I’m a mathematician interested in homotopy theory and algebraic geometry.

I recently received a Ph.D. in mathematics from Northwestern University as a student of Paul Goerss and am currently a visiting researcher at the University of Duisburg–Essen. Starting this fall I will be a postdoc at MIT.

Email: hoyois@math.northwestern.edu

CV (June 2014)

**A quadratic refinement of the Grothendieck–Lefschetz–Verdier trace formula**(to appear in A>) [pdf, arXiv]

A Lefschetz fixed point theorem in stable motivic homotopy theory.**The motivic Steenrod algebra in positive characteristic**(with Shane Kelly and Paul Arne Østvær) [arXiv]**From algebraic cobordism to motivic cohomology**(to appear in Crelle) [pdf, arXiv]

A proof of the Hopkins–Morel equivalence in motivic homotopy theory.**The étale symmetric Künneth theorem**(draft, June 2012) [pdf]

**A note on étale homotopy**[pdf]

An exposition of higher Galois theory for ∞-topoi and its connection to the étale homotopy type of Artin–Mazur–Friedlander.- Notes on the birational classification of surfaces. [pdf]
- Notes on the first reconstruction theorem in Gromov–Witten theory. [pdf]
- Notes on the Nisnevich topology and Thom spaces in motivic homotopy theory, with a proof of the motivic tubular neighborhood theorem. [pdf]
**Chern character and derived algebraic geometry**(Master thesis, EPFL) [pdf, slides, poster]**Sur la cohomologie des schémas**(EPFL, 8th semester) [pdf]

Basic scheme theory from the geometric viewpoint. Definition and properties of sheaf cohomology and of Čech cohomology. Computation of the cohomology of affine schemes and of projective spaces.**The Syntax of First-Order Logic**(EPFL, 6th and 7th semesters) [pdf]

A constructive treatment of various topics in first-order logic: Herbrand’s theorem and the epsilon theorems; Craig’s interpolation lemma; Gödel’s first incompleteness theorem (two proofs); a detailed account of Gödel’s second incompleteness theorem; basic Zermelo–Fraenkel set theory; the consistency of the axiom of choice and of the generalized continuum hypothesis.**Décompositions paradoxales**(EPFL, 5th semester) [pdf]

This is an exploration of the notion of*equidecomposability*in a set being acted upon by a group. Applications include the generalized Banach–Tarski paradox, the Sierpiński–Mazurkiewicz paradox, and the von Neumann paradox in the plane. The equivalence between the amenability and the nonparadoxality of discrete groups is proved (Tarski’s theorem).**Sur la constante de Khinchin**(with Stéphane Flotron and Ludovic Pirl, EPFL, 4th semester) [pdf]

Khinchin’s theorem states that there exists a real number*K*, Khinchin’s constant, such that the sequence of partial geometric means of the elements of the continuous fraction of almost any real number converges to*K*. This text contains an elementary discussion of continuous fractions and two different proofs of this result: Khinchin’s original proof and a more conceptual proof using ergodic theory.