Finite or infinite? One key to algebraic cycles - Burt Totaro
Burt Totaro University of California, Los Angeles; Member, School of Mathematics February 2, 2015 Algebraic cycles are linear combinations of algebraic subvarieties of an algebraic variety. We want to know whether all algebraic subvarieties can be built from finitely many, in a suitable s
From playlist Mathematics
Hodge theory, coniveau and algebraic cycles - Claire Voisin
Claire Voisin Centre national de la recherche scientifique; Distinguished Visiting Professor, School of Mathematics October 6, 2014 My talk will be a broad introduction to what is the (mostly conjectural) higher dimensional generalization of Abel's theorem on divisors on Riemann surfaces,
From playlist Mathematics
Ariyan Javanpeykar: Arithmetic and algebraic hyperbolicity
Abstract: The Green-Griffiths-Lang-Vojta conjectures relate the hyperbolicity of an algebraic variety to the finiteness of sets of “rational points”. For instance, it suggests a striking answer to the fundamental question “Why do some polynomial equations with integer coefficients have onl
From playlist Algebraic and Complex Geometry
Learning to write an algebraic proof
👉 Learn how to write an algebraic proof. Algebraic proofs are used to help students understand how to write formal proofs where we have a statement and a reason. In the case of an algebraic proof the statement will be the operations used to solve an algebraic equation and the reason will
From playlist Parallel Lines and a Transversal
AlgTopReview: An informal introduction to abstract algebra
This is a review lecture on some aspects of abstract algebra useful for algebraic topology. It provides some background on fields, rings and vector spaces for those of you who have not studied these objects before, and perhaps gives an overview for those of you who have. Our treatment is
From playlist Algebraic Topology
Roberto Villaflor Loyola: Periods of linear algebraic cycles in Fermat varieties
The lecture was held within the framework of the Hausdorff Trimester Program: Periods in Number Theory, Algebraic Geometry and Physics. Abstract: In this talk we will show how a theorem of Carlson and Griffiths can be used to compute periods of linear algebraic cycles inside Fermat variet
From playlist HIM Lectures: Trimester Program "Periods in Number Theory, Algebraic Geometry and Physics"
How to write an algebraic proof
👉 Learn how to write an algebraic proof. Algebraic proofs are used to help students understand how to write formal proofs where we have a statement and a reason. In the case of an algebraic proof the statement will be the operations used to solve an algebraic equation and the reason will
From playlist Parallel Lines and a Transversal
Teruhisa Koshikawa - Some cases of the Hodge standard conjecture
The Hodge standard conjecture remains wide open. The numerical version for abelian fourfolds has been proved recently by Ancona. In this talk, I will first explain a proof of the Hodge standard conjecture for squares of K3 surfaces based on our previous work. In the remaining time, I will
From playlist Franco-Asian Summer School on Arithmetic Geometry (CIRM)
Algebraic geometry 44: Survey of curves
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It gives an informal survey of complex curves of small genus.
From playlist Algebraic geometry I: Varieties
Maxima and Minima for Quadratic and Cubics | Algebraic Calculus One | Wild Egg
Tangents of algebraic curves are best defined purely algebraically, without recourse to limiting arguments! We apply our techniques for finding such tangents to derive some familiar results for quadratic and cubic polynomial functions and their maxima and minima. We compare also with the c
From playlist Algebraic Calculus One
A search for an algebraic equivalence analogue of motivic theories - Eric Friedlander
Vladimir Voevodsky Memorial Conference Topic: A search for an algebraic equivalence analogue of motivic theories Speaker: Eric Friedlander Affiliation: University of Southern California Date: September 13, 2018 For more video please visit http://video.ias.edu
From playlist Mathematics
Standard conjecture of Künneth type with torsion coefficients - Junecue Suh
Joint IAS/Princeton University Number Theory Seminar Topic: Standard conjecture of Künneth type with torsion coefficients Speaker: Junecue Suh Affiliation: University of California, Santa Cruz Date: Thursday, April 21 A. Venkatesh asked us the question, in the context of torsion auto
From playlist Joint IAS/PU Number Theory Seminar
Topological and arithmetic intersection numbers attached to real quadratic cycles -Henri Darmon
Workshop on Motives, Galois Representations and Cohomology Around the Langlands Program Topic: Topological and arithmetic intersection numbers attached to real quadratic cycles Speaker: Henri Darmon Affiliation: McGill University Date: November 8, 2017 For more videos, please visit http
From playlist Mathematics
Shimura Varieties and the Bernstein Center - Tom Haines
Shimura Varieties and the Bernstein Center - Tom Haines University of Maryland; von Neumann Fellow, School of Mathematics December 6, 2010 The local Langlands conjecture (LLC) seeks to parametrize irreducible smooth representations of a p-adic group G in terms of Weil-Deligne parameters. B
From playlist Mathematics
Gonçalo Tabuada - 1/3 Noncommutative Counterparts of Celebrated Conjectures
Some celebrated conjectures of Beilinson, Grothendieck, Kimura, Tate, Voevodsky, Weil, and others, play a key central role in algebraic geometry. Notwithstanding the effort of several generations of mathematicians, the proof of (the majority of) these conjectures remains illusive. The aim
From playlist Summer School 2020: Motivic, Equivariant and Non-commutative Homotopy Theory
Shintaro Nishikawa: Sp(n,1) admits a proper 1-cocycle for a uniformly bounded representation
Talk by Shintaro Nishikawa in Global Noncommutative Geometry Seminar (Americas) http://www.math.wustl.edu/~xtang/NCG-Seminar.html on June 17, 2020.
From playlist Global Noncommutative Geometry Seminar (Americas)
Yves Andre: A Remark on the Tate Conjecture
Talk by Yves Andres in Global Noncommutative Geometry Seminar (Americas) on May 6, 2022, https://globalncgseminar.org/talks/tba-31/
From playlist Global Noncommutative Geometry Seminar (Americas)
Yifeng Liu - Derivative of L-functions for unitary groups (3/3)
In this lecture series, we will focus on the recent advance on the Beilinson-Bloch conjecture for unitary Shimura varieties, more precisely, a Gross-Zagier type formula for automorphic forms on unitary groups of higher ranks. We will start from the general theory of height pairings between
From playlist Franco-Asian Summer School on Arithmetic Geometry (CIRM)
Chao Li - 1/2 Geometric and Arithmetic Theta Correspondences
Geometric/arithmetic theta correspondences provide correspondences between automorphic forms and cohomology classes/algebraic cycles on Shimura varieties. I will give an introduction focusing on the example of unitary groups and highlight recent advances in the arithmetic theory (also know
From playlist 2022 Summer School on the Langlands program
Algebraic geometry 1 Introduction
This lecture is part of an online algebraic geometry course (Berkeley math 256A fall 2020), based on chapter I of "Algebraic geometry" by Hartshorne. The full set of lectures is in the playlist "Algebraic geometry I: varieties". (The course continues in the playlist "Algebraic geometry I
From playlist Algebraic geometry I: Varieties