PPT-Symmetries and Groups

Raymond Flood Gresham Professor of Geometry Overview Group of Symmetries of the equilateral triangle Compare the group of symmetries of a square and a rectangle Symmetries of the platonic solids. to Solve . Difficult Logic Puzzles. Igor Markov. University of Michigan, EECS. Outline. A brief introduction to the field of . Electronic Design Automation. Integrated circuits, design tools, research challenges. models of gravity. Rabin Banerjee. *,. . 1. , . Debraj Roy. *, 2. 1. rabin@bose.res.in, . 2. debraj@bose.res.in. *. S. N. Bose National Centre. for Basic Sciences,. . Kolkata, India.. . Overview of the problem. SEVENTH EDITION. Joseph A. . Gallian. Chapter . 1: . Introduction to Groups. Symmetries of a Square . The Dihedral Groups . 1.1 . Symmetries of a Square . The Square 1/3. The Square 2/3. The S. quare 3/3. Frank Farris. Rosettes and friezes. Wallpaper. Color-reversing symmetry. Rosettes and Friezes. Visual identification of pattern types. Mathematical details checked using complex numbers. Sources: Book from Princeton . Thank you, Emmy. 1. Symmetries and Conservation Laws. An example of conservation. Suppose we have the system . The equations of motion are. So.  . Symmetries and Conservation Laws. 2. What just happened?. Danny Brown. outline. What is a group?. Symmetry groups. Some more groups. Permutations. Shuffles and bell-ringing. Even more symmetry. Rotation and reflection. Direct and indirect symmetries. what is a group?. Pierre-Hugues Beauchemin. PHY 006 –. Talloire. , May 2013. Symmetries in nature. Many objects in nature presents a high level of symmetry, indicating that the forces that produced these objects feature the same symmetries. Gregory Moore. a project with Jeff Harvey. DaveDay. , Caltech, Feb. 25, 2016. Motivation. Search for a conceptual . explanation of. Mathieu . Moonshine phenomena. . Proposal: It . is related . Groups: . A Geometric Introduction. Robert “Dr. Bob” Gardner, Fall . 2015 (Revised and Corrected Version). In the third week of class (in Section I.4 of . Fraleigh. ), you will see the definition of a “group.”. : Extracting Building Blocks from Correspondences. Javor. . Kalojanov. , Martin . Bokeloh. , Michael Wand, Leonidas . Guibas. , Hans-Peter Seidel, Philipp . Slusallek. Overview. Partial Symmetries. Inverse Procedural . Frank Farris. Rosettes and friezes. Wallpaper. Color-reversing symmetry. Rosettes and Friezes. Visual identification of pattern types. Mathematical details checked using complex numbers. Sources: Book from Princeton . Marek . Zrałek. University of Silesia, Katowice. Workshop on . Discrete Symmetries and Entanglement. 10. 06. 2017, . Kraków. Outline. Introduction. Discrete symmetries in Space Time and charge . c. Gregory Moore. a project with Jeff Harvey. DaveDay. , Caltech, Feb. 25, 2016. Motivation. Search for a conceptual . explanation of. Mathieu . Moonshine phenomena. . Proposal: It . is related . : Classify all of the ways in which…. . (1) bounded objects. . (2) border patterns. . (3) wallpaper patterns. …can be symmetric. . Eventual Goal. : Classify all of the ways in which….