In this talk, we will define elliptic curves and, more importantly, we will try to motivate why they are central to modern number theory. Elliptic curves are ubiquitous not only in number theory, but also in algebraic geometry, complex analysis, cryptography, physics, and beyond. They were
From playlist An Introduction to the Arithmetic of Elliptic Curves
Giovanni Felder - Elliptic quantum groups and elliptic equivariant cohomology
Abstract: I will report on joint work with R. Rimanyi and A. Varchenko. We define an elliptic version of the stable envelope of Maulik and Okounkov for the equivariant elliptic cohomology of cotangent bundles of Grassmannians. It is a version of the construction proposed by Aganagic and
From playlist Algebraic Analysis in honor of Masaki Kashiwara's 70th birthday
Complex analysis: Elliptic functions
This lecture is part of an online undergraduate course on complex analysis. We start the study of elliptic (doubly periodic) functions by constructing some examples, and finding some conditions that their poles and zeros must satisfy. For the other lectures in the course see https://www
From playlist Complex analysis
Elliptic Curves - Lecture 6a - Ramification (continued)
This video is part of a graduate course on elliptic curves that I taught at UConn in Spring 2021. The course is an introduction to the theory of elliptic curves. More information about the course can be found at the course website: https://alozano.clas.uconn.edu/math5020-elliptic-curves/
From playlist An Introduction to the Arithmetic of Elliptic Curves
Automorphic Cohomology I (General Theory) - Phillip Griffiths
Automorphic Cohomology I (General Theory) Phillip Griffiths Institute for Advanced Study February 16, 2011 These two talks will be about automorphic cohomology in the non-classical case. For more videos, visit http://video.ias.edu
From playlist Mathematics
Aurel PAGE - Cohomology of arithmetic groups and number theory: geometric, ... 2
In this lecture series, the first part will be dedicated to cohomology of arithmetic groups of lower ranks (e.g., Bianchi groups), their associated geometric models (mainly from hyperbolic geometry) and connexion to number theory. The second part will deal with higher rank groups, mainly
From playlist École d'Été 2022 - Cohomology Geometry and Explicit Number Theory
Ana Caraiani, Modularity over CM fields
VaNTAGe Seminar, May 24, 2022 License: CC-BY-NC-SA Links to some of the papers mentioned in the talk: Freitas-Le Hung-Siksek: https://arxiv.org/abs/1310.7088 Poonen-Schaefer-Stoll: https://arxiv.org/abs/math/0508174 Harris-Lan-Taylor-Thorne: https://link.springer.com/article/10.1186/s406
From playlist Modularity and Serre's conjecture (in memory of Bas Edixhoven)
A Riemann-Roch theorem in Bott-Chern cohomology - Jean-Michel Bismut
Jean-Michel Bismut Université Paris-Sud April 21, 2014 If MM is a complex manifold, the Bott-Chern cohomology H(⋅,⋅)BC(M,C)HBC(⋅,⋅)(M,C) of MM is a refinement of de Rham cohomology, that takes into account the p,q p,q grading of smooth differential forms. By results of Bott and Chern, vect
From playlist Mathematics
Aurel PAGE - Cohomology of arithmetic groups and number theory: geometric, ... 1
In this lecture series, the first part will be dedicated to cohomology of arithmetic groups of lower ranks (e.g., Bianchi groups), their associated geometric models (mainly from hyperbolic geometry) and connexion to number theory. The second part will deal with higher rank groups, mainly
From playlist École d'Été 2022 - Cohomology Geometry and Explicit Number Theory
Bianca Viray, The Brauer group and the Brauer-Manin obstruction on K3 surfaces
VaNTAGe seminar, February 23, 2021
From playlist Arithmetic of K3 Surfaces
Paul GUNNELLS - Cohomology of arithmetic groups and number theory: geometric, ... 1
In this lecture series, the first part will be dedicated to cohomology of arithmetic groups of lower ranks (e.g., Bianchi groups), their associated geometric models (mainly from hyperbolic geometry) and connexion to number theory. The second part will deal with higher rank groups, mainly
From playlist École d'Été 2022 - Cohomology Geometry and Explicit Number Theory
Lewis Combes - Computing Selmer groups attached to mod p Galois representations
Selmer groups attached to a p-adic Galois representation have been studied thoroughly, but their mod p cousins have so far received less attention. In this talk we explain the construction of the p-adic Selmer group, how it translates to the mod p setting, and give some progress on underst
From playlist École d'Été 2022 - Cohomology Geometry and Explicit Number Theory
Cup Products in Automorphic Cohomology - Matthew Kerr
Matthew Kerr Washington University in St. Louis March 30, 2012 In three very interesting and suggestive papers, H. Carayol introduced new aspects of complex geometry and Hodge theory into the study of non-classical automorphic representations -- in particular, those involving the totally d
From playlist Mathematics
Bjorn Poonen, Heuristics for the arithmetic of elliptic curves
VaNTAGe seminar on Sep 1, 2020. License: CC-BY-NC-SA. Closed captions provided by Brian Reinhart.
From playlist Rational points on elliptic curves
Alessandra Sarti, Old and new on the symmetry groups of K3 surfaces
VaNTAGe Seminar, Feb 9, 2021
From playlist Arithmetic of K3 Surfaces
Edgar Costa, From counting points to rational curves on K3 surfaces
VaNTAGe Seminar, Jan 26, 2021
From playlist Arithmetic of K3 Surfaces
Charles Rezk: Elliptic cohomology and elliptic curves (Part 2)
The lecture was held within the framework of the Felix Klein Lectures at Hausdorff Center for Mathematics on the 3. June 2015
From playlist HIM Lectures 2015
Stark-Heegner cycles for Bianchi modular forms by Guhan Venkat
PERFECTOID SPACES ORGANIZERS: Debargha Banerjee, Denis Benois, Chitrabhanu Chaudhuri, and Narasimha Kumar Cheraku DATE & TIME: 09 September 2019 to 20 September 2019 VENUE: Madhava Lecture Hall, ICTS, Bangalore Scientific committee: Jacques Tilouine (University of Paris, France) Eknath
From playlist Perfectoid Spaces 2019
An introduction to group (and Galois) cohomology (part 1)
This is part 1 of an introduction to group (and Galois) cohomology, with a particular emphasis on the applications to the cohomology of fields, and elliptic curves.
From playlist An Introduction to the Arithmetic of Elliptic Curves
Richard Rimanyi - Stable Envelopes, Bow Varieties, 3d Mirror Symmetry
There are many bridges connecting geometry with representation theory. A key notion in one of these connections, defined by Maulik-Okounkov, Okounkov, Aganagic-Okounkov, is the "stable envelope (class)". The stable envelope fits into the story of characteristic classes of singularities as
From playlist 2021 IHES Summer School - Enumerative Geometry, Physics and Representation Theory