Number Theory (at CIRM)

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source: Centre International de Rencontres Mathématiques     2014年8月12日

Jean-Pierre Serre: How to prove that Galois groups are "large" 53:38 Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities.
The Galois groups of the title are those which are associated with elliptic curves over number fields; I shall explain the methods which were introduced in the 1960's in order to prove that they are large, and the questions about them which are still open fifty years later.
Recording during the thematic meeting: "Heights, modularity, transcendence " the May 12, 2014 at the Centre International de Rencontres Mathématiques (Marseille, France)
Filmmaker: Guillaume Hennenfent
Jean Pierre Serre: Distributions des valeurs propres des Frobenius des variétés abéliennes ... 1:00:04
Harald Helfgott: Towards ternary Goldbach's conjecture 57:12
Fabien Pazuki: Bounds for the number of rational points on curves over global fields 53:58
János Pintz: Polignac numbers and the consecutive gaps between primes 51:54
Gilles Lachaud: Formulas for the limiting distribution of traces of Frobenius 48:59
Jan-Hendrik Evertse: On Scmidt's subspace theorem 58:27
Mike Zieve: Unlikely intersections of polynomial orbits 40:05
Winnie Li: Towers of Ramanujan graphs 1:02:48
Peter Scholze: p-adic cohomology of the Lubin-Tate tower 55:21
Cameron L. Stewart: A refinement of the abc conjecture 33:22
Andrzej Schinzel: The Congruence f ( x ) + g ( y ) + c = 0 (mod xy ) 30:27
Daniel Bertrand: Generalized Jacobians and Pellian polynomials 34:42
Igor Shparlinski: Group structures of elliptic curves #1 59:06
Igor Shparlinski: Group structures of elliptic curves #2 59:44
Igor Shparlinski: Group structures of elliptic curves #3 59:41
Jared Weinstein: Local Shimura varieties for p-adic fields 1:03:52
Heinrich Matzat: Braids and Galois groups 1:07:25
Wim Veys : Zeta functions and monodromy 1:03:25
Chantal David: Distributions of Frobenius of elliptic curves #1 56:29
Chantal David: Distributions of Frobenius of elliptic curves #2 1:00:47
Nathan Jones: Distributions of Frobenius of elliptic curves #3 58:25
Nathan jones: Distributions of Frobenius of elliptic curves #4 1:04:13
Chantal David: Distributions of Frobenius of elliptic curves #5 1:02:11
Nathan Jones : Distributions of Frobenius of elliptic curves #6 45:16
Andrew Sutherland: Introduction to Sato-Tate distributions 1:03:38
Andrew Sutherland: Moment sequences of Sato-Tate groups 58:06
Andrew Sutherland: Computing Sato-Tate statistics 1:11:19
Francesc Fité: The generalized Sato-Tate conjecture 58:52
Francesc Fité: Sato-Tate axioms 53:53
Francesc Fité: The Galois type of an Abelian surface 1:04:05
Peter Stevenhagen: The Chebotarev density theorem 1:02:29
Peter Stevenhagen: Character sums for primitive root densities 1:05:46
Kevin Buzzard: Pre-adic and adic spaces 1:05:13
Freydoon Shahidi: On equality of arithmetic and analytic exterior square root numbers 1:07:06
Christian Elsholtz: Hilbert cubes in arithmetic sets 31:47
Jean-Marie de Koninck: On the proximity of additive and multiplicative functions 45:39
Hugh Montgomery: Moments of a Thue-Morse generating function 24:03
Michael Drmota: Automatic sequences along squares and primes 44:10
Olivier Ramaré: Some news on bilinear decomposition of the Möbius function 46:31
Alena Pirutka: Algebraic cycles on varieties over finite fields 48:59
Andrew Sutherland: Computing the image of Galois representations attached to elliptic curves 28:54
Marco Streng: Generators for the group of modular units for Γ1(N) over the rationals 27:48
Ernst-Ulrich Gekeler: Algebraic curves with many rational points over non-prime finite fields 1:00:38
Aurore Guillevic: Computing discrete logarithms in GF(pn): practical improvement of ... 25:53
Scott Ahlgren: Algebraic and transcendental formulas for the smallest parts function 42:45
Jan Bruinier: Classes of Heegner divisors and traces of singular moduli 52:18
Karl Mahlburg: Automorphic forms and classical partition identities 47:50
Boris Pioline : A string theorist view point on the genus-two Kawazumi-Zhang invariant 49:57
Sander Zwegers: Fourier coefficients of meromorphic Jacobi forms 53:23
Entretien au CIRM : Jean-Pierre SERRE avec Jean-Louis COLLIOT-THELENE 55:12
Winnie Li: Unramified graph covers of finite degree 47:12
José Felipe Voloch: Generators of elliptic curves over finite fields 34:20
Pär Kurlberg: Class number statistics for imaginary quadratic fields Pär Kurlberg 42:18
William Banks: Primes, exponential sums, and L-functions 41:17
James Arthur: Beyond Endoscopy and elliptic terms in the trace formula 1:13:55
Fiona Murnaghan: Tame relatively supercuspidal representations 1:08:59
Shou-Wu Zhang: Congruent number problem and BSD conjecture 49:01
Wee Teck Gan: Theta lifts of tempered representations and Langlands parameter 1:01:59
Raphaël Beuzart-Plessis: The local Gan-Gross-Prasad conjecture for unitary groups 59:51
Dipendra Prasad: The local Langlands correspondence: functoriality, L-functions, gamma ... 1:41:58
Omer Offen : The relative trace formula 1:01:45
Omer Offen: Period integrals of automorphic forms 1:06:12
Omer Offen : Distinction by a symmetric subgroup 1:02:04
Omer Offen : Distinction and the geometric lemma 1:03:04
Nikos Frantzikinakis: Ergodicity of the Liouville system implies the Chowla conjecture 1:00:09
Harald Helfgott: The diameter of the symmetric group: ideas and tools 48:05
Peter Sarnak: Integral points on Markoff type cubic surfaces and dynamics 1:02:30
Benjamin Weiss: The unsolved problems of Halmos 57:15
James Maynard: Primes with missing digits 1:01:13
Peter Sarnak: Möbius randomness and dynamics six years later 1:12:38
Interview at Cirm: Michael Harris 21:36
Anke Pohl: Isomorphisms between eigenspaces of slow and fast transfer operators 58:06
Javier Fresán: Exponential motives 1:04:28
Youness Lamzouri: Large character sums 44:59
Sigrid Grepstad: Bounded remainder sets for the discrete and continuous irrational rotation 32:39
Zeev Rudnick: Angles of Gaussian primes 42:14
Anne de Roton: Small sumsets in continuous and discrete settings 41:56
James Maynard: Large gaps between primes in subsets 49:39
30 ans d'AGCCT 23:13