mathematics

Gabriele Vezzosi

Gabriele Vezzosi 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 Gabriele Vezzosi rather than just read about it. In short: Gabriele Vezzosi is an Italian mathematician, born in Florence, Italy. His main interest is algebraic geometry.

Key takeaways

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

Reference excerpt

Gabriele Vezzosi is an Italian mathematician, born in Florence, Italy. His main interest is algebraic geometry. Vezzosi earned an MS degree in Physics at the University of Florence, under the supervision of Alexandre M. Vinogradov, and a PhD in Mathematics at the Scuola Normale Superiore in Pisa, under the supervision of Angelo Vistoli. His first papers dealt with differential calculus over commutative rings, intersection theory, (equivariant) algebraic K-theory, motivic homotopy theory, and existence of vector bundles on singular algebraic surfaces. Around 2001–2002 he started his collaboration with Bertrand Toën. Together, they created homotopical algebraic geometry (HAG), whose more relevant part is derived algebraic geometry (DAG), which is by now a powerful and widespread theory. Slightly later, this theory was reconsidered, and highly expanded by Jacob Lurie. More recently, Vezzosi together with Tony Pantev, Bertrand Toën and Michel Vaquié defined a derived version of symplectic structures and studied important properties and examples (an important instance being Kai Behrend's symmetric obstruction theories); further together with Damien Calaque these authors introduced and studied a derived version of Poisson and coisotropic structures with applications to deformation quantization. Lately Toën and Vezzosi (partly in collaboration with Anthony Blanc and Marco Robalo) moved to applications of derived and non-commutative geometry to arithmetic geometry, especially to Spencer Bloch's conductor conjecture. Vezzosi also defined a derived version of quadratic forms, and in collaboration with Benjamin Hennion and Mauro Porta, proved a very general formal gluing result along non-linear flags with hints of application to a yet conjectural Geometric Langlands program for varieties of dimension bigger than 1. Together with Benjamin Antieau, Vezzosi proved a Hochschild–Kostant–Rosenberg theorem (HKR) for varieties of dimension p in characteristic p. In 2015 he organised the Oberwolfach Seminar on Derived Geometry at the Mathematical Research Institute of Oberwolfach in Germany, and is an organiser of the one-semester thematic program at Mathematical Sciences Research Institute in Berkeley, California in 2019 on Derived algebraic geometry. Vezzosi spent his career so far in Pisa, Florence, Bologna and Paris, has had three PhD students (Schürg, Porta and Melani) and is full professor at the University of Florence (Italy).

References

External links Personal web page Gabriele Vezzosi at the Mathematics Genealogy Project Gabriele Vezzosi Wikipedia entry in german Ncatlab entry on derived algebraic geometry Talk at Kashiwara's Conference (IHES, France) June 2017

Illustrations

Worked examples

Example 1 — a first encounter with Gabriele Vezzosi

Start with the simplest possible case. Write down what Gabriele Vezzosi 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 Gabriele Vezzosi 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 Gabriele Vezzosi 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 Gabriele Vezzosi

In research: Gabriele Vezzosi 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 Gabriele Vezzosi 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: Gabriele Vezzosi is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1968 births, Academic staff of the University of Florence, Algebraic geometers, so understanding it makes those chapters shorter.
In everyday life: Look for Gabriele Vezzosi 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 Gabriele Vezzosi in 20 minutes

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

Frequently asked questions

What is Gabriele Vezzosi in simple terms?

Gabriele Vezzosi is an Italian mathematician, born in Florence, Italy. His main interest is algebraic geometry.

Why does Gabriele Vezzosi 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 Gabriele Vezzosi?

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 Gabriele Vezzosi.