B. Bhatt (IAS) Integral structures on de Rham cohomology
Conférence de mi-parcours du programme ANR
Théorie de Hodge p-adique et Développements (ThéHopaD)­


Adam Harper (University of Warwick)

It is a standard heuristic that sums of oscillating number theoretic functions, like the M\"obius function or Dirichlet characters, should exhibit squareroot cancellation. It is often very difficult to prove anything as strong as that, and we generally expect that if we could prove squareroot cancellation it would be the best possible bound. I will discuss recent results showing that, in fact, certain averages of multiplicative functions exhibit a bit more than squareroot cancellation

MAY 01, 2017

Heisuke Hironaka: “Resolution of Singularities in Algebraic Geometry”

Algebraic geometry in general has three fundamental types in terms of its baseground: (I) ℚ (and its fields extensions), (II)    (p) with a prime number p  0 (and every finite field), and at last (III) ℤ in the case of the arithmetic geometry. In those three cases I will talk about resolution of singularities by means of blowups with permissible centers in smooth ambient spaces. (I) is done in 1964, (II) is proven recently with new concept and technique, while (III) is by combination of (I) and (II). Technically elaborate but conceptually interesting is the case of (II).



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The Riemann Hypothesis: a million dollar mystery - Emanuel Carneiro - 2017

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The Tangent Space and the Module of Kahler Differentials of the Universal Deformation Ring

Deformations of Galois Representations Introduction

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Proportion of zeros of combinations of derivatives of Riemann-Xi function on the critical line

Speaker: Sneha Chaubey

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Abstract: A function P(n, m) of two variables which is a polynomial of degree less than d1 in the n
variable, and a p
olynomial of degree less than d2 in the m variable, is automatically a polynomial of degree
less than d1 + d2 " 1 jointly in the n, m variables. In joint work with Tamar Ziegler, we generalise this
“concatenation of degrees” phenomenon to the Gowers unifomity norms; roughly speaking, we show that
a function f(n, m) which is “Gowers anti-uniform” of order d1 in the n variable and Gowers anti-uniform
of order d2 in the m variable is automatically Gowers anti-uniform of order d1 + d2 " 1 jointly in n, m.
An analogous ergodic theory concatenation theorem is also obtained for the characteristic factors of the
Gowers-Host-Kra seminorms.
As an application of this concatenation theorem, we can control certain “averaged local Gowers uniformity
norms” by “global Gowers uniformity norms”, which among other things yields asymptotics for the
number of polynomial patterns in the primes.

Date: Tuesday Jul 21, 2015 09:00 - 09:50
Combinatorics Meets Ergodic Theorynation theorems for the Gowers uniformity norms, and applications" Terence Tao [2015]


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Cosets and Lagrange’s Theorem
New Paradigms in Invariant Theory" - Roger Howe, Yale University [2011]


  Singularities of Ka
                            ler-Einstein Metrics and Complete Calabi-Yau Manifolds
Jean-Pierre Demailly - Kobayashi pseudo-metrics, entire curves and hyperbolicity of ... (Part 1)

What is a Manifold? Lesson 17 - Metric spaces (an aside)


What_is_a_Manifold_Lesson_16: The Mobius strip


What is a Manifold? Lesson 15: The cylinder as a quotient space


What is a Manifold? Lesson 14: Quotient Spaces


What is a Manifold? Lesson 13: The tangent bundle - an illustration.


What is a Manifold? Lesson 12: Fiber Bundles - Formal Description


What is a Manifold? Lesson 11: The Cotangent Space


What is a Manifold? Lesson 10: Tangent Space - Basis Vectors


What is a Manifold? Lesson 9: The Tangent Space-Definition


What is a Manifold? Lesson 8: Diffeomorphisms


What is a Manifold? Lesson 7: Differentiable Manifolds


What is a Manifold? Lesson 6: Topological Manifolds


What is a Manifold? Lesson 5: Compactness, Connectedness, and Topological Properties


What is a Manifold? Lesson 4: Countability and Continuity


What is a Manifold? Lesson 3: Separation


What is a Manifold? Lesson 2: Elementary Definitions


What is a Manifold? Lesson 1: Point Set Topology and Topological Spaces

Introduction to Topology: From the Konigsberg Bridges to Geographic Information Systems.

Minimal  Surfaces
Analytic Low-Dimensional Dynamics

Hyperbolicity isgeneric D=1
Hyperolic is not generic D>1
manderbrois set

Abstract: The first cohomology of a hyperbolic 3-manifold has two natural norms: the Thurston norm, which measure topological complexity of surfaces representing the dual homology class, and the harmonic norm, which is just the L^2 norm on the corresponding space of harmonic 1-forms. Bergeron-Sengun-Venkatesh recently showed that these two norms are closely related, at least when the injectivity radius is bounded below. Their work was motivated by the connection of the harmonic norm to the Ray-Singer analytic torsion and issues of torsion growth in homology of towers of finite covers. After carefully introducing both norms, I will discuss new results that refine and clarify the precise relationship between them; a key tool here will be a third norm based on least-area surfaces. This is joint work with Jeff Brock and will feature some pretty pictures that are joint work with Anil Hirani.