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Maryam Mirzakhani Maryam Mirzakhani (Persian: مریم میرزاخانی, pronounced [mæɾˈjæm miːɾzɑːxɑːˈniː]; 3 May 1977 – 14 July 2017) was an Iranian[5][6][1] mathematician and a professor of mathematics at Stanford University.[7][8][9] Her research topics included Teichmüller theory, hyperbolic geometry, ergodic theory, and symplectic geometry.[1] On 13 August 2014, Mirzakhani was honored with the Fields Medal, the most prestigious award in mathematics.[10][11] Thus, she became both the first woman and the first Iranian to be honored with the award.[12] The award committee cited her work in "the dynamics and geometry of Riemann surfaces and their moduli spaces".[13] On 14 July 2017, Mirzakhani died of breast cancer at the age of 40.[14]Contents1 Early life and education 2 Career 3 Research work 4 Personal life 5 De [...More...]  "Maryam Mirzakhani" on: Wikipedia Yahoo 

Seoul Seoul Seoul (/soʊl/; 서울; Korean: [sʌ.ul] ( listen)), officially the Seoul Seoul Special Special Metropolitan City – is the capital[10] and largest metropolis of the Republic of Korea Korea (commonly known as South Korea).[1] Seoul Seoul forms the heart of the Seoul Seoul Capital Area, and includes the surrounding Incheon Incheon metropolis and Gyeonggi province, altogether home to roughly half of the country's population.[11][12] Strategically situated on the Han River, Seoul's history stretches back over two thousand years, when it was founded in 18 BC by the people of Baekje, one of the Three Kingdoms of Korea. The city was later designated the capital of Korea Korea under the Joseon Joseon dynasty [...More...]  "Seoul" on: Wikipedia Yahoo 

Marina Ratner Marina Evseevna Ratner (Russian: Мари́на Евсе́евна Ра́тнер; October 30, 1938 – July 7, 2017[1]) was a professor of mathematics at the University of California, Berkeley University of California, Berkeley who worked in ergodic theory.[2] Around 1990, she proved a group of major theorems concerning unipotent flows on homogeneous spaces, known as Ratner's theorems.[3] Ratner was elected to the American Academy of Arts and Sciences in 1992,[4] awarded the Ostrowski Prize in 1993 and elected to the National Academy of Sciences the same year. In 1994, she was awarded the John J. Carty Award from the National Academy of Sciences.[5] Biographical information[edit] Born in Moscow, Russian SFSR Russian SFSR to a Jewish family, her father was a plant physiologist and mother, a chemist [...More...]  "Marina Ratner" on: Wikipedia Yahoo 

Symplectic Geometry Symplectic geometry Symplectic geometry is a branch of differential geometry and differential topology that studies symplectic manifolds; that is, differentiable manifolds equipped with a closed, nondegenerate 2form. Symplectic geometry Symplectic geometry has its origins in the Hamiltonian formulation of classical mechanics where the phase space of certain classical systems takes on the structure of a symplectic manifold.[1]Contents1 Introduction 2 Comparison with Riemannian geometry 3 Examples and structures 4 Name 5 See also 6 Notes 7 References 8 External linksIntroduction[edit] A symplectic geometry is defined on a smooth evendimensional space that is a differentiable manifold. On this space is defined a geometric object, the symplectic form, that allows for the measurement of sizes of twodimensional objects in the space [...More...]  "Symplectic Geometry" on: Wikipedia Yahoo 

Moduli Space In algebraic geometry, a moduli space is a geometric space (usually a scheme or an algebraic stack) whose points represent algebrogeometric objects of some fixed kind, or isomorphism classes of such objects. Such spaces frequently arise as solutions to classification problems: If one can show that a collection of interesting objects (e.g., the smooth algebraic curves of a fixed genus) can be given the structure of a geometric space, then one can parametrize such objects by introducing coordinates on the resulting space [...More...]  "Moduli Space" on: Wikipedia Yahoo 

Breast Cancer Breast Breast cancer is cancer that develops from breast tissue.[9] Signs of breast cancer may include a lump in the breast, a change in breast shape, dimpling of the skin, fluid coming from the nipple, a newly inverted nipple, or a red or scaly patch of skin.[1][2] In those with distant spread of the disease, there may be bone pain, swollen lymph nodes, shortness of breath, or yellow skin.[10] Risk factors for developing breast cancer include being female, obesity, lack of physical exercise, drinking alcohol, hormone replacement therapy during menopause, ionizing radiation, early age at first menstruation, having children late or not at [...More...]  "Breast Cancer" on: Wikipedia Yahoo 

Closed Geodesic In differential geometry and dynamical systems, a closed geodesic on a Riemannian manifold is a geodesic that returns to its starting point with the same tangent direction. It may be formalized as the projection of a closed orbit of the geodesic flow on the tangent space of the manifold.Contents1 Definition 2 Examples 3 See also 4 ReferencesDefinition[edit] In a Riemannian manifold (M,g), a closed geodesic is a curve γ : R → M displaystyle gamma :mathbb R rightarrow M that is a geodesic for the metric g and is periodic. Closed geodesics can be characterized by means of a variational principle [...More...]  "Closed Geodesic" on: Wikipedia Yahoo 

Earthquake Map In hyperbolic geometry, an earthquake map is a method of changing one hyperbolic manifold into another, introduced by William Thurston (1986). Earthquake maps[edit] Given a simple closed geodesic on an oriented hyperbolic surface and a real number t, one can cut the manifold along the geodesic, slide the edges a distance t to the left, and glue them back. This gives a new hyperbolic surface, and the (possibly discontinuous) map between them is an example of a left earthquake. More generally one can do the same construction with a finite number of disjoint simple geodesics, each with a real number attached to it. The result is called a simple earthquake. An earthquake is roughly a sort of limit of simple earthquakes, where one has an infinite number of geodesics, and instead of attaching a positive real number to each geodesic one puts a measure on them. A geodesic lamination of a hyperbolic surface is a closed subset with a foliation by geodesics [...More...]  "Earthquake Map" on: Wikipedia Yahoo 

Ergodicity In probability theory, an ergodic dynamical system is one that, broadly speaking, has the same behavior averaged over time as averaged over the space of all the system's states in its phase space. In physics the term implies that a system satisfies the ergodic hypothesis of thermodynamics. A random process is ergodic if its time average is the same as its average over the probability space, known in the field of thermodynamics as its ensemble average. The state of an ergodic process after a long time is nearly independent of its initial state.[1] The term "ergodic" was derived from the Greek words έργον (ergon: "work") and οδός (odos: "path," "way") [...More...]  "Ergodicity" on: Wikipedia Yahoo 

Alex Eskin Alex Eskin (born May 19, 1965) is an American mathematician. He works on rational billiards and geometric group theory. For his contribution to joint work with David Fisher and Kevin Whyte establishing the quasiisometric rigidity of sol, he was awarded the 2007 Clay Research Award.[1] Eskin was born in Moscow. He is the son of a RussianJewish mathematician Gregory I. Eskin (b. 1936, Kiev), a professor at UCLA. The family emigrated to Israel in 1974 and in 1982 to the United States. Eskin earned his doctorate from Princeton University in 1993, under supervision of Peter Sarnak.[2] He has been a professor at University of Chicago since 1999. In 2012 he became a fellow of the American Mathematical Society.[3] In April 2015 Eskin was elected a member of the U.S. National Academy of Sciences.[4][5] References[edit]^ "Archived copy". Archived from the original on 20110626 [...More...]  "Alex Eskin" on: Wikipedia Yahoo 

International Mathematical Union The International Mathematical Union (IMU) is an international nongovernmental organization devoted to international cooperation in the field of mathematics across the world. It is a member of the International Council for Science International Council for Science (ICSU) and supports the International Congress of Mathematicians. Its members are national mathematics organizations from more than 80 countries.[1] The objectives of the International Mathematical Union (IMU) are to promote international cooperation in mathematics. By supporting and assisting the International Congress of Mathematicians International Congress of Mathematicians (ICM) and other international scientific meetings/conferences [...More...]  "International Mathematical Union" on: Wikipedia Yahoo 

Hyperbolic Geometry In mathematics, hyperbolic geometry (also called Bolyai–Lobachevskian geometry or Lobachevskian geometry) is a nonEuclidean geometry [...More...]  "Hyperbolic Geometry" on: Wikipedia Yahoo 

Dynamics (mechanics) Dynamics is the branch of applied mathematics (specifically classical mechanics) concerned with the study of forces and torques and their effect on motion, as opposed to kinematics, which studies the motion of objects without reference to its causes. Isaac Newton Isaac Newton defined the fundamental physical laws which govern dynamics in physics, especially his second law of motion.Contents1 Principles 2 Linear and rotational dynamics 3 Force 4 Newton's laws 5 See also 6 References 7 Further readingPrinciples[edit] Generally speaking, researchers involved in dynamics study how a physical system might develop or alter over time and study the causes of those changes. In addition, Newton established the fundamental physical laws which govern dynamics in physics. By studying his system of mechanics, dynamics can be understood. In particular, dynamics is mostly related to Newton's second law of motion [...More...]  "Dynamics (mechanics)" on: Wikipedia Yahoo 

Jordan Ellenberg Jordan Stuart Ellenberg (born 1971) is an American mathematician who is a professor of mathematics at the University of Wisconsin–Madison.[2] His research involves arithmetic geometry. He received both his A.B. and Ph.D. from Harvard University.Contents1 Early life 2 Career 3 Personal Life 4 Works4.1 Nonfiction 4.2 Novels 4.3 Essays5 References 6 External linksEarly life[edit] Ellenberg was born in Potomac, Maryland. He was a child prodigy who taught himself to read at the age of two by watching Sesame Street.[3] His mother discovered his ability one day while she was driving on the Capital Beltway when her toddler informed her: "The sign says `Bethesda is to the right.'" In second grade, he helped his teenage babysitter with her math homework. By fourth grade, he was participating in high school competitions (such as the American Regions Mathematics Mathematics League) as a member of the Montgomery County math team [...More...]  "Jordan Ellenberg" on: Wikipedia Yahoo 

Hassan Rouhani President of Iran IncumbentFirst termPresidential campaignGeneral electionCabinet membersConfirmationsInauguration International tripsJCPOANegotiations Joint Plan of Action Iran Iran nuclear deal framework United Nations Security Council United Nations Security Council Resolution 2231 Iran Iran Nuclear Achievements Protection Act Iranian Government's Reciprocal and Proportional Action in Implementing the JCPOA Act Iran Iran and ISILIranian involvement in the Syrian Civil War Iranian intervention in IraqWorld Against Violence and ExtremismSecond termReelection campaignGeneral electionInauguration Cabinet membersConfirmations2017–18 protestsBooksIslamic Revolution: Roots and Challenges Fundaments of Political Thoughts of Imam Khomeini Memoirs of Dr. Hassan Rouhani; Vol. 1: The Islamic Revolution Introduction to Islamic Countries Islamic Political Thought; Vol [...More...]  "Hassan Rouhani" on: Wikipedia Yahoo 

Erdős Number The Erdős number Erdős number (Hungarian: [ˈɛrdøːʃ]) describes the "collaborative distance" between mathematician Paul Erdős Paul Erdős and another person, as measured by authorship of mathematical papers. The same principle has been applied in other fields where a pa [...More...]  "Erdős Number" on: Wikipedia Yahoo 