Symplectic geometrySymplectic geometry is a branch of differential geometry and differential topology that studies symplectic manifolds; that is, differentiable manifolds equipped with a closed, nondegenerate 2-form. 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.Poisson manifoldIn differential geometry, a field in mathematics, a Poisson manifold is a smooth manifold endowed with a Poisson structure. The notion of Poisson manifold generalises that of symplectic manifold, which in turn generalises the phase space from Hamiltonian mechanics.
University of California, BerkeleyPublic university in Berkeley, CaliforniaThe University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California) is a publicland-grantresearch university in Berkeley, California, United States. Founded in 1868 and named after the Anglo-Irish philosopher and clergyman George Berkeley, it is the state's first land-grant university and the founding campus of the University of California system. Berkeley has an enrollment of more than 45,000 students.
Differential geometryBranch of mathematics A triangle immersed in a saddle-shape plane (a hyperbolic paraboloid), as well as two diverging ultraparallel lines Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of vector calculus, linear algebra and multilinear algebra. The field has its origins in the study of spherical geometry as far back as antiquity.
Jerrold E. MarsdenJerrold Eldon Marsden (August 17, 1942 – September 21, 2010) was a Canadian mathematician. He was the Carl F. Braun professor of engineering, control and dynamical systems at the California Institute of Technology. Marsden is listed as an ISI highly cited researcher.
American Mathematical SocietyThe American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, advocacy and other programs. The society is one of the four parts of the Joint Policy Board for Mathematics and a member of the Conference Board of the Mathematical Sciences.
Irving SegalIrving Ezra Segal (1918–1998) was an American mathematician known for work on theoretical quantum mechanics. He shares credit for what is often referred to as the Segal–Shale–Weil representation. Early in his career, Segal became known for his developments in quantum field theory and in functional and harmonic analysis, in particular his innovation of the algebraic axioms known as C*-algebra.
James MunkresJames Raymond Munkres (August 18, 1930 – July 30, 2026) was an American mathematician and academic who was professor of mathematics at MIT and is the author of several texts in the area of topology, including Topology (an undergraduate-level text), Analysis on Manifolds, Elements of Algebraic Topology, and Elementary Differential Topology. He is also the author of Elementary Linear Algebra.
Massachusetts Institute of TechnologyPrivate research university in Cambridge, Massachusetts, United States The Massachusetts Institute of Technology (MIT) is a privateresearch university in Cambridge, Massachusetts, United States. William Barton Rogers founded MIT to accelerate American industrialization through scientific knowledge.
Gian-Carlo RotaGian-Carlo Rota (April 27, 1932 – April 18, 1999) was an Italian-American mathematician and philosopher. He spent most of his career at the Massachusetts Institute of Technology, where he worked in combinatorics, functional analysis, probability theory, and phenomenology. Early life and educationRota was born in Vigevano, Italy.
Roslyn High SchoolRoslyn High School is a publichigh school in Roslyn Heights, in Nassau County, New York, United States. It is the only high school in the Roslyn Union Free School District, serving all of the district's students in grades 9 through 12. HistoryThe property that Roslyn High School sits on was donated in the 1920s by Clarence and Katherine Mackay, both famous figures in Roslyn's history.
MathematicsField of knowledgeIlluminated letter P at the beginning of Adelard of Bath's translation of Euclid's Elements, which starts "Punctum est illud cui pars non est" ('A point is that which has no part'). Geometry is shown personified as a woman, following Martianus Capella's De nuptiis Philologiae et Mercurii.Mathematics is a field of knowledge concerned with abstract concepts such as numbers, geometric shapes, sets, functions, and probabilities.*As an Amazon Associate I earn from qualifying purchases.