Information: - Physics beyond the Standard Model (BSM) refers to the theoretical developments needed to explain the deficiencies of the Standard Model, such as the origin of mass, the strong CP problem, neutrino oscillations, matterantimatter asymmetry, and the nature of dark matter and dark energy. Another problem lies within the mathematical framework of the Standard Model itselfthe Standard Model is inconsistent with that of general relativity, to the point that one or both theories break down under certain conditions (for example within known spacetime singularities like the Big Bang and black hole event horizons). - The Ivy League is a collegiate athletic conference comprising sports teams from eight private institutions of higher education in the Northeastern United States. The conference name is also commonly used to refer to those eight schools as a group beyond the sports context. The eight institutions are Brown University, Columbia University, Cornell University, Dartmouth College, Harvard University, the University of Pennsylvania, Princeton University, and Yale University. The term "Ivy League" has connotations of academic excellence, selectivity in admissions, and social elitism. - The Minimal Supersymmetric Standard Model (MSSM) is an extension to the Standard Model that realizes supersymmetry. MSSM is the minimal supersymmetrical model as it considers only "the [minimum] number of new particle states and new interactions consistent with phenomenology". Supersymmetry pairs bosons with fermions; therefore every Standard Model particle has a partner that has yet to be discovered. If the superparticles are found, it may be analogous to discovering dark matter and depending on the details of what might be found, it could provide evidence for grand unification and might even, in principle, provide hints as to whether string theory describes nature. The failure to find evidence for supersymmetry using the Large Hadron Collider since 2010 has led to suggestions that the theory should be abandoned. - In physics, classical mechanics is one of the two major sub-fields of mechanics, along with quantum mechanics. Classical mechanics is concerned with the set of physical laws describing the motion of bodies under the influence of a system of forces. The study of the motion of bodies is an ancient one, making classical mechanics one of the oldest and largest subjects in science, engineering and technology. It is also known as Newtonian mechanics, though textbook authors often consider Newtonian mechanics as one of the three main formalisms of classical mechanics, along with Lagrangian mechanics and Hamiltonian mechanics. - Differential geometry is a mathematical discipline that uses the techniques of differential calculus, integral calculus, linear algebra and multilinear algebra to study problems in geometry. The theory of plane and space curves and surfaces in the three-dimensional Euclidean space formed the basis for development of differential geometry during the 18th century and the 19th century. - Geometry (from the ; "geo-" "earth", "-metron" "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. A mathematician who works in the field of geometry is called a geometer. - In quantum mechanics, a boson is a particle that follows BoseEinstein statistics. Bosons make up one of the two classes of particles, the other being fermions. The name boson was coined by Paul Dirac to commemorate the contribution of the Indian physicist Satyendra Nath Bose in developing, with Einstein, BoseEinstein statisticswhich theorizes the characteristics of elementary particles. Examples of bosons include fundamental particles such as photons, gluons, and W and Z bosons (the four force-carrying gauge bosons of the Standard Model), the recently discovered Higgs boson, and the hypothetical graviton of quantum gravity; composite particles (e.g. mesons and stable nuclei of even mass number such as deuterium (with one proton and one neutron, mass number = 2), helium-4, or lead-208); and some quasiparticles (e.g. Cooper pairs, plasmons, and phonons). - In mathematics and physics, a phase space of a dynamical system is a space in which all possible states of a system are represented, with each possible state corresponding to one unique point in the phase space. For mechanical systems, the phase space usually consists of all possible values of position and momentum variables. The concept of phase space was developed in the late 19th century by Ludwig Boltzmann, Henri Poincare, and Willard Gibbs. - In mathematics, the investigator Sophus Lie initiated lines of study involving integration of differential equations, transformation groups, and contact of spheres that have come to be called Lie theory. For instance, the latter subject is Lie sphere geometry. This article addresses his approach to transformation groups, which is one of the areas of mathematics, and was worked out by Wilhelm Killing and Elie Cartan. - Symplectic 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. - Particle physics (also high energy physics) is the branch of physics that studies the nature of the particles that constitute "matter" (particles with mass) and "radiation" (massless particles). Although the word "particle" can refer to various types of very small objects (e.g. protons, gas particles, or even household dust), "particle physics" usually investigates the irreducibly smallest detectable particles and the irreducibly fundamental force fields necessary to explain them. By our current understanding, these elementary particles are excitations of the quantum fields that also govern their interactions. The currently dominant theory explaining these fundamental particles and fields, along with their dynamics, is called the Standard Model. Thus, modern particle physics generally investigates the Standard Model and its various possible extensions, e.g. to the newest "known" particle, the Higgs boson, or even to the oldest known force field, gravity. - In particle physics, supersymmetry (SUSY) is a proposed type of spacetime symmetry that relates two basic classes of elementary particles: bosons, which have an integer-valued spin, and fermions, which have a half-integer spin. Each particle from one group is associated with a particle from the other, known as its superpartner, the spin of which differs by a half-integer. In a theory with perfectly "unbroken" supersymmetry, each pair of superpartners would share the same mass and internal quantum numbers besides spin. For example, there would be a "selectron" (superpartner electron), a bosonic version of the electron with the same mass as the electron, that would be easy to find in a laboratory. Thus, since no superpartners have been observed, if supersymmetry exists it must be a spontaneously broken symmetry so that superpartners may differ in mass. Spontaneously-broken supersymmetry could solve many mysterious problems in particle physics including the hierarchy problem. The simplest realization of spontaneously-broken supersymmetry, the so-called Minimal Supersymmetric Standard Model, is one of the best studied candidates for physics beyond the Standard Model. - Shlomo Zvi Sternberg (born 1936), is an American mathematician known for his work in geometry, particularly symplectic geometry and Lie theory. - In theoretical physics, the hierarchy problem is the large discrepancy between aspects of the weak force and gravity. There is no scientific consensus on why, for example, the weak force is 10 times stronger than gravity. - Harvard University is a private Ivy League research university in Cambridge, Massachusetts, established in 1636, whose history, influence, and wealth have made it one of the world's most prestigious universities. - A research university is a university that expects all its tenured and tenure-track faculty to continuously engage in research, as opposed to merely requiring it as a condition of an initial appointment or tenure. Such universities can be recognized by their strong focus on innovative research and the prestige of their brand names. On the one hand, research universities strive to recruit faculty who are the most brilliant minds in their disciplines in the world, and their students enjoy the opportunity to learn from such experts. On the other hand, new students are often disappointed to realize their undergraduate courses at research universities are overly academic and fail to provide vocational training with immediate "real world" applications; but many employers value degrees from research universities because they know that such coursework develops fundamental skills like critical thinking. - In mathematics, a Hopf algebra, named after Heinz Hopf, is a structure that is simultaneously an (unital associative) algebra and a (counital coassociative) coalgebra, with these structures' compatibility making it a bialgebra, and that moreover is equipped with an antiautomorphism satisfying a certain property. The representation theory of a Hopf algebra is particularly nice, since the existence of compatible comultiplication, counit, and antipode allows for the construction of tensor products of representations, trivial representations, and dual representations. - In particle physics, a fermion (a name coined by Paul Dirac from the surname of Enrico Fermi) is any particle characterized by FermiDirac statistics. These particles obey the Pauli exclusion principle. Fermions include all quarks and leptons, as well as any composite particle made of an odd number of these, such as all baryons and many atoms and nuclei. Fermions differ from bosons, which obey BoseEinstein statistics. - The Standard Model of particle physics is a theory concerning the electromagnetic, weak, and strong nuclear interactions, as well as classifying all the subatomic particles known. It was developed throughout the latter half of the 20th century, as a collaborative effort of scientists around the world. The current formulation was finalized in the mid-1970s upon experimental confirmation of the existence of quarks. Since then, discoveries of the top quark (1995), the tau neutrino (2000), and the Higgs boson (2012) have given further credence to the Standard Model. Because of its success in explaining a wide variety of experimental results, the Standard Model is sometimes regarded as the "theory of almost everything". - In mathematics, a symplectic manifold is a smooth manifold, "M", equipped with a closed nondegenerate differential 2-form, , called the symplectic form. The study of symplectic manifolds is called symplectic geometry or symplectic topology. Symplectic manifolds arise naturally in abstract formulations of classical mechanics and analytical mechanics as the cotangent bundles of manifolds. For example, in the Hamiltonian formulation of classical mechanics, which provides one of the major motivations for the field, the set of all possible configurations of a system is modeled as a manifold, and this manifold's cotangent bundle describes the phase space of the system. - Steve Shnider is professor of mathematics at Bar Ilan University . He received a PhD in Mathematics from Harvard University in 1972 , under Shlomo Sternberg . His main interests are in the differential geometry of fiber bundles ; algebraic methods in the theory of deformation of geometric structures ; symplectic geometry ; supersymmetry ; operads ; and Hopf algebras . - A mathematician is someone who uses an extensive knowledge of mathematics in his/her work, typically to solve mathematical problems. - In particle physics, a superpartner (also sparticle) is a hypothetical elementary particle. Supersymmetry is one of the synergistic theories in current high-energy physics that predicts the existence of these "shadow" particles. - In geometry, Euclidean space encompasses the two-dimensional Euclidean plane, the three-dimensional space of Euclidean geometry, and certain other spaces. It is named after the Ancient Greek mathematician Euclid of Alexandria. The term "Euclidean" distinguishes these spaces from other types of spaces considered in modern geometry. Euclidean spaces also generalize to higher dimensions. - Heinz Hopf (19 November 1894 3 June 1971) was a German mathematician who worked on the fields of topology and geometry. He was one of the greatest mathematicians of the 20th century. Given the information, choose the subject and object entities that have the relation of 'occupation'.
The answer to this question is:
steve shnider , mathematician