## Research interests

Arithmetic algebraic geometry, algebraic cycles, Hodge theory, motives, A^1-homotopy theory of schemes, homotopical algebra, category theory

## Teaching

MATH244 Linear Algebra and Geometry, MATH444 Elliptic Curves, MATH448 Algebraic Geometry

## PhD students

Anwar Alameddin, Oliver Eivind Anderson, Lucas de Souza das Dores and Stefano Nicotra

## Former PhD students

Kalyan Banerjee One-dimensional algebraic cycles on nonsingular cubic fourfolds in P^5
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Joe Palacios Baldeon. Geometric symmetric powers in the homotopy categories of schemes over a field
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## Recent papers

Bloch's conjecture for the surface of Craighero and Gattazzo
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arXiv:1609.04074

Motivic obstruction to rationality of a very general cubic hypersurface in P^5. Part I
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arXiv:1605.09434

Rational equivalence for line configurations on cubic hypersurfaces in P^5 (with K. Banerjee)
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arXiv:1405.6430

Positive model structures for abstract symmetric spectra (with S. Gorchinskiy)
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arXiv:1108.3509

A^1-connectivity on Chow monoids v.s. rational equivalence of algebraic cycles. European Journal of Mathematics. Volume 2, Issue 1 (2016) 169 - 195
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Algebraic cycles on quadric sections of cubics in P^4 under the action of symplectomorphisms (with A. Tikhomirov) Proc. of the Edinburgh Math. Soc. 59 (2016) 377 - 392
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Symmetric powers in abstract homotopy categories (with S. Gorchinskiy) Advances in Mathematics. Volume 292 (2016) 707 - 754
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## Conferences organized

Edge Days 2016: workshop on birational geometry and reduction to positive characteristic

Birational geometry and algebraic cycles