field_of_work robert griess
The Savannah ___MASK63___ is a major ___MASK63___ 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 ___MASK63___ and the Chattooga ___MASK63___ , form the northernmost part of the border . The Savannah ___MASK63___ drainage basin extends into the southeastern side of the Appalachian Mountains just inside North Carolina , bounded by the Eastern Continental Divide . The ___MASK63___ is around long . It is formed by the confluence of the Tugaloo ___MASK63___ and the Seneca ___MASK63___ . Today this confluence is submerged beneath Lake Hartwell . The Tallulah Gorge is located on the Tallulah ___MASK63___ , a tributary of the Tugaloo ___MASK63___ that forms the northwest branch of the Savannah ___MASK63___ . 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 ___MASK96___ . The Association of American Universities ( AAU ) is an international organization of leading ___MASK25___ universities devoted to maintaining a strong system of academic ___MASK25___ and education . It consists of 60 universities in the United States ( both public and private ) and two universities in Canada . In ___MASK88___ and abstract ___MASK91___ , ___MASK52___ studies the algebraic structures known as groups . The concept of a group is central to abstract ___MASK91___ : 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 ___MASK88___ , and the methods of ___MASK52___ have influenced many parts of ___MASK91___ . Linear algebraic groups and Lie groups are two branches of ___MASK52___ that have experienced advances and have become subject areas in their own right . 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 ___MASK63___ , 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 ___MASK44___ , Savannah is today an industrial center and an important Atlantic seaport . It is Georgia ' s fifth - largest city and third - largest metropolitan area . The ___MASK44___ 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 University of Michigan ( U - M , UM , UMich , or U of M ), frequently referred to simply as " Michigan ," is a public ___MASK25___ 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 . In the area of modern ___MASK91___ known as ___MASK52___ , the Monster group " M " ( also known as the Fischer  Griess Monster , or the Friendly Giant ) is the largest sporadic simple group , having order In ___MASK4___ 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 . In ___MASK88___ , the Griess ___MASK91___ is a commutative non - associative ___MASK91___ 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 ___MASK91___ and acts absolutely irreducibly on the 196883 - dimensional orthogonal complement of this 1 - space . ___MASK88___ ( 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 ___MASK88___ . A ___MASK25___ university is a university that expects all its tenured and tenure - track faculty to continuously engage in ___MASK25___ , 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 ___MASK25___ and the prestige of their brand names . On the one hand , ___MASK25___ 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 ___MASK25___ universities are overly academic and fail to provide vocational ___MASK3___ with immediate " real world " applications ; but many employers value degrees from ___MASK25___ universities because they know that such coursework develops fundamental skills like critical thinking . In the mathematical fields of linear ___MASK91___ and ___MASK51___ , 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 ". Robert Louis Griess , Jr . ( born 1945 , Savannah , Georgia ) is a ___MASK50___ working on finite simple groups and vertex algebras . Currently , Griess is a professor of ___MASK88___ at University of Michigan . He constructed the monster group using the Griess ___MASK91___ . 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 .