BEGIN:VCALENDAR VERSION:2.0 PRODID:-//Drupal iCal API//EN X-WR-CALNAME:Events items teaser X-WR-TIMEZONE:America/Toronto BEGIN:VTIMEZONE TZID:America/Toronto X-LIC-LOCATION:America/Toronto BEGIN:DAYLIGHT TZNAME:EDT TZOFFSETFROM:-0500 TZOFFSETTO:-0400 DTSTART:20240310T070000 END:DAYLIGHT BEGIN:STANDARD TZNAME:EST TZOFFSETFROM:-0400 TZOFFSETTO:-0500 DTSTART:20231105T060000 END:STANDARD END:VTIMEZONE BEGIN:VEVENT UID:69fafd71cf5de DTSTART;TZID=America/Toronto:20240402T100000 SEQUENCE:0 TRANSP:TRANSPARENT DTEND;TZID=America/Toronto:20240402T110000 URL:https://uwaterloo.ca/pure-mathematics-number-theory/events/criterion-se ts-quadratic-forms-over-number-fields SUMMARY:Criterion sets for quadratic forms over number fields CLASS:PUBLIC DESCRIPTION:JAKUB KRÁSENSKÝ\, CZECH TECHNICAL UNIVERSITY IN PRAGUE\n\nBy the celebrated 15 theorem of Conway and Schneeberger\, a classical\npositi ve definite quadratic form over Z is universal if it represents\neach elem ent of {1\,2\,3\,5\,6\,7\,10\,14\,15}. Moreover\, this is the minimal\nset with this property. In 2005\, B.M. Kim\, M.-H. Kim and B.-K. Oh\nshowed t hat such a finite criterion set exists in a much general\nsetting\, but th e uniqueness of the criterion set is lost. Since then\,\nthe question of u niqueness for particular situations has been studied\nby several authors.\ n\nWe will discuss the analogous questions for totally positive definite\n quadratic forms over totally real number fields. Here again\, the\nexisten ce of criterion sets for universality is known\, and Lee\ndetermined the s et for Q(sqrt5). We will show the uniqueness and a\nstrong connection with indecomposable integers. A part of our\nuniqueness result is (to our best knowledge) new even over Z. This is\njoint work with G. Romeo and V. Kala .\n\nZoom\nlink: https://uwaterloo.zoom.us/j/98937322498?pwd=a3RpZUhxTkd6 LzFXTmcwdTBCMWs0QT09 DTSTAMP:20260506T083601Z END:VEVENT BEGIN:VEVENT UID:69fafd71d1620 DTSTART;TZID=America/Toronto:20240326T100000 SEQUENCE:0 TRANSP:TRANSPARENT DTEND;TZID=America/Toronto:20240326T110000 URL:https://uwaterloo.ca/pure-mathematics-number-theory/events/fourier-opti mization-prime-gaps-and-least-quadratic-non SUMMARY:Fourier optimization\, prime gaps\, and the least quadratic non-res idue CLASS:PUBLIC DESCRIPTION:MICAH MILINOVICH\, UNIVERSITY OF MISSISSIPPI\n\nThere are many situations where one imposes certain conditions on a\nfunction and its Fo urier transform and then wants to optimize a\ncertain quantity. I will d escribe two such Fourier optimization\nframeworks that can be used to stud y classical problems in number\ntheory: bounding the maximum gap between consecutive primes assuming\nthe Riemann hypothesis and bounding for the size of the least\nquadratic non-residue modulo a prime assuming the gene ralized Riemann\nhypothesis (GRH) for Dirichlet L-functions. The resulting extremal\nproblems can be stated in accessible terms\, but finding the ex act\nanswer appears to be rather subtle. Instead\, we experimentally find\ nupper and lower bounds for our desired quantity that are numerically\nclo se. If time allows\, I will discuss how a similar Fourier\noptimization fr amework can be used to bound the size of the least\nprime in an arithmetic progression on GRH. This is based upon joint\nworks with E. Carneiro (ICT P)\, E. Quesada-Herrera (TU Graz)\, A. Ramos\n(SISSA)\, and K. Soundararaj an (Stanford). \n\nMC 5417 DTSTAMP:20260506T083601Z END:VEVENT BEGIN:VEVENT UID:69fafd71d2049 DTSTART;TZID=America/Toronto:20240319T100000 SEQUENCE:0 TRANSP:TRANSPARENT DTEND;TZID=America/Toronto:20240319T110000 URL:https://uwaterloo.ca/pure-mathematics-number-theory/events/approximatio n-rational-points-and-characterization SUMMARY:Approximation of rational points and a characterization of projecti ve\nspace CLASS:PUBLIC DESCRIPTION:AKASH SENGUPTA\, DEPARTMENT OF PURE MATHEMATICS\, UNIVERSITY OF WATERLOO\n\nGiven a real number x\, how well can we approximate it using rational\nnumbers? This question has been classically studied by Dirichlet \,\nLiouville\, Roth et al\, and the approximation exponent of a real numb er\nx measures how well we can approximate x. Similarly\, given an\nalgebr aic variety X over a number field k and a point x in X\, we can\nask how w ell can we approximate x using k-rational points? McKinnon\nand Roth gener alized the approximation exponent to this setting and\nshowed that several classical results also generalize to rational\npoints algebraic varieties .\n\nIn this talk\, we will define a new variant of the approximation\ncon stant which also captures the geometric properties of the variety\nX. We w ill see that this geometric approximation constant is closely\nrelated to the behavior of rational curves on X. In particular\, I’ll\ntalk about a result showing that if the approximation constant is\nlarger than the dim ension of X\, then X must be isomorphic to\nprojective space. This talk is based on joint work with David\nMcKinnon.\n\nMC 5417 DTSTAMP:20260506T083601Z END:VEVENT BEGIN:VEVENT UID:69fafd71d28f3 DTSTART;TZID=America/Toronto:20240312T100000 SEQUENCE:0 TRANSP:TRANSPARENT DTEND;TZID=America/Toronto:20240312T110000 URL:https://uwaterloo.ca/pure-mathematics-number-theory/events/eta-quotient s-whose-derivatives-are-eta-quotients SUMMARY:eta-Quotients whose Derivatives are eta-Quotients CLASS:PUBLIC DESCRIPTION:AMIR AKBARY\, UNIVERSITY OF LETHBRIDGE\n\nThe Dedekind eta func tion is defined by the infinite product\n\\[\n\\eta(z) = e^{\\pi i z/12}\\ prod_{n=1}^\\infty (1 - e^{2 \\pi i z}) =\nq^{1/24}\\prod_{n=1}^\\infty (1 - q^n).\n\\]\nand\n\\[\nf(z) = \\prod_{t\\mid N} \\eta^{r_t}(tz)\,\n\\]\n where the exponent r_t are integers. Let k be an even positive\ninteger\, p be a prime\, and m be a nonnegative integer. We find an\nupper bound for orders of zeros (at cusps) of a linear combination of\nclassical Eisenste in series of weight k and level p^m. As an immediate\nconsequence\, we fin d the set of all eta quotients that are linear\ncombinations of these Eise nstein series and\, hence\, the set of all eta\nquotients of level p^m who se derivatives are also eta quotients.\n\nThis is joint work with Zafer Se lcuk Aygin (Northwestern Polytechnic).\n\nMC 5417 DTSTAMP:20260506T083601Z END:VEVENT BEGIN:VEVENT UID:69fafd71d3644 DTSTART;TZID=America/Toronto:20240305T100000 SEQUENCE:0 TRANSP:TRANSPARENT DTEND;TZID=America/Toronto:20240305T110000 URL:https://uwaterloo.ca/pure-mathematics-number-theory/events/some-bounds- arakelov-zhang-pairing SUMMARY:Some Bounds on the Arakelov-Zhang Pairing CLASS:PUBLIC DESCRIPTION:PETER OBERLY\, UNIVERSITY OF ROCHESTER\n\nThe Arakelov--Zhang p airing (also called the dynamical height pairing)\nis a kind of dynamical distance between two rational maps defined over\na number field. This pair ing has applications in arithmetic dynamics\,\nespecially as a tool to stu dy the preperiodic points common to two\nrational maps. We will discuss so me bounds on the Arakelov-Zhang\npairing of f and g in terms of the coeffi cients of f and investigate\nsome simple consequences of this result. \n\ nMC 5417 DTSTAMP:20260506T083601Z END:VEVENT BEGIN:VEVENT UID:69fafd71d3f6f DTSTART;TZID=America/Toronto:20240227T110000 SEQUENCE:0 TRANSP:TRANSPARENT DTEND;TZID=America/Toronto:20240227T120000 URL:https://uwaterloo.ca/pure-mathematics-number-theory/events/remarks-form ula-ramanujan SUMMARY:Remarks on a formula of Ramanujan CLASS:PUBLIC DESCRIPTION:ANDRÉS CHIRRE\, PONTIFICAL CATHOLIC UNIVERSITY OF PERU\n\nIn t his talk\, we will discuss a well-known formula of Ramanujan and\nits rela tionship with the partial sums of the Möbius function. Under\nsome conjec tures\, we analyze a finer structure of the involved terms.\nIt is a joint work with Steven M. Gonek.\n\nZoom link:\nhttps://uwaterloo.zoom.us/j/989 37322498?pwd=a3RpZUhxTkd6LzFXTmcwdTBCMWs0QT09 DTSTAMP:20260506T083601Z END:VEVENT BEGIN:VEVENT UID:69fafd71d48a2 DTSTART;TZID=America/Toronto:20240213T100000 SEQUENCE:0 TRANSP:TRANSPARENT DTEND;TZID=America/Toronto:20240213T110000 URL:https://uwaterloo.ca/pure-mathematics-number-theory/events/twisted-addi tive-divisor-problem-0 SUMMARY:A twisted additive divisor problem CLASS:PUBLIC DESCRIPTION:ALEX COWAN\, HARVARD UNIVERSITY\n\nWhat correlation is there be tween the number of divisors of N and the\nnumber of divisors of N + 1? Th is is known as the classical additive\ndivisor problem. This talk will be about a generalized form of this\nquestion: I’ll give asymptotics for a shifted convolution of\nsum-of-divisors functions with nonzero powers and twisted by Dirichlet\ncharacters. The spectral methods of automorphic form s used to prove\nthe main result are quite general\, and I’ll present a conceptual\noverview. One step of the proof uses a less well-known techniq ue\ncalled “automorphic regularization” for obtaining the spectral\nde composition of a combination of Eisenstein series which is not\nobviously square-integrable.\n\nMC 5417 DTSTAMP:20260506T083601Z END:VEVENT BEGIN:VEVENT UID:69fafd71d5047 DTSTART;TZID=America/Toronto:20240206T100000 SEQUENCE:0 TRANSP:TRANSPARENT DTEND;TZID=America/Toronto:20240206T110000 URL:https://uwaterloo.ca/pure-mathematics-number-theory/events/twisted-addi tive-divisor-problem SUMMARY:A twisted additive divisor problem CLASS:PUBLIC DESCRIPTION:ALEX COWEN\, HARVARD UNIVERSITY\n\nWhat correlation is there be tween the number of divisors of N and the\nnumber of divisors of N+1? This is known as the classical additive\ndivisor problem. This talk will be ab out a generalized form of this\nquestion: I'll give asymptotics for a shif ted convolution of\nsum-of-divisors functions with nonzero powers and twis ted by Dirichlet\ncharacters. The spectral methods of automorphic forms us ed to prove\nthe main result are quite general\, and I'll present a concep tual\noverview. One step of the proof uses a less well-known technique\nca lled \"automorphic regularization\" for obtaining the spectral\ndecomposit ion of a combination of Eisenstein series which is not\nobviously square-i ntegrable.\n\nMC 5417 DTSTAMP:20260506T083601Z END:VEVENT BEGIN:VEVENT UID:69fafd71d580d DTSTART;TZID=America/Toronto:20240130T100000 SEQUENCE:0 TRANSP:TRANSPARENT DTEND;TZID=America/Toronto:20240130T110000 URL:https://uwaterloo.ca/pure-mathematics-number-theory/events/circle-metho d-and-binary-correlation-problems SUMMARY:Circle method and binary correlation problems CLASS:PUBLIC DESCRIPTION:KUNJAKANAN NATH\, UNIVERSITY OF ILLINOIS\, URBANA-CHAMPAIGN\n\n One of the key problems in number theory is to understand the\ncorrelation between two arithmetic functions. In general\, it is an\nextremely diffic ult question and often leads to famous open problems\nlike the Twin Prime Conjecture\, the Goldbach Conjecture\, and the\nChowla Conjecture\, to nam e a few. In this talk\, we will discuss a few\nbinary correlation problems involving primes\, square-free integers\,\nand integers with restricted d igits. The objective is to demonstrate\nthe application of Fourier analysi s (aka the circle method) in\nconjunction with the arithmetic structure of the given sequence and\nthe bilinear form method to solve these problems. \n\nZoom\nlink: https://uwaterloo.zoom.us/j/98937322498?pwd=a3RpZUhxTkd6L zFXTmcwdTBCMWs0QT09 DTSTAMP:20260506T083601Z END:VEVENT BEGIN:VEVENT UID:69fafd71d6035 DTSTART;TZID=America/Toronto:20240123T100000 SEQUENCE:0 TRANSP:TRANSPARENT DTEND;TZID=America/Toronto:20240123T110000 URL:https://uwaterloo.ca/pure-mathematics-number-theory/events/hasse-princi ple-random-homogeneous-polynomials-thin-sets SUMMARY:The Hasse principle for random homogeneous polynomials in thin sets CLASS:PUBLIC DESCRIPTION:KISEOK YEON\, PURDUE UNIVERSITY\n\nIn this talk\, we introduce a framework via the circle method in order\nto confirm the Hasse principle for random homogeneous polynomials in\nthin sets. We first give a motivat ion for developing this framework by\nproviding an overall history of the problems of confirming the Hasse\nprinciple for homogeneous polynomials. N ext\, we provide a sketch of\nthe proof of our main result and show a part of the estimates used in\nthe proof. Furthermore\, by using our recent jo int work with H. Lee and\nS. Lee\, we discuss the global solubility for ra ndom homogeneous\npolynomials in thin sets.\n\nZoom\nlink: https://uwate rloo.zoom.us/j/98937322498?pwd=a3RpZUhxTkd6LzFXTmcwdTBCMWs0QT09 DTSTAMP:20260506T083601Z END:VEVENT END:VCALENDAR