query: field_of_work richard a. parker
supports: 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. Coding theory is the study of the properties of codes and their respective fitness for specific applications. Codes are used for data compression, cryptography, error-correction, and networking. Codes are studied by various scientific disciplinessuch as information theory, electrical engineering, mathematics, linguistics, and computer sciencefor the purpose of designing efficient and reliable data transmission methods. This typically involves the removal of redundancy and the correction or detection of errors in the transmitted data. Ernst Witt (June 26, 1911  July 3, 1991) was a German mathematician, one of the leading algebraists of his time. He was born on the island of Als (German: "Alsen"). Shortly after his birth, he and his parents moved to China, and he did not return to Europe until he was nine. In mathematics, a Moufang loop is a special kind of algebraic structure. It is similar to a group in many ways but need not be associative. Moufang loops were introduced by . Smooth Moufang loops have an associated algebra, the Malcev algebra, similar in some ways to how a Lie group has an associated Lie algebra. The United Kingdom of Great Britain and Northern Ireland, commonly known as the United Kingdom (UK) or Britain, is a sovereign country in western Europe. Lying off the north-western coast of the European mainland, it includes the island of Great Britain (the name of which is also loosely applied to the whole country), the north-eastern part of the island of Ireland, and many smaller islands. Northern Ireland is the only part of the UK that shares a land border with another sovereign statethe Republic of Ireland. Apart from this land border, the UK is surrounded by the Atlantic Ocean, with the North Sea to its east, the English Channel to its south and the Celtic Sea to its south-south-west, giving it the 12th-longest coastline in the world. The Irish Sea lies between Great Britain and Ireland. With an area of , the UK is the 78th-largest sovereign state in the world and the 11th-largest in Europe. It is also the 21st-most populous country, with an estimated 65.1 million inhabitants. Together, this makes it the fourth most densely populated country in the European Union. In topology, knot theory is the study of mathematical knots. While inspired by knots which appear in daily life in shoelaces and rope, a mathematician's knot differs in that the ends are joined together so that it cannot be undone. In mathematical language, a knot is an embedding of a circle in 3-dimensional Euclidean space, R (in topology, a circle isn't bound to the classical geometric concept, but to all of its homeomorphisms). Two mathematical knots are equivalent if one can be transformed into the other via a deformation of R upon itself (known as an ambient isotopy); these transformations correspond to manipulations of a knotted string that do not involve cutting the string or passing the string through itself. Number theory or, in older usage, arithmetic is a branch of pure mathematics devoted primarily to the study of the integers. It is sometimes called "The Queen of Mathematics" because of its foundational place in the discipline. Number theorists study prime numbers as well as the properties of objects made out of integers (e.g., rational numbers) or defined as generalizations of the integers (e.g., algebraic integers). In abstract algebra, a finite group is a mathematical group with a finite number of elements. A group is a set of elements together with an operation which associates, to each ordered pair of elements, an element of the set. With a finite group, the set is finite.  The Celtic Sea (; ) is the area of the Atlantic Ocean off the south coast of Ireland bounded to the east by Saint George's Channel; other limits include the Bristol Channel, the English Channel, and the Bay of Biscay, as well as adjacent portions of Wales, Cornwall, Devon, and Brittany. The southern and western boundaries are delimited by the continental shelf, which drops away sharply. The Isles of Scilly are an archipelago of small islands in the sea. A shire is a traditional term for a division of land, found in the United Kingdom and Australia. It was first used in Wessex from the beginning of Anglo-Saxon settlement, and spread to most of the rest of England in the tenth century. The River Cam is the main river flowing through Cambridge in eastern England. After leaving Cambridge, it flows north and east into the Great Ouse to the south of Ely at Pope's Corner. The Great Ouse connects the Cam to the North Sea at King's Lynn: The total distance from Cambridge to the sea is about and is navigable for punts, small boats, and rowing craft. The Great Ouse also connects to England's canal system via the Middle Level Navigations and the River Nene. In total, the Cam runs for around from its furthest source (near Debden in Essex) to its confluence with the Great Ouse.  A census of the population of the United Kingdom is taken every ten years. The 2011 census was held in all countries of the UK on 27 March 2011. It was the first UK census which could be completed online via the Internet. The Office for National Statistics (ONS) is responsible for the census in England and Wales, the General Register Office for Scotland (GROS) is responsible for the census in Scotland, and the Northern Ireland Statistics and Research Agency (NISRA) is responsible for the census in Northern Ireland. Combinatorial game theory (CGT) is a branch of mathematics and theoretical computer science that typically studies sequential games with perfect information. Study has been largely confined to two-player games that have a "position" in which the players take turns changing in defined ways or "moves" to achieve a defined winning condition. CGT has not traditionally studied games of chance or those that use imperfect or incomplete information, favoring games that offer perfect information in which the state of the game and the set of available moves is always known by both players. However, as mathematical techniques advance, the types of game that can be mathematically analyzed expands, thus the boundaries of the field are ever changing. Scholars will generally define what they mean by a "game" at the beginning of a paper, and these definitions often vary as they are specific to the game being analyzed and are not meant to represent the entire scope of the field. In mathematics, a Lie group is a group that is also a differentiable manifold, with the property that the group operations are compatible with the smooth structure. Lie groups are named after Sophus Lie, who laid the foundations of the theory of continuous transformation groups. The term "groupes de Lie" first appeared in French in 1893 in the thesis of Lies student Arthur Tresse. 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. 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 Princeton University is a private Ivy League research university in Princeton, New Jersey, United States. The North Sea is a marginal sea of the Atlantic Ocean located between Great Britain, Scandinavia, Germany, the Netherlands, Belgium, and France. An epeiric (or "shelf") sea on the European continental shelf, it connects to the ocean through the English Channel in the south and the Norwegian Sea in the north. It is more than long and wide, with an area of around . West Sussex is a county in the south of England, bordering East Sussex (with Brighton and Hove) to the east, Hampshire to the west and Surrey to the north, and to the south the English Channel. Chichester in the southwest is the county town and only city in West Sussex, with the largest towns being Crawley, Worthing and Horsham. 
  West Sussex has a range of scenery, including wealden, downland and coastal. The highest point of the county is Blackdown, at 280 metres (919 ft). It has a number of stately homes including Goodwood, Petworth House and Uppark and also castles such as Arundel Castle and Bramber Castle. Over half the county is protected countryside, offering walking, cycling and other recreational opportunities. East Sussex is a county in South East England. It is bordered by the counties of Kent to the north and east, Surrey to the north west and West Sussex to the west, and to the south by the English Channel. A country is a region that is identified as a distinct national entity in political geography. A country may be an independent sovereign state or one that is occupied by another state, as a non-sovereign or formerly sovereign political division, or a geographic region associated with sets of previously independent or differently associated people with distinct political characteristics. Regardless of the physical geography, in the modern internationally accepted legal definition as defined by the League of Nations in 1937 and reaffirmed by the United Nations in 1945, a resident of a country is subject to the independent exercise of legal jurisdiction. 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. Recreational mathematics is a term for mathematics carried out for recreation (entertainment) rather than as a strictly research and application-based professional activity. Although it is not necessarily limited to being an endeavor for amateurs, it often involves mathematical puzzles and games. In mathematics, the Leech lattice is an even unimodular lattice  in 24-dimensional Euclidean space, which is one of the best models for the kissing number problem. It was discovered by . It may also have been discovered (but unpublished) by Ernst Witt in 1940. A mathematician is someone who uses an extensive knowledge of mathematics in his/her work, typically to solve mathematical problems. England is a country that is part of the United Kingdom. It shares land borders with Scotland to the north and Wales to the west. The Irish Sea lies northwest of England and the Celtic Sea lies to the southwest. England is separated from continental Europe by the North Sea to the east and the English Channel to the south. The country covers five-eighths of the island of Great Britain (which lies in the North Atlantic) in its centre and south; and includes over 100 smaller islands such as the Isles of Scilly, and the Isle of Wight. The English Channel ("the Sleeve" [hence ] "Sea of Brittany" "British Sea"), also called simply the Channel, is the body of water that separates southern England from northern France, and joins the southern part of the North Sea to the rest of the Atlantic Ocean. A cellular automaton (pl. cellular automata, abbrev. CA) is a discrete model studied in computability theory, mathematics, physics, complexity science, theoretical biology and microstructure modeling. Cellular automata are also called cellular spaces, tessellation automata, homogeneous structures, cellular structures, tessellation structures, and iterative arrays. In geometry and mathematical group theory, a unimodular lattice is an integral lattice of determinant 1 or 1. For a lattice in "n"-dimensional Euclidean space, this is equivalent to requiring that the volume of any fundamental domain for the lattice be 1. In mathematics, and more specifically in abstract algebra, an algebraic structure is a set (called carrier set or underlying set) with one or more finitary operations defined on it that satisfies a list of axioms. In mathematics, a Malcev algebra (or Maltsev algebra or MoufangLie algebra) over a field is a nonassociative algebra that is antisymmetric, so that The Isle of Wight is a county and the largest and second-most populous island in England. It is located in the English Channel, about 4 miles (6 km) off the coast of Hampshire, separated by the Solent. The island has resorts that have been holiday destinations since Victorian times, and is known for its mild climate, coastal scenery, and verdant landscape of fields, downland and chines. In geometry, a kissing number is defined as the number of non-overlapping unit spheres that can be arranged such that they each touch another given unit sphere. For a lattice packing the kissing number is the same for every sphere, but for an arbitrary sphere packing the kissing number may vary from one sphere to another. Other names for kissing number that have been used are Newton number (after the originator of the problem), and contact number. In mathematics, a Lie algebra (not ) is a vector space together with a non-associative multiplication called "Lie bracket" formula_1. When an algebraic product is defined on the space, the Lie bracket is the commutator formula_2. Hampshire (; abbreviated Hants, archaically known as the County of Southampton) is a county on the southern coast of England in the United Kingdom. The county town of Hampshire is Winchester, the former capital city of England. Hampshire is the most populous ceremonial county in the United Kingdom (excluding the metropolitan counties) with almost half of the county's population living within the South Hampshire conurbation which includes the cities of Southampton and Portsmouth. The larger South Hampshire metropolitan area has a population of 1,547,000. Hampshire is notable for housing the birthplaces of the Royal Navy, British Army, and Royal Air Force. It is bordered by Dorset to the west, Wiltshire to the north-west, Berkshire to the north, Surrey to the north-east, and West Sussex to the east. The southern boundary is the coastline of the English Channel and the Solent, facing the Isle of Wight. For the Egyptologist Richard A. Parker , see Richard Anthony Parker . Richard A. Parker ( b. 29 January 1953 , in Surrey ) is a mathematician and freelance computer programmer in Cambridge , England . He invented many of the algorithms for computing the modular character tables of finite simple groups . He discovered the relation between Niemeier lattices and deep holes of the Leech lattice , and constructed Parker 's Moufang loop of order 213 ( which was used by John Horton Conway in his construction of the monster group ) . Surrey is a county in the south east of England and also one of the home counties bordering Greater London. Surrey shares borders with Kent to the east, East Sussex to the south-east, West Sussex to the south, Hampshire to the west and south-west and Berkshire to the north-west. The county town is Guildford. Surrey County Council sits extraterritorially at Kingston upon Thames, administered as part of Greater London since 1965. With a resident population of 1.1 million, Surrey is the most densely populated and third most populated county in the South East region, after Kent and Hampshire. John Horton Conway FRS (born 26 December 1937) is an English mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory. He has also contributed to many branches of recreational mathematics, notably the invention of the cellular automaton called the Game of Life. Conway is currently Professor Emeritus of Mathematics at Princeton University in New Jersey. Cambridge is a university city and the county town of Cambridgeshire, England, on the River Cam about north of London. At the United Kingdom Census 2011, its population was 123,867, including 24,488 students. The home counties are the counties of England that surround London (although several of them do not border it). The counties generally included in the list are Berkshire, Buckinghamshire, Essex, Hertfordshire, Kent, Surrey, and Sussex. Other counties more distant from Londonsuch as Bedfordshire, Cambridgeshire, Hampshire and Oxfordshireare also sometimes regarded as home counties due to their proximity to London and their connection to the London regional economy.
candidates: abstract algebra algebra australia computer science cryptography data compression economy electrical engineering english entertainment french game theory geography geometry group theory information theory invention knot theory lattice linguistics mathematician mathematics navy number theory physics research river statistics topology
answer: group theory