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BEGIN:VEVENT
SUMMARY:Jon Keating (University of Oxford)
DTSTART:20210118T160000Z
DTEND:20210118T170000Z
DTSTAMP:20260422T225824Z
UID:IML_NT/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/IML_NT/1/">J
 oint Moments</a>\nby Jon Keating (University of Oxford) as part of IML Num
 ber Theory semester (spring 2021)\n\n\nAbstract\nI will discuss the joint 
 moments of the Riemann zeta-function and its\nderivative\, and the corresp
 onding joint moments of the characteristic\npolynomials of random unitary 
 matrices and their derivatives.\n
LOCATION:https://researchseminars.org/talk/IML_NT/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emmanuel Kowalski (ETH)
DTSTART:20210125T160000Z
DTEND:20210125T170000Z
DTSTAMP:20260422T225824Z
UID:IML_NT/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/IML_NT/2/">T
 he shapes of exponential sums</a>\nby Emmanuel Kowalski (ETH) as part of I
 ML Number Theory semester (spring 2021)\n\n\nAbstract\nWe will survey the 
 functional limit theorems for partial sums of\nexponential sums over finit
 e fields\, starting from the case of\nKloosterman paths\, covering recent 
 developments as well as\napplications and open problems.\n
LOCATION:https://researchseminars.org/talk/IML_NT/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Valentin Blomer (Universität Bonn)
DTSTART:20210210T171500Z
DTEND:20210210T181500Z
DTSTAMP:20260422T225824Z
UID:IML_NT/3
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/IML_NT/3/">U
 niform Titchmarsh divisor problems</a>\nby Valentin Blomer (Universität B
 onn) as part of IML Number Theory semester (spring 2021)\n\n\nAbstract\nTh
 e classical Titchmarsh divisor problem asks for the asymptotic\nevaluation
  of the divisor function over shifted primes. It is\nintimately related wi
 th primes in long arithmetic progressions. Modern\nmethods can produce str
 ong error terms for fixed shifts\, but no\nprogress since the 1960s has be
 en made on the dual problem of summing\nd(n-p) for p < n or the related pr
 oblem of Hooley and Linnik of\nrepresenting a number a sum of a prime and 
 two squares. I will survey\napproaches and techniques towards the Titchmar
 sh divisor problem and\nits variations\, and present new results obtained 
 in joint work with\nEdgar Assing and Junxian Li. The methods involve a ble
 nd of classical\nanalytic number theory\, automorphic forms and algebraic 
 geometry.\n
LOCATION:https://researchseminars.org/talk/IML_NT/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Fiorilli (Université Paris-Sud)
DTSTART:20210208T160000Z
DTEND:20210208T164500Z
DTSTAMP:20260422T225824Z
UID:IML_NT/4
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/IML_NT/4/">H
 igher 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 and of Ba
 rban\, Davenport and Halberstam\, the variances of primes in intervals and
  in arithmetic progressions have been widely studied and continue to be an
  active topic of research. However\, much less is known about higher momen
 ts. Hooley established a bound on the third moment in progressions\, which
  was later sharpened by Vaughan for a variant involving a major arcs appro
 ximation. Little is known for moments of order four or higher\, other than
  the conjecture of Hooley and the conditional result of Montgomery-Soundar
 arajan. In this talk I will discuss recent joint work with Régis de la Br
 etèche on weighted moments in intervals and on weighted moments of moment
 s in progressions. In particular we will show how to deduce sharp uncondit
 ional omega results on all weighted even moments in certain ranges.\n
LOCATION:https://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:20260422T225824Z
UID:IML_NT/5
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/IML_NT/5/">H
 igher moments of primes in intervals and in arithmetic progressions\, II</
 a>\nby Régis de la Bretèche (Université Paris Diderot\, Paris 7) as par
 t of IML Number Theory semester (spring 2021)\n\n\nAbstract\nThis is the s
 econd part of the talk of Daniel Fiorilli. We will explain the proofs of o
 ur theorem about the moments of moments of primes in arithmetic progressio
 ns.\n
LOCATION:https://researchseminars.org/talk/IML_NT/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joni Teravainen (University of Oxford)
DTSTART:20210215T160000Z
DTEND:20210215T170000Z
DTSTAMP:20260422T225824Z
UID:IML_NT/6
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/IML_NT/6/">S
 ums of two almost twin primes</a>\nby Joni Teravainen (University of Oxfor
 d) as part of IML Number Theory semester (spring 2021)\n\n\nAbstract\nIn 1
 975\, Montgomery and Vaughan proved that the number of\nexceptions to the 
 binary Goldbach problem is power-saving. I will\ndiscuss work where we obt
 ain a nearly power-saving exceptional set for\nnumbers that are not the su
 m of two "almost twin primes". This is\njoint work with Lasse Grimmelt.\n
LOCATION:https://researchseminars.org/talk/IML_NT/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sacha Mangerel (University of Montreal)
DTSTART:20210217T171500Z
DTEND:20210217T181500Z
DTSTAMP:20260422T225824Z
UID:IML_NT/7
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/IML_NT/7/">D
 iscrepancy Problems for Multiplicative Functions over F_q[t]</a>\nby Sacha
  Mangerel (University of Montreal) as part of IML Number Theory semester (
 spring 2021)\n\n\nAbstract\nAn equivalent form of the famous Erdos Discrep
 ancy Problem\, proved by\nTao building on the work of the Polymath5 projec
 t\, states that any\ncompletely multiplicative function taking values on t
 he unit circle has\nunbounded partial sums. It was observed in the course 
 of the Polymath5\nproject that the same is not true if one considers the m
 ost natural\ntranslation of this problem to the ring F_q[t] of polynomials
  over a\nfinite field.\n\nWe will discuss recent joint work with O. Klurma
 n and J. Teräväinen\ndemonstrating that the function field discrepancy p
 roblem depends\nheavily on the way the elements of the sums are ordered\, 
 in contrast to\nthe integer setting. In particular\, we will introduce thr
 ee different\nnotions of discrepancy\, and discuss the problem of classify
 ing those\ncompletely multiplicative functions that have uniformly bounded
  partial\nsums with respect to each of these notions.  We will also addres
 s the\nproblem of bounding the minimal rate of growth of unbounded partial
 \nsums\, which is the subject of some speculation in the integer setting.\
 n
LOCATION:https://researchseminars.org/talk/IML_NT/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Steve Lester (King's College)
DTSTART:20210303T171500Z
DTEND:20210303T181500Z
DTSTAMP:20260422T225824Z
UID:IML_NT/8
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/IML_NT/8/">L
 attice points on hyperbolic circles</a>\nby Steve Lester (King's College) 
 as part of IML Number Theory semester (spring 2021)\n\n\nAbstract\nThe hyp
 erbolic lattice point problem is to determine the\nnumber of translates of
  a given point in the complex upper half-plane by\nelements of a discrete 
 subgroup of PSL_2(R) that lie within a hyperbolic\ncircle. This may be vie
 wed as a non-Euclidean analogue of the Gauss\ncircle problem. In this talk
  I will give an overview of some results on\nthe hyperbolic lattice point 
 problem and will also present some recent\nwork concerning the angular dis
 tribution of lattice points lying on\nhyperbolic circles. This is joint wi
 th Dimitrios Chatzakos\, Pär\nKurlberg\, and Igor Wigman.\n
LOCATION:https://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:20260422T225824Z
UID:IML_NT/9
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/IML_NT/9/">T
 he distribution of the Estermann function and other quantum modular forms<
 /a>\nby Sandro Bettin & Sary Drappeau (University of Genova & Université 
 d'Aix-Marseille) as part of IML Number Theory semester (spring 2021)\n\n\n
 Abstract\nFor a rational a/q\, the Estermann function is defined as the ad
 ditive 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 functiona
 l equation which encodes Voronoi's summation formula. \n\nIt is natural to
  ask how the central values D(1/2\,a/q) are distributed as the\nrational a
 /q varies.  In contrast with the case of multiplicative twists of\nL-funct
 ions\, D(s\,a/q) does not have an Euler product and thus the usual\nmachin
 ery 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 between the\n
 values 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 variable.\n
LOCATION:https://researchseminars.org/talk/IML_NT/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sarah Peluse (Princeton/IAS)
DTSTART:20210310T171500Z
DTEND:20210310T181500Z
DTSTAMP:20260422T225824Z
UID:IML_NT/10
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/IML_NT/10/">
 Modular zeros in the character table of the symmetric group</a>\nby Sarah 
 Peluse (Princeton/IAS) as part of IML Number Theory semester (spring 2021)
 \n\n\nAbstract\nIn 2017\, Miller conjectured\, based on computational evid
 ence\, that for\nany fixed prime $p$ the density of entries in the charact
 er table of $S_n$ that\nare divisible by $p$ goes to $1$ as $n$ goes to in
 finity. I’ll describe a proof of\nthis conjecture\, which is joint work 
 with K. Soundararajan. I will also discuss the\n(still open) problem of de
 termining the asymptotic density of zeros in the\ncharacter table of $S_n$
 \, where it is not even clear from computational data\nwhat one should exp
 ect.\n
LOCATION:https://researchseminars.org/talk/IML_NT/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kaisa Matomäki (University of Turku)
DTSTART:20210308T160000Z
DTEND:20210308T170000Z
DTSTAMP:20260422T225824Z
UID:IML_NT/11
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/IML_NT/11/">
 Moments of Dirichlet $L$-functions</a>\nby Kaisa Matomäki (University of 
 Turku) as part of IML Number Theory semester (spring 2021)\n\n\nAbstract\n
 I will discuss my on-going joint work with Vorrapan Chandee\, Xiannan\nLi\
 , and Maksym Radziwill on moments of Dirichlet $L$-functions. I will\nmost
 ly concentrate on our result giving an asymptotic formula for the\neighth 
 moment of Dirichlet L-functions averaged over primitive\ncharacters modul
 o $q$\, over all moduli $q \\leq Q$ and with a short\naverage on the crit
 ical line. Previously this result was known only\nconditionally on the Gen
 eralized Riemann Hypothesis by work of Chandee\nand Li whereas a correspon
 ding unconditional result for the sixth\nmoment was known by work of Conre
 y\, Iwaniec and Soundararajan..\n
LOCATION:https://researchseminars.org/talk/IML_NT/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aled Walker (Cambridge)
DTSTART:20210315T160000Z
DTEND:20210315T170000Z
DTSTAMP:20260422T225824Z
UID:IML_NT/12
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/IML_NT/12/">
 Poissonian gap distributions of dilated sequences</a>\nby Aled Walker (Cam
 bridge) as part of IML Number Theory semester (spring 2021)\n\n\nAbstract\
 nIn the late 1990s\, Rudnick and Sarnak conjectured that the gap\ndistribu
 tion of the sequence of dilated squares modulo 1\, at least for a\ngeneric
  dilate\, should agree with the gap distribution of a set of\nuniformly di
 stributed random points modulo 1.  This conjecture is still\ncompletely op
 en. Nonetheless\, the conjecture has stimulated a great deal\nof work\, st
 udying these gap distributions of dilated squares and dilates\nof other se
 quences\, particularly focussed on the associated correlation\nfunctions. 
 Recently\, connections were discovered to certain notions from\nadditive c
 ombinatorics and sum-product theory. In this talk I will\ndiscuss some of 
 the work I've been involved with on pair correlations\nand triple correlat
 ions related to these problems\, studying dilates of\nthe primes\, the squ
 ares\, and of generic sequences -- sometimes jointly\nwith various subsets
  of Thomas Bloom\, Sam Chow\, Ayla Gafni\, and Niclas\nTechnau.\n
LOCATION:https://researchseminars.org/talk/IML_NT/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anders Södergren (Chalmers)
DTSTART:20210317T171500Z
DTEND:20210317T181500Z
DTSTAMP:20260422T225824Z
UID:IML_NT/13
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/IML_NT/13/">
 Can a random lattice and its dual be independent?</a>\nby Anders Södergre
 n (Chalmers) as part of IML Number Theory semester (spring 2021)\n\n\nAbst
 ract\nIn this talk I will discuss Rogers' mean value formula in\nthe space
  of unimodular lattices as well as a recent generalization of\nRogers' for
 mula. In particular\, I will describe a formula for mean\nvalues of produc
 ts of Siegel transforms with arguments taken from both\na lattice and its 
 dual lattice. The main application is a result on\nthe joint distribution 
 of the vector lengths in a random lattice and\nits dual lattice in the lim
 it as the dimension of the lattices tends\nto infinity\, and provides a pa
 rtial affirmative answer to the question\nin the title. This is joint work
  with Andreas Strömbergsson.\n
LOCATION:https://researchseminars.org/talk/IML_NT/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrew Granville (U de Montreal)
DTSTART:20210322T160000Z
DTEND:20210322T170000Z
DTSTAMP:20260422T225824Z
UID:IML_NT/14
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/IML_NT/14/">
 Exponential sums with multiplicative coefficients and applications</a>\nby
  Andrew Granville (U de Montreal) as part of IML Number Theory semester (s
 pring 2021)\n\n\nAbstract\nIn joint work with R\\'egis de la Bret\\`eche w
 e develop what\npretentiousness tells us about exponential sums and variou
 s arithmetic\nproblems involving the circle method.\n
LOCATION:https://researchseminars.org/talk/IML_NT/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Morten Risager (University of Copenhagen)
DTSTART:20210324T171500Z
DTEND:20210324T181500Z
DTSTAMP:20260422T225824Z
UID:IML_NT/15
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/IML_NT/15/">
 Bounds on shifted convolution sums</a>\nby Morten Risager (University of C
 openhagen) as part of IML Number Theory semester (spring 2021)\n\n\nAbstra
 ct\nShifted convolution sums for automorphic forms have been\nstudied for 
 about 100 years. Famous instances include sum in the\nadditive divisor pro
 blem and in the hyperbolic lattice point problem. We\ndiscuss various boun
 ds and some thoughts on how to improve them. We also\ndiscuss various aver
 age bounds.\n
LOCATION:https://researchseminars.org/talk/IML_NT/15/
END:VEVENT
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