BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Institute of Mathematics and Informatics - ECPv6.0.8//NONSGML v1.0//EN
CALSCALE:GREGORIAN
METHOD:PUBLISH
X-WR-CALNAME:Institute of Mathematics and Informatics
X-ORIGINAL-URL:https://math.bas.bg
X-WR-CALDESC:Събития за Institute of Mathematics and Informatics
REFRESH-INTERVAL;VALUE=DURATION:PT1H
X-Robots-Tag:noindex
X-PUBLISHED-TTL:PT1H
BEGIN:VTIMEZONE
TZID:Europe/Sofia
BEGIN:DAYLIGHT
TZOFFSETFROM:+0200
TZOFFSETTO:+0300
TZNAME:EEST
DTSTART:20250330T010000
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:+0300
TZOFFSETTO:+0200
TZNAME:EET
DTSTART:20251026T010000
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
DTSTART;TZID=Europe/Sofia:20250430T160000
DTEND;TZID=Europe/Sofia:20250430T173000
DTSTAMP:20260419T102700
CREATED:20250424T092412Z
LAST-MODIFIED:20250424T093036Z
UID:17661-1746028800-1746034200@math.bas.bg
SUMMARY:Семинар по геометрия на МЦМН
DESCRIPTION:Следващата сбирка на Семинара по геометрия на МЦМН\nще се проведе в сряда\, 30 април 2025 г. от 16:00 ч. в зала 403 и онлайн в Zoom: \nДоклад на тема \nBinary Quadratic Forms and Conway’s Topographs (Lecture 1 of 3)\n\nще изнесе Nikita Kalinin\, Guangdong Technion Israel Institute of Technology. \n\nСледващите две лекции ще бъдат на 07.05.2025 и 14.05.2025 от 16:00 ч.\n\nAbstract: Binary quadratic forms are as elementary as they are mysterious—much like prime numbers. In 1997\, John Conway introduced topographs\, a powerful geometric tool that provides a geometric visualization of binary quadratic forms and their values. These lectures will explore how topographs\, combined with telescoping summation techniques\, yield elegant formulas — some with intuitive geometric interpretations. For instance\, consider the following result: \nLet \n\(A = \big\{ (x\, y) \mid  x\,y\in \mathbb{Z}_{\geq 0}^2\, \det(x \ \ y) = 1 \big\}\,\) \nthe set of pairs of lattice vectors in the first quadrant spanning a parallelogram of oriented area 1. Then\, \n\(4 \displaystyle\sum_{(x\,y) \in A} \frac{1}{|x|^2 \cdot |y|^2 \cdot |x+y|^2} = \pi.\) \nLecture Outline \n1. Introduction to Binary Quadratic Forms and Conway’s Topographs\nWe will begin with the basics of binary quadratic forms and their classification\, followed by an introduction to Conway’s topographs—a visual and geometric framework for understanding them. \n2. Class Number Formula and Summation over Topographs\nBuilding on the first lecture\, we will explore the class number formula and how summation identities arise naturally from the structure of topographs. \n3. Evaluation of Lattice Sums via Telescoping over Topographs\nThe final lecture will focus on telescoping techniques\, demonstrating how they can be used to evaluate intricate lattice sums—such as the one above—with geometric meaning. \n\n\nZoom link:\nhttps://us02web.zoom.us/j/86186281353?pwd=6CARUygJaA3HiTNAt3norZQRFt8fIL.1
URL:https://math.bas.bg/event/%d1%81%d0%b5%d0%bc%d0%b8%d0%bd%d0%b0%d1%80-%d0%bf%d0%be-%d0%b3%d0%b5%d0%be%d0%bc%d0%b5%d1%82%d1%80%d0%b8%d1%8f-%d0%bd%d0%b0-%d0%bc%d1%86%d0%bc%d0%bd-15/
LOCATION:Институт по математика и информатика – БАН\, Block 8\, 1113 БАН IV км.\, София\, Bulgaria
CATEGORIES:Редовен семинар
ORGANIZER;CN="%D0%98%D0%BD%D1%81%D1%82%D0%B8%D1%82%D1%83%D1%82%20%D0%BF%D0%BE%20%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0%20%D0%B8%20%D0%B8%D0%BD%D1%84%D0%BE%D1%80%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0%20-%20%D0%91%D0%90%D0%9D":MAILTO:office@math.bas.bg
END:VEVENT
END:VCALENDAR