query: field_of_work mark goresky
supports: 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. Robert Mark Goresky ( born 1950 ) is a Canadian mathematician who invented intersection homology with Robert MacPherson . He received his Ph.D. from Brown University in 1976 . His thesis , titled Geometric Cohomology and Homology of Stratified Objects , was written under the direction of MacPherson . Many of the results in his thesis were published in 1981 by the American Mathematical Society . He has taught at the University of British Columbia in Vancouver , and Northeastern University . In 2012 he became a fellow of the American Mathematical Society . In algebraic topology, a branch of mathematics, singular homology refers to the study of a certain set of algebraic invariants of a topological space "X", the so-called homology groups formula_1. Intuitively spoken, singular homology counts, for each dimension "n", the "n"-dimensional holes of a space. Singular homology is a particular example of a homology theory, which has now grown to be a rather broad collection of theories. Of the various theories, it is perhaps one of the simpler ones to understand, being built on fairly concrete constructions. A mathematical problem is a problem that is amenable to being represented, analyzed, and possibly solved, with the methods of mathematics. This can be a real-world problem, such as computing the orbits of the planets in the solar system, or a problem of a more abstract nature, such as Hilbert's problems.<br>
  It can also be a problem referring to the nature of mathematics itself, such as Russell's Paradox. A knight is a person granted an honorary title of "knighthood" by a monarch or other political leader for service to the monarch or country, especially in a military capacity. Historically, in Europe, knighthood was conferred upon mounted warriors. During the High Middle Ages, knighthood was considered a class of lower nobility. By the Late Middle Ages, the rank had become associated with the ideals of chivalry, a code of conduct for the perfect courtly Christian warrior. Often, a knight was a vassal who served as a fighter for a lord, with payment in the form of land holdings. The lords trusted the knights, who were skilled in battle on horseback. Since the early modern period, the title of knight is purely honorific, usually bestowed by a monarch, as in the British honours system, often for non-military service to the country. The modern female equivalent in the United Kingdom is Dame. The Canadian titles debate has been ongoing since the presentation to the Canadian House of Commons of the Nickle Resolution in 1917. This resolution marked the earliest attempt to establish a Canadian government policy requesting the sovereign not to grant knighthoods, baronetcies, and peerages to Canadians and set the precedent for later policies restricting Canadians from accepting titles from foreign countries. Dissatisfaction with the British honours system led to the gradual creation of a separate system for Canada. An earl is a member of the nobility. The title is Anglo-Saxon in origin, akin to the Scandinavian form jarl, and meant "chieftain", particularly a chieftain set to rule a territory in a king's stead. In Scandinavia, it became obsolete in the Middle Ages and was replaced by duke ("hertig"/"hertug"/"hertog"). In later medieval Britain, it became the equivalent of the continental count (in England in the earlier period, it was more akin to a duke; in Scotland it assimilated the concept of mormaer). However, earlier in Scandinavia, "jarl" could also mean a sovereign prince. For example, the rulers of several of the petty kingdoms of Norway had the title of "jarl" and in many cases they had no less power than their neighbours who had the title of king. Alternative names for the "Earl/Count" rank in the nobility structure are used in other countries, such as Hakushaku during the Japanese Imperial era. In mathematics, topology (from the Greek , "place", and , "study") is concerned with the properties of space that are preserved under continuous deformations, such as stretching and bending, but not tearing or gluing. This can be studied by considering a collection of subsets, called open sets, that satisfy certain properties, turning the given set into what is known as a topological space. Important topological properties include connectedness and compactness. A mathematician is someone who uses an extensive knowledge of mathematics in his/her work, typically to solve mathematical problems. In topology, a branch of mathematics, intersection homology is an analogue of singular homology especially well-suited for the study of singular spaces, discovered by Mark Goresky and Robert MacPherson in the fall of 1974 and developed by them over the next few years.
candidates: class computing early modern period high middle ages mathematician mathematics middle ages military topology
answer: topology