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:6825b7408855d DTSTART;TZID=America/Toronto:20240402T100000 SEQUENCE:0 TRANSP:TRANSPARENT DTEND;TZID=America/Toronto:20240402T110000 URL:/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:Summary \n\nJAKUB KRÁSENSKÝ\, CZECH TECHNICAL UNIVERSITY IN P RAGUE\n\nBy the celebrated 15 theorem of Conway and Schneeberger\, a class ical\npositive definite quadratic form over Z is universal if it represent s\neach element 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 that such a finite criterion set exists in a much general\nsett ing\, but the uniqueness of the criterion set is lost. Since then\,\nthe q uestion of uniqueness for particular situations has been studied\nby sever al authors.\n\nWe will discuss the analogous questions for totally positiv e definite\nquadratic forms over totally real number fields. Here again\, the\nexistence of criterion sets for universality is known\, and Lee\ndete rmined the set for Q(sqrt5). We will show the uniqueness and a\nstrong con nection 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= a3RpZUhxTkd6LzFXTmcwdTBCMWs0QT09\n DTSTAMP:20250515T094328Z END:VEVENT BEGIN:VEVENT UID:6825b7408b799 DTSTART;TZID=America/Toronto:20240326T100000 SEQUENCE:0 TRANSP:TRANSPARENT DTEND;TZID=America/Toronto:20240326T110000 URL:/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:Summary \n\nMICAH MILINOVICH\, UNIVERSITY OF MISSISSIPPI\n\nThe re are many situations where one imposes certain conditions on a\nfunction and its Fourier transform and then wants to optimize a\ncertain quantit y. I will describe two such Fourier optimization\nframeworks that can be used to study classical problems in number\ntheory: bounding the maximum gap between consecutive primes assuming\nthe Riemann hypothesis and boun ding for the size of the least\nquadratic non-residue modulo a prime assum ing the generalized Riemann\nhypothesis (GRH) for Dirichlet L-functions. T he resulting extremal\nproblems can be stated in accessible terms\, but fi nding the exact\nanswer appears to be rather subtle. Instead\, we experime ntally find\nupper and lower bounds for our desired quantity that are nume rically\nclose. If time allows\, I will discuss how a similar Fourier\nopt imization framework can be used to bound the size of the least\nprime in a n arithmetic progression on GRH. This is based upon joint\nworks with E. C arneiro (ICTP)\, E. Quesada-Herrera (TU Graz)\, A. Ramos\n(SISSA)\, and K. Soundararajan (Stanford). \n\nMC 5417\n DTSTAMP:20250515T094328Z END:VEVENT BEGIN:VEVENT UID:6825b7408c03f DTSTART;TZID=America/Toronto:20240319T100000 SEQUENCE:0 TRANSP:TRANSPARENT DTEND;TZID=America/Toronto:20240319T110000 URL:/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:Summary \n\nAKASH SENGUPTA\, DEPARTMENT OF PURE MATHEMATICS\, U NIVERSITY OF WATERLOO\n\nGiven a real number x\, how well can we approxima te it using rational\nnumbers? This question has been classically studied by Dirichlet\,\nLiouville\, Roth et al\, and the approximation exponent of a real number\nx measures how well we can approximate x. Similarly\, give n an\nalgebraic variety X over a number field k and a point x in X\, we ca n\nask how well can we approximate x using k-rational points? McKinnon\nan d Roth generalized the approximation exponent to this setting and\nshowed that several classical results also generalize to rational\npoints algebra ic varieties.\n\nIn this talk\, we will define a new variant of the approx imation\nconstant which also captures the geometric properties of the vari ety\nX. We will see that this geometric approximation constant is closely\ nrelated to the behavior of rational curves on X. In particular\, I’ll\n talk about a result showing that if the approximation constant is\nlarger than the dimension of X\, then X must be isomorphic to\nprojective space. This talk is based on joint work with David\nMcKinnon.\n\nMC 5417\n DTSTAMP:20250515T094328Z END:VEVENT BEGIN:VEVENT UID:6825b7408c824 DTSTART;TZID=America/Toronto:20240312T100000 SEQUENCE:0 TRANSP:TRANSPARENT DTEND;TZID=America/Toronto:20240312T110000 URL:/pure-mathematics-number-theory/events/eta-quotient s-whose-derivatives-are-eta-quotients SUMMARY:eta-Quotients whose Derivatives are eta-Quotients CLASS:PUBLIC DESCRIPTION:Summary \n\nAMIR AKBARY\, UNIVERSITY OF LETHBRIDGE\n\nThe Dedek ind eta function 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\\]\nwhere 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\nupp er bound for orders of zeros (at cusps) of a linear combination of\nclassi cal Eisenstein series of weight k and level p^m. As an immediate\nconseque nce\, we find the set of all eta quotients that are linear\ncombinations o f these Eisenstein series and\, hence\, the set of all eta\nquotients of l evel p^m whose derivatives are also eta quotients.\n\nThis is joint work w ith Zafer Selcuk Aygin (Northwestern Polytechnic).\n\nMC 5417\n DTSTAMP:20250515T094328Z END:VEVENT BEGIN:VEVENT UID:6825b7408d06f DTSTART;TZID=America/Toronto:20240305T100000 SEQUENCE:0 TRANSP:TRANSPARENT DTEND;TZID=America/Toronto:20240305T110000 URL:/pure-mathematics-number-theory/events/some-bounds- arakelov-zhang-pairing SUMMARY:Some Bounds on the Arakelov-Zhang Pairing CLASS:PUBLIC DESCRIPTION:Summary \n\nPETER OBERLY\, UNIVERSITY OF ROCHESTER\n\nThe Arake lov--Zhang pairing (also called the dynamical height pairing)\nis a kind o f dynamical distance between two rational maps defined over\na number fiel d. This pairing has applications in arithmetic dynamics\,\nespecially as a tool to study the preperiodic points common to two\nrational maps. We wil l discuss some bounds on the Arakelov-Zhang\npairing of f and g in terms o f the coefficients of f and investigate\nsome simple consequences of this result. \n\nMC 5417\n DTSTAMP:20250515T094328Z END:VEVENT BEGIN:VEVENT UID:6825b7408d810 DTSTART;TZID=America/Toronto:20240227T110000 SEQUENCE:0 TRANSP:TRANSPARENT DTEND;TZID=America/Toronto:20240227T120000 URL:/pure-mathematics-number-theory/events/remarks-form ula-ramanujan SUMMARY:Remarks on a formula of Ramanujan CLASS:PUBLIC DESCRIPTION:Summary \n\nANDRÉS CHIRRE\, PONTIFICAL CATHOLIC UNIVERSITY OF PERU\n\nIn this talk\, we will discuss a well-known formula of Ramanujan a nd\nits relationship with the partial sums of the Möbius function. Under\ nsome conjectures\, we analyze a finer structure of the involved terms.\nI t is a joint work with Steven M. Gonek.\n\nZoom link:\nhttps://uwaterloo.z oom.us/j/98937322498?pwd=a3RpZUhxTkd6LzFXTmcwdTBCMWs0QT09\n DTSTAMP:20250515T094328Z END:VEVENT BEGIN:VEVENT UID:6825b7408dfb8 DTSTART;TZID=America/Toronto:20240213T100000 SEQUENCE:0 TRANSP:TRANSPARENT DTEND;TZID=America/Toronto:20240213T110000 URL:/pure-mathematics-number-theory/events/twisted-addi tive-divisor-problem-0 SUMMARY:A twisted additive divisor problem CLASS:PUBLIC DESCRIPTION:Summary \n\nALEX COWAN\, HARVARD UNIVERSITY\n\nWhat correlation is there between the number of divisors of N and the\nnumber of divisors of N + 1? This is known as the classical additive\ndivisor problem. This t alk will be about a generalized form of this\nquestion: I’ll give asympt otics for a shifted convolution of\nsum-of-divisors functions with nonzero powers and twisted by Dirichlet\ncharacters. The spectral methods of auto morphic forms used to prove\nthe main result are quite general\, and I’l l present a conceptual\noverview. One step of the proof uses a less well-k nown technique\ncalled “automorphic regularization” for obtaining the spectral\ndecomposition of a combination of Eisenstein series which is not \nobviously square-integrable.\n\nMC 5417\n DTSTAMP:20250515T094328Z END:VEVENT BEGIN:VEVENT UID:6825b7408e702 DTSTART;TZID=America/Toronto:20240206T100000 SEQUENCE:0 TRANSP:TRANSPARENT DTEND;TZID=America/Toronto:20240206T110000 URL:/pure-mathematics-number-theory/events/twisted-addi tive-divisor-problem SUMMARY:A twisted additive divisor problem CLASS:PUBLIC DESCRIPTION:Summary \n\nALEX COWEN\, HARVARD UNIVERSITY\n\nWhat correlation is there between the number of divisors of N and the\nnumber of divisors of N+1? This is known as the classical additive\ndivisor problem. This tal k will be about a generalized form of this\nquestion: I'll give asymptotic s for a shifted convolution of\nsum-of-divisors functions with nonzero pow ers and twisted by Dirichlet\ncharacters. The spectral methods of automorp hic forms used to prove\nthe main result are quite general\, and I'll pres ent a conceptual\noverview. One step of the proof uses a less well-known t echnique\ncalled \"automorphic regularization\" for obtaining the spectral \ndecomposition of a combination of Eisenstein series which is not\nobviou sly square-integrable.\n\nMC 5417\n DTSTAMP:20250515T094328Z END:VEVENT BEGIN:VEVENT UID:6825b7408ef4a DTSTART;TZID=America/Toronto:20240130T100000 SEQUENCE:0 TRANSP:TRANSPARENT DTEND;TZID=America/Toronto:20240130T110000 URL:/pure-mathematics-number-theory/events/circle-metho d-and-binary-correlation-problems SUMMARY:Circle method and binary correlation problems CLASS:PUBLIC DESCRIPTION:Summary \n\nKUNJAKANAN NATH\, UNIVERSITY OF ILLINOIS\, URBANA-C HAMPAIGN\n\nOne of the key problems in number theory is to understand the\ ncorrelation between two arithmetic functions. In general\, it is an\nextr emely difficult question and often leads to famous open problems\nlike the Twin Prime Conjecture\, the Goldbach Conjecture\, and the\nChowla Conject ure\, to name a few. In this talk\, we will discuss a few\nbinary correlat ion problems involving primes\, square-free integers\,\nand integers with restricted digits. The objective is to demonstrate\nthe application of Fou rier analysis (aka the circle method) in\nconjunction with the arithmetic structure of the given sequence and\nthe bilinear form method to solve the se problems.\n\nZoom\nlink: https://uwaterloo.zoom.us/j/98937322498?pwd=a 3RpZUhxTkd6LzFXTmcwdTBCMWs0QT09\n DTSTAMP:20250515T094328Z END:VEVENT BEGIN:VEVENT UID:6825b7408f719 DTSTART;TZID=America/Toronto:20240123T100000 SEQUENCE:0 TRANSP:TRANSPARENT DTEND;TZID=America/Toronto:20240123T110000 URL:/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:Summary \n\nKISEOK YEON\, PURDUE UNIVERSITY\n\nIn this talk\, w e introduce a framework via the circle method in order\nto confirm the Has se principle for random homogeneous polynomials in\nthin sets. We first gi ve a motivation for developing this framework by\nproviding an overall his tory of the problems of confirming the Hasse\nprinciple for homogeneous po lynomials. Next\, 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 o ur recent joint work with H. Lee and\nS. Lee\, we discuss the global solub ility for random homogeneous\npolynomials in thin sets.\n\nZoom\nlink: h ttps://uwaterloo.zoom.us/j/98937322498?pwd=a3RpZUhxTkd6LzFXTmcwdTBCMWs0QT0 9\n DTSTAMP:20250515T094328Z END:VEVENT END:VCALENDAR