Jacob Lurie: 1/5 Tamagawa numbers in the function field case [2019]
Slides for this talk: http://swc-alpha.math.arizona.edu/video/2019/2019LurieLecture1Slides.pdf Lecture notes: http://swc.math.arizona.edu/aws/2019/2019LurieNotes.pdf Let G be a semisimple algebraic group defined over the field Q of rational numbers and let G(Q) denote the group of ration
From playlist Number Theory
Jacob Lurie - Tamagawa Numbers and Nonabelian Poincare Duality, I [2013]
Jacob Lurie Wednesday, August 28 3:10PM Tamagawa Numbers and Nonabelian Poincare Duality, I Gelfand Centennial Conference: A View of 21st Century Mathematics MIT, Room 34-101, August 28 - September 2, 2013 Abstract: Let q and q0 be positive definite integral quadratic forms. We say that
From playlist Number Theory
Tamagawa Numbers of Linear Algebraic Groups over (...) - Rosengarten - Workshop 2 - CEB T2 2019
Zev Rosengarten (Hebrew University of Jerusalem) / 26.06.2019 Tamagawa Numbers of Linear Algebraic Groups over Function Fields In 1981, Sansuc obtained a formula for Tamagawa numbers of reductive groups over number fields, modulo some then unknown results on the arithmetic of simply con
From playlist 2019 - T2 - Reinventing rational points
Dennis Gaitsgory - Tamagawa Numbers and Nonabelian Poincare Duality, II [2013]
Dennis Gaitsgory Wednesday, August 28 4:30PM Tamagawa Numbers and Nonabelian Poincare Duality, II Gelfand Centennial Conference: A View of 21st Century Mathematics MIT, Room 34-101, August 28 - September 2, 2013 Abstract: This will be a continuation of Jacob Lurie’s talk. Let X be an al
From playlist Number Theory
Weil conjectures 4 Fermat hypersurfaces
This talk is part of a series on the Weil conjectures. We give a summary of Weil's paper where he introduced the Weil conjectures by calculating the zeta function of a Fermat hypersurface. We give an overview of how Weil expressed the number of points of a variety in terms of Gauss sums. T
From playlist Algebraic geometry: extra topics
Weil conjectures 1 Introduction
This talk is the first of a series of talks on the Weil conejctures. We recall properties of the Riemann zeta function, and describe how Artin used these to motivate the definition of the zeta function of a curve over a finite field. We then describe Weil's generalization of this to varie
From playlist Algebraic geometry: extra topics
Special Values of Zeta Functions (Lecture 2) by Matthias Flach
PROGRAM ELLIPTIC CURVES AND THE SPECIAL VALUES OF L-FUNCTIONS (HYBRID) ORGANIZERS: Ashay Burungale (CalTech/UT Austin, USA), Haruzo Hida (UCLA), Somnath Jha (IIT Kanpur) and Ye Tian (MCM, CAS) DATE: 08 August 2022 to 19 August 2022 VENUE: Ramanujan Lecture Hall and online The program pla
From playlist ELLIPTIC CURVES AND THE SPECIAL VALUES OF L-FUNCTIONS (2022)
What is the Riemann Hypothesis?
This video provides a basic introduction to the Riemann Hypothesis based on the the superb book 'Prime Obsession' by John Derbyshire. Along the way I look at convergent and divergent series, Euler's famous solution to the Basel problem, and the Riemann-Zeta function. Analytic continuation
From playlist Mathematics
The Tamagawa Number Formula via Chiral Homology - Dennis Gaitsgory
Dennis Gaitsgory Harvard University March 1, 2012 Let X a curve over F_q and G a semi-simple simply-connected group. The initial observation is that the conjecture of Weil's which says that the volume of the adelic quotient of G with respect to the Tamagawa measure equals 1, is equivalent
From playlist Mathematics
Recent developments in non-commutative Iwasawa theory I - David Burns
David Burns March 25, 2011 For more videos, visit http://video.ias.edu
From playlist Mathematics
Special Values of Zeta Functions (Lecture 1) by Matthias Flach
PROGRAM ELLIPTIC CURVES AND THE SPECIAL VALUES OF L-FUNCTIONS (HYBRID) ORGANIZERS: Ashay Burungale (CalTech/UT Austin, USA), Haruzo Hida (UCLA), Somnath Jha (IIT Kanpur) and Ye Tian (MCM, CAS) DATE: 08 August 2022 to 19 August 2022 VENUE: Ramanujan Lecture Hall and online The program pla
From playlist ELLIPTIC CURVES AND THE SPECIAL VALUES OF L-FUNCTIONS (2022)
Kannan Soundararajan - 4/4 L-functions
Kannan Soundararajan - L-functions
From playlist École d'été 2014 - Théorie analytique des nombres
Dennis Gaitsgory - The Tamagawa number formula over function fields
Séminaire Paris Pékin Tokyo / Mercredi 17 novembre 2015 Let G be a semi-simple and simply connected group and X an algebraic curve. We consider Bun_G(X), the moduli space of G-bundles on X. In their celebrated paper, Atiyah and Bott gave a formula for the cohomology of Bun_G, namely H^*(B
From playlist Conférences Paris Pékin Tokyo
Jeffrey Achter, Equidistribution counts abelian varieties
VaNTAGe Seminar, February 22, 2022 License: CC-BY-NC-SA Links to some of the papers mentioned in this talk are listed below. Sutherland: https://arxiv.org/abs/1604.01256 Gekeler: https://academic.oup.com/imrn/article/2003/37/1999/863196 Job Rauch: https://www.universiteitleiden.nl/binar
From playlist Curves and abelian varieties over finite fields