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.
Abstract: The most important gifts of great mathematicians are often the questions that they ask but fail to answer. (Can you think of one?) At the dawn of the 20th century, Henri Poincaré asked two questions that have generated a wealth of mathematics in the ensuing 100 years. One of the questions was only recently answered (when Perelman solved the Poincaré Conjecture). We will focus on another a problem, Poincaré's Last Geometric Theorem, that was solved quickly (by Brouwer) but that spawned as-yet-unsolved generalizations. The theorem is easy to state and understand, and by proving a simplified version we will get a taste for the generalizations. Multivariable Calc. and/or Differential Eq. would make excellent background for this talk, but are not necessary. I will try to make all concepts accessible to anyone who has hd some calculus.

Dr. Margaret Symington gave this presentation to the Math Club November 14, 2012. Thanks to Dr. Symington and to the Math Club for letting me capture the talk and to Dr. Jon Hanke for his technical support with this project.
The fight of the devil of Algebra against the angel of Topology (bigger than) in Algebraic Topology

Princeton/IAS Symplectic Geometry Seminar
Topic: Packaging the construction of Kuranishi structure on the moduli space of pseudo-holomorphic curve

John Tate

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