provi
 des a partial affirmative answer to the question\nin the title. This is jo
 int work with Andreas Strömbergsson.\n
LOCATION:https://stable.researchseminars.org/talk/IML_NT/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrew Granville (U de Montreal)
DTSTART:20210322T160000Z
DTEND:20210322T170000Z
DTSTAMP:20260404T131148Z
UID:IML_NT/14
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/IML_N
 T/14/">Exponential sums with multiplicative coefficients and applications<
 /a>\nby Andrew Granville (U de Montreal) as part of IML Number Theory seme
 ster (spring 2021)\n\n\nAbstract\nIn joint work with R\\'egis de la Bret\\
 `eche we develop what\npretentiousness tells us about exponential sums and
  various arithmetic\nproblems involving the circle method.\n
LOCATION:https://stable.researchseminars.org/talk/IML_NT/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Morten Risager (University of Copenhagen)
DTSTART:20210324T171500Z
DTEND:20210324T181500Z
DTSTAMP:20260404T131148Z
UID:IML_NT/15
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/IML_N
 T/15/">Bounds on shifted convolution sums</a>\nby Morten Risager (Universi
 ty of Copenhagen) as part of IML Number Theory semester (spring 2021)\n\n\
 nAbstract\nShifted convolution sums for automorphic forms have been\nstudi
 ed for about 100 years. Famous instances include sum in the\nadditive divi
 sor problem and in the hyperbolic lattice point problem. We\ndiscuss vario
 us bounds and some thoughts on how to improve them. We also\ndiscuss vario
 us average bounds.\n
LOCATION:https://stable.researchseminars.org/talk/IML_NT/15/
END:VEVENT
END:VCALENDAR