## 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

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

Symmetric powers in abstract homotopy categories (with S. Gorchinskiy) Advances in Mathematics. Volume 292 (2016) 707 - 754
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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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Positive model structures for abstract symmetric spectra (with S. Gorchinskiy)
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arXiv:1108.3509

Non-trivial elements in the Abel-Jacobi kernels of higher dimensional varieties. Advances in Mathematics. Volume 241 (2013) 162 - 191 (with S. Gorchinskiy)
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Transcendence degree of zero-cycles and the structure of Chow motives. Central European Journal of Mathematics. Volume 10, No. 2 (2012) 559 - 568 (with S. Gorchinskiy)
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Motives and representability of algebraic cycles on threefolds over a field. Journal of Algebraic Geometry. Volume 21 (2012) No. 2, 347 - 373 (with S. Gorchinskiy)
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(see also the corrigendum)

## Conferences

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

Birational geometry and algebraic cycles