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DTSTART;TZID=Europe/Sofia:20250507T160000
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SUMMARY:Geometry Seminar of ICMS
DESCRIPTION:The next session of the Geometry Seminar of ICMS\nwill be held on Wednesday\, May 7\, 2025\, at 4:00 pm\, in room 403 and via Zoom. \nA talk on: \nBinary Quadratic Forms and Conway’s Topographs (Lecture 2 of 3)\nwill be delivered by Nikita Kalinin\, Guangdong Technion Israel Institute of Technology. \nThe next lecture will be held on 14.05.2025 at 4:00 pm. \n\nAbstract: \n\nBinary 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\n\n\n\nRecording and slides of the first lecture:\nhttps://youtu.be/z7Pz33JyCuA?si=rQ2L4yXJHMdiDkpe\nhttps://kilin-math.github.io/assets/numbers/telescopic_presentation1.pdf
URL:https://math.bas.bg/event/geometry-seminar-of-icms-13/?lang=en
LOCATION:Institute of Mathematics and Informatics\, BAS\, Akad.G.Bonchev St\, bl. 8\, 1113\, Sofia\, Bulgaria
CATEGORIES:Regular Seminar
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DTSTART;TZID=Europe/Sofia:20250513T140000
DTEND;TZID=Europe/Sofia:20250513T151500
DTSTAMP:20250512T115003Z
CREATED:20250512T114627Z
LAST-MODIFIED:20250512T115003Z
UID:17735-1747144800-1747149300@math.bas.bg
SUMMARY:ICMS Seminar
DESCRIPTION:A meeting of the ICMS seminar will be held on May 13\, 2205\, at 2:00 pm\, in Room 403 of IMI – BAS. \nSpeaker: Milan Zlatanovic (University of Niš) \nTitle: Non-symmetric gravitational theorys \nAbstract: We will consider a connection with totally skew-symmetric torsion on non-symmetric (semi-) Riemann manifolds that satisfy Einstein’s metric condition (EMC). We proved that an almost Hermitian manifold is a non-symmetric Riemann manifold that satisfies EMC if and only if it is a Nearly Kahler manifold. We will also show what happens in the case of para Hermitian manifold\, contact\, and para-contact manifolds that satisfy EMC. We show that a connection with skew symmetric torsion satisfying EMC exists on an almost contact metric manifolds when it is D-homothetic to a cosymplectic manifold. We proved the structure theorem for the new class of almost contact metric manifold and special attention we have focused on dimension 5. As a natural continuation of this research\, we dealt with the case of Lorentzian manifolds. \nThis is joint work with Stefan Ivanov and Nikola Stanchev.\nFor more information: https://icms.bg/category/icms-seminar/ \n 
URL:https://math.bas.bg/event/icms-seminar-31/?lang=en
LOCATION:Institute of Mathematics and Informatics\, BAS\, Akad.G.Bonchev St\, bl. 8\, 1113\, Sofia\, Bulgaria
CATEGORIES:Regular Seminar
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