Apollonian sphere packing

Apollonian packings and the quintessential thin group - Elena Fuchs

Speaker: Elena Fuchs (UIUC) Title: Apollonian packings and the quintessential thin group Abstract: In this talk we introduce the Apollonian group, sometimes coined the “quintessential” thin group, which is the underlying symmetry group of Apollonian circle packings. We review some of the e

From playlist My Collaborators

Studying Apollonian Circle Packings using Group Theory

This video is in response to a colleague who asked for short videos about how we use group theory in our research. One of my interests is Apollonian circle packings. Some links: Wikipedia: https://en.wikipedia.org/wiki/Apollonian_gasket An article in New Scientist by Dana Mackenzie: ht

From playlist Joy of Mathematics

Diophantine analysis in thin orbits - Alex Kontorovich

Special Seminar Topic: Diophantine analysis in thin orbits Speaker: Alex Kontorovich Affiliation: Rutgers University; von Neumann Fellow, School of Mathematics Date: December 8, 2017 For more videos, please visit http://video.ias.edu

From playlist Mathematics

Apollonian circle packings via spectral methods - Hee Oh (Yale University)

notes for this talk: https://docs.google.com/viewer?url=http://www.msri.org/workshops/652/schedules/14556/documents/1680/assets/17222 Effective circle count for Apollonian circle packings, via spectral methods Hee Oh Brown University We will describe a recent effective counting result f

From playlist Number Theory

Combinatorics and Geometry to Arithmetic of Circle Packings - Nakamura

Speaker: Kei Nakamura (Rutgers) Title: Combinatorics and Geometry to Arithmetic of Circle Packings Abstract: The Koebe-Andreev-Thurston/Schramm theorem assigns a conformally rigid fi-nite circle packing to a convex polyhedron, and then successive inversions yield a conformally rigid infin

From playlist Mathematics

Geometry and arithmetic of sphere packings - Alex Kontorovich

Members' Seminar Topic: Geometry and arithmetic of sphere packings Speaker: A nearly optimal lower bound on the approximate degree of AC00 Speaker:Alex Kontorovich Affiliation: Rutgers University Date: October 23, 2017 For more videos, please visit http://video.ias.edu

From playlist Mathematics

Inverse problem by Abhinav Kumar

DISCUSSION MEETING SPHERE PACKING ORGANIZERS: Mahesh Kakde and E.K. Narayanan DATE: 31 October 2019 to 06 November 2019 VENUE: Madhava Lecture Hall, ICTS Bangalore Sphere packing is a centuries-old problem in geometry, with many connections to other branches of mathematics (number the

From playlist Sphere Packing - 2019

Thin Groups and Applications - Alex Kontorovich

Analysis and Beyond - Celebrating Jean Bourgain's Work and Impact May 21, 2016 More videos on http://video.ias.edu

From playlist Analysis and Beyond

Introduction Sphere Packing problems by Abhinav Kumar

DISCUSSION MEETING SPHERE PACKING ORGANIZERS: Mahesh Kakde and E.K. Narayanan DATE: 31 October 2019 to 06 November 2019 VENUE: Madhava Lecture Hall, ICTS Bangalore Sphere packing is a centuries-old problem in geometry, with many connections to other branches of mathematics (number the

From playlist Sphere Packing - 2019

Upper bounds by Abhinav Kumar

Discussion Meeting Sphere Packing ORGANIZERS: Mahesh Kakde and E.K. Narayanan DATE: 31 October 2019 to 06 November 2019 VENUE: Madhava Lecture Hall, ICTS Bangalore Sphere packing is a centuries-old problem in geometry, with many connections to other branches of mathematics (number the

From playlist Sphere Packing - 2019

Alex Kontorovich - On the Strong Density Conjecture for Apollonian Circle Packings [2012]

slides for this talk: https://docs.google.com/viewer?url=http://www.msri.org/workshops/652/schedules/14560/documents/1681/assets/17223 Abstract: The Strong Density Conjecture states that for a given primitive integral Apollonian circle packing, every sufficiently large admissible (passing

From playlist Number Theory

Alex Kontorovich - Diophantine problems in thin orbits

Diophantine problems in thin orbits

From playlist 28ème Journées Arithmétiques 2013

The Generalized Ramanujan Conjectures and Applications (Lecture 2) by Peter Sarnak

Lecture 2: Thin Groups and Expansion Abstract: Infinite index subgroups of matrix groups like SL(n,Z) which are Zariski dense in SL(n), arise in many geometric and diophantine problems (eg as reflection groups,groups connected with elementary geometry such as integral apollonian packings,

From playlist Generalized Ramanujan Conjectures Applications by Peter Sarnak

Alex Kontorovich - Numbers and Fractals [2017]

It is a very good time to be a mathematician. This millennium, while only a teenager, has already seen spectacular breakthroughs on problems like the Poincar´e Conjecture (solved by Grisha Perelman, who declined both a Fields Medal and a million dollar Clay Prize) and the near-resolution o

From playlist Mathematics

Sabyasachi Mukherjee: Interbreeding in conformal dynamics, and its applications near and far

HYBRID EVENT Recorded during the meeting "Advancing Bridges in Complex Dynamics" the September 24, 2021 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM

From playlist Virtual Conference

GLU Seminar: "The geometry of number theory, through Mobius transformations" by Katherine Stange

Speaker: Katherine Stange Title: The geometry of number theory, through Mobius transformations Abstract: Mobius transformations beautifully illustrate the geometry of complex numbers. My own interest arose when playing with some questions from number theory. I’ll show you some of the hid

From playlist My Math Talks

Positive definite kernels on spheres by E K Narayanan

DISCUSSION MEETING SPHERE PACKING ORGANIZERS: Mahesh Kakde and E.K. Narayanan DATE: 31 October 2019 to 06 November 2019 VENUE: Madhava Lecture Hall, ICTS Bangalore Sphere packing is a centuries-old problem in geometry, with many connections to other branches of mathematics (number the

From playlist Sphere Packing - 2019