query: field_of_work robert griess
supports: In the mathematical fields of linear algebra and functional analysis, the orthogonal complement of a subspace "W" of a vector space "V" equipped with a bilinear form "B" is the set "W" of all vectors in "V" that are orthogonal to every vector in "W". Informally, it is called the perp, short for perpendicular complement. It is a subspace of "V". In the area of modern algebra known as group theory, the Monster group "M" (also known as the FischerGriess Monster, or the Friendly Giant) is the largest sporadic simple group, having order In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. Thus a line has a dimension of one because only one coordinate is needed to specify a point on itfor example, the point at 5 on a number line. A surface such as a plane or the surface of a cylinder or sphere has a dimension of two because two coordinates are needed to specify a point on itfor example, both a latitude and longitude are required to locate a point on the surface of a sphere. The inside of a cube, a cylinder or a sphere is three-dimensional because three coordinates are needed to locate a point within these spaces. The American Civil War was a civil war in the United States fought from 1861 to 1865. The Union faced secessionists in eleven Southern states grouped together as the Confederate States of America. The Union won the war, which remains the bloodiest in U.S. history. The Savannah River is a major river in the southeastern United States, forming most of the border between the states of South Carolina and Georgia. Two tributaries of the Savannah, the Tugaloo River and the Chattooga River, form the northernmost part of the border. The Savannah River drainage basin extends into the southeastern side of the Appalachian Mountains just inside North Carolina, bounded by the Eastern Continental Divide. The river is around long. It is formed by the confluence of the Tugaloo River and the Seneca River. Today this confluence is submerged beneath Lake Hartwell. The Tallulah Gorge is located on the Tallulah River, a tributary of the Tugaloo River that forms the northwest branch of the Savannah River. In mathematics and abstract algebra, group theory studies the algebraic structures known as groups. 
  The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces, can all be seen as groups endowed with additional operations and axioms. Groups recur throughout mathematics, and the methods of group theory have influenced many parts of algebra. Linear algebraic groups and Lie groups are two branches of group theory that have experienced advances and have become subject areas in their own right. The American Revolution was a political upheaval that took place between 1765 and 1783 during which colonists in the Thirteen American Colonies rejected the British monarchy and aristocracy, overthrew the authority of Great Britain, and founded the United States of America. The University of Michigan (U-M, UM, UMich, or U of M), frequently referred to simply as "Michigan," is a public research university in Ann Arbor, Michigan, United States. Founded in 1817 in Detroit as the "Catholepistemiad", or University of Michigania, 20 years before the Michigan Territory became a state, the University of Michigan is the state's oldest university. In 1821, the university was officially renamed the University of Michigan. It moved to Ann Arbor in 1837 onto of what is now known as Central Campus. Since its establishment in Ann Arbor, the university campus has expanded to include more than 584 major buildings with a combined area of more than spread out over a Central Campus and North Campus, two satellite campuses in Flint and Dearborn, and a Center in Detroit. The University was a founding member of the Association of American Universities. Robert Louis Griess , Jr. ( born 1945 , Savannah , Georgia ) is a mathematician working on finite simple groups and vertex algebras . Currently , Griess is a professor of mathematics at University of Michigan . He constructed the monster group using the Griess algebra . He received the AMS Leroy P. Steele Prize for a Seminal Contribution to Research in 2010 . In 2012 he became a fellow of the American Mathematical Society . In mathematics, the Griess algebra is a commutative non-associative algebra on a real vector space of dimension 196884 that has the Monster group "M" as its automorphism group. It is named after mathematician R. L. Griess, who constructed it in 1980 and subsequently used it in 1982 to construct "M". The Monster fixes (vectorwise) a 1-space in this algebra and acts absolutely irreducibly on the 196883-dimensional orthogonal complement of this 1-space. The Association of American Universities (AAU) is an international organization of leading research universities devoted to maintaining a strong system of academic research and education. It consists of 60 universities in the United States (both public and private) and two universities in Canada. 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.  Mathematics (from Greek  "máthma", knowledge, study, learning) is the study of topics such as quantity (numbers), structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics. Savannah is the oldest city in the U.S. state of Georgia and is the county seat of Chatham County. Established in 1733 on the Savannah River, the city of Savannah became the British colonial capital of the Province of Georgia and later the first state capital of Georgia. A strategic port city in the American Revolution and during the American Civil War, Savannah is today an industrial center and an important Atlantic seaport. It is Georgia's fifth-largest city and third-largest metropolitan area.
candidates: algebra american civil war group theory history mathematician mathematics physics research river track united states of america
answer: group theory