BEGIN:VCALENDAR VERSION:2.0 PRODID:-//CERN//INDICO//EN BEGIN:VEVENT SUMMARY:Number Theory Day 2026 DTSTART;VALUE=DATE-TIME:20260305T093000Z DTEND;VALUE=DATE-TIME:20260305T163000Z DTSTAMP;VALUE=DATE-TIME:20260419T182907Z UID:indico-event-11297@ictp.it DESCRIPTION:\n Organizers: Emanuel Carneiro (ICTP)\, Pietro Corvaja (Unive rsity of Udine) and Umberto Zannier (SNS - Pisa)Program:\n 10:30 - 11:20: Francesco Amoroso (Univ. of Torino\, Italy)\n Title: Bounded height prob lems and applications\n Abstract: PDF\n 11:30 - 12:20: Christoph Aistleit ner (TU - Graz\, Austria)\n@font-face\n {font-family:"Cambria Math"\;\n pa nose-1:2 4 5 3 5 4 6 3 2 4\;\n mso-font-charset:0\;\n mso-generic-font-fam ily:roman\;\n mso-font-pitch:variable\;\n mso-font-signature:-536870145 11 07305727 0 0 415 0\;}@font-face\n {font-family:Calibri\;\n panose-1:2 15 5 2 2 2 4 3 2 4\;\n mso-font-charset:0\;\n mso-generic-font-family:swiss\;\ n mso-font-pitch:variable\;\n mso-font-signature:-469750017 -1040178053 9 0 511 0\;}@font-face\n {font-family:Lato\;\n panose-1:2 15 5 2 2 2 4 3 2 3 \;\n mso-font-charset:0\;\n mso-generic-font-family:swiss\;\n mso-font-pit ch:variable\;\n mso-font-signature:-520092929 1342237951 33 0 415 0\;}p.Ms oNormal\, li.MsoNormal\, div.MsoNormal\n {mso-style-unhide:no\;\n mso-styl e-qformat:yes\;\n mso-style-parent:""\;\n margin:0cm\;\n mso-pagination:wi dow-orphan\;\n font-size:12.0pt\;\n font-family:"Calibri"\,sans-serif\;\n mso-ascii-font-family:Calibri\;\n mso-ascii-theme-font:minor-latin\;\n mso -fareast-font-family:Calibri\;\n mso-fareast-theme-font:minor-latin\;\n ms o-hansi-font-family:Calibri\;\n mso-hansi-theme-font:minor-latin\;\n mso-b idi-font-family:"Times New Roman"\;\n mso-bidi-theme-font:minor-bidi\;\n m so-fareast-language:EN-US\;}span.c9dxtc\n {mso-style-name:c9dxtc\;\n mso-s tyle-unhide:no\;}p.zfr3q\, li.zfr3q\, div.zfr3q\n {mso-style-name:zfr3q\;\ n mso-style-unhide:no\;\n mso-margin-top-alt:auto\;\n margin-right:0cm\;\n mso-margin-bottom-alt:auto\;\n margin-left:0cm\;\n mso-pagination:widow-o rphan\;\n font-size:12.0pt\;\n font-family:"Times New Roman"\,serif\;\n ms o-fareast-font-family:"Times New Roman"\;}.MsoChpDefault\n {mso-style-type :export-only\;\n mso-default-props:yes\;\n font-family:"Calibri"\,sans-ser if\;\n mso-ascii-font-family:Calibri\;\n mso-ascii-theme-font:minor-latin\ ;\n mso-fareast-font-family:Calibri\;\n mso-fareast-theme-font:minor-latin \;\n mso-hansi-font-family:Calibri\;\n mso-hansi-theme-font:minor-latin\;\ n mso-bidi-font-family:"Times New Roman"\;\n mso-bidi-theme-font:minor-bid i\;\n mso-font-kerning:0pt\;\n mso-ligatures:none\;\n mso-fareast-language :EN-US\;}div.WordSection1\n {page:WordSection1\;} \n Title: Conitnued frac tion expansion of rationals with fixed denominator\n Abstract: In this ta lk I will report on recent joint work with Bence Borda and Manuel Hauke on the distribution of partial quotients of reduced fractions p/q. Here q is understood to be fixed\, and p ranges through the set of coprime integers mod q. I will explain some of the history of the problem\, and point out the relation to Zaremba's conjecture and low-discrepancy sampling with the "good lattice points" method. Then I will explain the method of proof\, w hich is relatively elementary\, and uses Legendre's characterization of co nvergents and the behavior of continued fractions under an reversion of th eir ordering. \n 14:00 - 14:50: Aleksander Simonic (Univ. of Primorska\, Slovenia)\n Title: An explicit form of Ingham's zero density estimate\n A bstract: Ingham (1940) proved that $N(\\sigma\,T)\\ll T^{3(1-\\sigma)/(2- \\sigma)}\\log^{5}{T}$\, where $N(\\sigma\,T)$ counts the number of the no n-trivial zeros $\\rho$ of the Riemann zeta-function with $\\Re\\{\\rho\\} \\geq\\sigma\\geq 1/2$ and $0<\\Im\\{\\rho\\}\\leq T$. Such estimates are often valuable in the distribution theory of prime numbers. In this talk I will present an explicit version of this result with the exponent $(7-5\\ sigma)/(2-\\sigma)$ of the logarithmic factor. The crucial ingredient in t he proof is an explicit estimate with asymptotically correct main term for the fourth power moment of the Riemann zeta-function on the critical line \, a result which is of independent interest. This is joint work with Shas hi Chourasiya (UNSW Canberra). \n 15:00 - 15:50: Julian Demeio (Univ. of Hannover\, Germany)\n Title: Hilbert Modular Surfaces\, Hilbert Property\ , and the Inverse Galois Problem\n Abstract: I will talk on a recent work in collaboration with Damián Gvirtz-Chen\, where we show that the fourte en modular Hilbert surfaces of K3 type possess abundant rational curves. I n particular\, we show that they have enough rational curves to obtain the Hilbert property. We deduce a positive answer to the regular Inverse Galo is Problem for $\\operatorname{PSL}_2(\\mathbb{F}_{p^2})$ for a set of pri mes p of density $1-2^{-12}$.\n 16:30 - 17:20: Martin Widmer (TU - Graz\, Austria)\n Title: Universal quadratic forms over infinite extensions\n Ab stract: Every positive integer is the sum of four squares. An integral po sitive definite quadratic form that represents every positive integer is c alled universal (over the rationals). This notion generalizes to arbitrary totally real fields. It is well-known that that every totally real number field admits a universal quadratic form. For infinite extensions the situ ation is fundamentally different. Daans\, Kala and Man showed that in this case the Northcott property is an obstruction to the existence of such a form. However\, Northcott fields are very rare (in a suitable topological sense). We present a necessary condition for the existence of a universal quadratic form in a given number of variables which is new\, even in the c ase of number fields. As an application we show that most totally real fie lds do not admit a universal quadratic form. This is joint work with Nicol as Daans\, Siu Hang Man\, Vitezslav Kala\, and Pavlo Yatsyna. \n  \n\n Z oom Link: https://zoom.us/meetings/97595235615/invitations?signature=_LFu Lzr70s9IytYLtukHJTGc2goeuCzPOWMoqYASu_Y\n\n\n//indico.ictp.it/event/11297/ LOCATION:ICTP Leonardo Building - Luigi Stasi Seminar Room URL://indico.ictp.it/event/11297/ END:VEVENT END:VCALENDAR