Spiral Challenge — Continuous Everywhere but Differentiable Nowhere

Megan Schmidt is obsessed with spirals. Her obsession got me hooked — for hours — on a math problem. I thought it would take maybe an hour or two, but I’m still at it and I’ve probably been working four or five hours. I’ve been having so much fun with it. Here’s the problem. Look at the […]

via Spiral Challenge — Continuous Everywhere but Differentiable Nowhere

Sara Zahedi won one of the 10 EMS prizes

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Sara Zahedi

* 1981 in Teheran (Iran)
Assistant Professor
Royal Institute of Technology (KTH), Sweden

EMS Prize 2016
„For her outstanding research regarding the development and analysis of numerical algorithms for partial differential equations with a focus on applications to problems with dynamically changing geometry.“

Research Interests
Sara Zahedis research interests lie in the development and analysis of computational methods, in particular finite element methods, for solving partial differential equations on dynamic geometries. The main application she has in mind is multiphase flows. She is also interested in numerical methods for representing and evolving interfaces separating immiscible fluids.

Curriculum Vitae: 

  • 2014: Assistant Professor in Numerical Analysis, KTH, Stockholm (Swe)
  • 2011: Postdoctoral Position, Uppsala University (Swe)
  • 2011: PhD in Numerical Analysis, KTH, Stockholm (Swe)
  • 2006: Master of Science with a major in Mathematics, KTH (Swe)
  • 2006: Teaching Assistant, Dept. of Numerical Analysis, KTH (Swe)
  • 2003: Teaching Assistant, Stockholm University (Swe)

More Information: 1 , 2 , 3 and 4 

Baum–Connes conjecture

In mathematics, specifically in operator K-theory, the Baum–Connes conjecture suggests a link between the K-theory of the C*-algebra of a group and the K-homology of the corresponding classifying space of proper actions of that group. The conjecture sets up a correspondence between different areas of mathematics, with the K-homology being related to geometry, differential operator theory, and homotopy theory, while the K-theory of the reduced {displaystyle C^{*}}C^*-algebra is a purely analytical object.

The conjecture, if true, would have some older famous conjectures as consequences. For instance, the surjectivity part implies the Kadison–Kaplansky conjecture for a discrete torsion-free group, and the injectivity is closely related to the Novikov conjecture.

The conjecture is also closely related to index theory, as the assembly map {displaystyle mu }mu is a sort of index, and it plays a major role in Alain Connesnoncommutative geometry program.

The origins of the conjecture go back to Fredholm theory, the Atiyah–Singer index theorem and the interplay of geometry with operator K-theory as expressed in the works of Brown, Douglas and Fillmore, among many other motivating subjects.

From Wikipedia, the free encyclopedia

More:

  1.  Introduction to the Baum-Connes Conjecture Alain VALETTE (PDF)
  2. A Survey on the Baum-Connes Conjecture (PDF)
  3. https://en.wikipedia.org/wiki/Baum–Connes_conjecture

 

Feynman Diagrams – Visual Depictions of Physics — Delightful & Distinctive COLRS

Source: Quanta Magazine, Jul 2016 Feynman diagrams look to be pictures of processes that happen in space and time, and in a sense they are, but they should not be interpreted too literally. What they show are not rigid geometric trajectories, but more flexible, “topological” constructions, reflecting quantum uncertainty. In other words, you can be […]

via Feynman Diagrams – Visual Depictions of Physics — Delightful & Distinctive COLRS

A Comprehensive Course in Analysis by Barry Simon

In the second half of 2015, the American Math Society will publish a five volume (total about 3200 pages) set of books that is a graduate analysis text with lots of additional bonus material. Included are hundreds of problems and copious notes which extend the text and provide historical background.  Efforts have been made to find simple and elegant proofs and to keeping the writing style clear

Part 1 Real Analysis:

Point Set Topology, Banach and Hilbert Space, Measure Theory, Fourier Series and Transforms, Distribution Theory, Locally Convex Spaces, Basics of Probability Theory, Hausdorff Measure and Dimension.

Part 2a Basic Complex Analysis:

Cauchy Integral Theorem, Consequences of the Cauchy Integral Theorem (including holomorphic iff analytic, Local Behavior, Phragmén-Lindelöf, Reflection Principle, Calculation of Integrals), Montel, Vitali and Hurwitz’s Theorems, Fractional Linear Transformations, Conformal Maps, Zeros and Product Formulae, Elliptic Functions, Global Analytic Functions, Picard’s Theorem.

Part 2b Advanced Complex Analysis:

Conformal metric methods, topics in analytic number theory,  Fuchsian ODEs and associated special functions, asymptotic methods, univalent functions, Nevanlinna theory.

Part 3 Harmonic Analysis:

Maximal functions and pointwise limits, harmonic functions and potential theory, phase space analysis, Hp spaces, more inequalities.

Part 4 Operator Theory:

Eigenvalue Perturbation Theory, Operator Basics, Compact Operators, Orthogonal Polynomials, Spectral Theory, Banach Algebras, Unbounded Self-Adjoint Operators.

Reference: Click Here

 

Maryam Mirzakhani: the first woman and the first Iranian honored with the Fields Medal

In 2014, Mirzakhani became both the first woman and the first Iranian honored with the Fields Medal, the most prestigious award in mathematics. The award committee cited her work in “the dynamics and geometry of Riemann surfaces and their moduli spaces.”

Her research topics include Teichmüller theory, hyperbolic geometry, ergodic theory, and symplectic geometry.

More Information: https://en.wikipedia.org/wiki/Maryam_Mirzakhani

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