mathematics

Mark Goresky

Mark Goresky is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Mark Goresky rather than just read about it. In short: Robert Mark Goresky is a Canadian mathematician who invented intersection homology with his advisor and life partner Robert MacPherson. Career Goresky received his Ph.D. from Brown University in 1976.

Key takeaways

Mark Goresky belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Mark Goresky to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Mark Goresky from memory before moving on to harder problems.

Reference excerpt

Robert Mark Goresky is a Canadian mathematician who invented intersection homology with his advisor and life partner Robert MacPherson.

Career Goresky 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.

Awards Goresky received a Sloan Research Fellowship in 1981. He received the Coxeter–James Prize in 1984 and the Jeffery-Williams Prize in 1996. In 2002, Goresky and MacPherson were jointly awarded the Leroy P. Steele Prize for Seminal Contribution to Research by the American Mathematical Society. In 2012 Goresky became a fellow of the American Mathematical Society.

Personal Goresky's PhD advisor, Robert D. MacPherson, later became his life partner. Their discovery of intersection homology made "both of them famous." After the collapse of the Soviet Union, they were instrumental in channeling aid to Russian mathematicians, especially many who had to hide their sexuality.

Selected publications Goresky, Mark; MacPherson, Robert, La dualité de Poincaré pour les espaces singuliers, C. R. Acad. Sci. Paris Sér. A-B 284 (1977), no. 24, A1549–A1551. MR 0440533 Goresky, Mark; MacPherson, Robert, Intersection homology theory, Topology 19 (1980), no. 2, 135–162. doi:10.1016/0040-9383(80)90003-8 MR 0572580 Goresky, Mark, Whitney stratified chains and cochains, Trans. Amer. Math. Soc. 267 (1981), 175–196. Goresky, Mark; MacPherson, Robert, Intersection homology. II, Inventiones Mathematicae 72 (1983), no. 1, 77–129. doi:10.1007/BF01389130 MR 0696691 Goresky, Mark; MacPherson, Robert, Stratified Morse Theory, Springer Verlag, N. Y. (1989), Ergebnisse vol. 14.

References

External links Home page Mark Goresky publications indexed by Google Scholar

Worked examples

Example 1 — a first encounter with Mark Goresky

Start with the simplest possible case. Write down what Mark Goresky claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Mark Goresky before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Mark Goresky ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Mark Goresky

In research: Mark Goresky appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Mark Goresky in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Mark Goresky is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1950 births, 20th-century American mathematicians, 21st-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Mark Goresky outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Mark Goresky in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Mark Goresky means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Mark Goresky out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Mark Goresky in simple terms?

Robert Mark Goresky is a Canadian mathematician who invented intersection homology with his advisor and life partner Robert MacPherson. Career Goresky received his Ph.D. from Brown University in 1976.

Why does Mark Goresky matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Mark Goresky?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Mark Goresky.