astronomy

Ismar Volić

Ismar Volić is a astronomy 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 Ismar Volić rather than just read about it. In short: Ismar Volić is a Bosnian-American mathematician. He is a professor of mathematics at Wellesley College and a co-founder of the Institute for Mathematics and Democracy.

Key takeaways

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

Reference excerpt

Ismar Volić is a Bosnian-American mathematician. He is a professor of mathematics at Wellesley College and a co-founder of the Institute for Mathematics and Democracy.

Education and career Volić completed his undergraduate degree at Boston University in 1998 and his Ph.D. in mathematics at Brown University in 2003 under the direction of Thomas Goodwillie. He was a Whyburn Research Instructor at the University of Virginia from 2003 to 2006. He has been teaching at Wellesley College since 2006. He was the department chair from 2022 to 2025. He was a visiting professor at Louvain-la-Neuve University, the University of Virginia, Harvard University, and MIT. In 2019, he co-founded the Institute for Mathematics and Democracy to "promote a deeper understanding of mathematics as a pivotal force in creating a democracy where people make informed political decisions and enact change based on objective and rigorous quantitative criteria". Volić is an active member of the Bosnian-Herzegovinian American Academy of Arts and Sciences, an organization dedicated to advancement of arts and science in Bosnia and Herzegovina. He was its treasurer in 2016–2019, vice-president in 2019–20, and its president in 2021–22. He travels to Bosnia and Herzegovina frequently through his involvement in various education and research activities, including advising Ph.D. students and working with various agencies to bring quality STEM education to the country.

Research Volić's research is in algebraic topology. He is the author of over thirty articles and two books and has delivered more than two hundred lectures in some twenty countries. He has contributed to the fields of calculus of functors, spaces of embeddings and immersions, configuration space integrals, finite type invariants, Milnor invariants, rational homotopy theory, topological data analysis, and social choice theory. Volić's book, Making Democracy Count: How Mathematics Improves Voting, Electoral Maps, and Representation, published by Princeton University Press in 2024, won the Mathematical Association of America's Euler Prize and was a finalist for the PROSE Award.

Selected papers "Political structures and the topology of simplicial complexes", with A. Mock, Mathematical Social Sciences, 114 (2021), 39–57 "Formality of the little N-discs operad", with P. Lambrechts, Memoirs of the American Mathematical Society, 239 (2014), no. 1079, 116 pp. "The rational homology of spaces of long knots in codimension >2", with P. Lambrechts and V. Turchin, Geometry & Topology, 14 (2010), 2151–2187. "Calculus of functors, operad formality, and rational homology of embedding spaces", with G. Arone and P. Lambrechts, Acta Mathematica, 199 (2007), no. 2, 153–198. "Finite type knot invariants and calculus of functors", Compositio Mathematica, 142 (2006), 222–250.

Books Making Democracy Count: How Mathematics Improves Voting, Electoral Maps, and Representation, Princeton University Press, 2024. 408 pp. Cubical homotopy theory, with B. Munson, New Mathematical Monographs, 25. Cambridge University Press, Cambridge, 2015. 625 pp.

Awards Volić was awarded a 2017-2018 Fulbright U.S. Scholar Archived 2020-05-30 at the Wayback Machine grant, which he used to visit University of Sarajevo. He was also selected as a Fulbright Specialist for three years in 2020. He has received several grants form the National Science Foundation as well as grants from the Simons Foundation and the Open Society Foundation. His work with the Institute for Mathematics and Democracy was funded by Schwab Charitable and the Hewlett Foundation. He was elected to the 2026 class of Fellows of the American Mathematical Society.

References

Illustrations

Worked examples

Example 1 — a first encounter with Ismar Volić

Start with the simplest possible case. Write down what Ismar Volić claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In astronomy, 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 Ismar Volić 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 Ismar Volić 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 Ismar Volić

In research: Ismar Volić appears in astronomy 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 Ismar Volić 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: Ismar Volić is common in secondary-school and first-year university syllabi. It links to neighbouring topics Boston University alumni, Brown University alumni, Fellows of the American Mathematical Society, so understanding it makes those chapters shorter.
In everyday life: Look for Ismar Volić 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 Ismar Volić in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Ismar Volić 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 Ismar Volić out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Ismar Volić in simple terms?

Ismar Volić is a Bosnian-American mathematician. He is a professor of mathematics at Wellesley College and a co-founder of the Institute for Mathematics and Democracy.

Why does Ismar Volić matter?

Because it connects several astronomy 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 Ismar Volić?

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 Ismar Volić.