Publications and preprints
New paper: How to give a bad math talk? (submitted for publication)
Grothendieck ring of varieties
Grothendieck ring of varieties
Motivic invariants of birational maps, arXiv:2207.07389 (with Hsueh-Yung Lin), to appear in Annals of mathematics.
Motivic invariants of birational maps, arXiv:2207.07389 (with Hsueh-Yung Lin), to appear in Annals of mathematics.
Factorization centers in dimension two and the Grothendieck ring of varieties, arXiv:2012.04806 (with Hsueh-Yung Lin, Susanna Zimmermann), to appear in Algebraic Geometry.
Factorization centers in dimension two and the Grothendieck ring of varieties, arXiv:2012.04806 (with Hsueh-Yung Lin, Susanna Zimmermann), to appear in Algebraic Geometry.
L-equivalence for degree five elliptic curves, elliptic fibrations and K3 surfaces, arXiv:1907.01335 (with Ziyu Zhang), Bull. London Math. Soc. 52 (2020) 395–409.
L-equivalence for degree five elliptic curves, elliptic fibrations and K3 surfaces, arXiv:1907.01335 (with Ziyu Zhang), Bull. London Math. Soc. 52 (2020) 395–409.
Variation of stable birational types of hypersurfaces, arXiv:1903.02111 (with an appendix by Claire Voisin), submitted.
Variation of stable birational types of hypersurfaces, arXiv:1903.02111 (with an appendix by Claire Voisin), submitted.
The motivic nearby fiber and degeneration of stable rationality, arXiv:1708.02790 (with Johannes Nicaise), Invent. Math. 217 (2019) 2, 377-413.
The motivic nearby fiber and degeneration of stable rationality, arXiv:1708.02790 (with Johannes Nicaise), Invent. Math. 217 (2019) 2, 377-413.
Grothendieck ring of varieties, D- and L-equivalence, and families of quadrics, arXiv:1612.07193 (with Alexander Kuznetsov), Selecta Math. (N.S.) 24 (2018), no. 4, 3475-3500.
Grothendieck ring of varieties, D- and L-equivalence, and families of quadrics, arXiv:1612.07193 (with Alexander Kuznetsov), Selecta Math. (N.S.) 24 (2018), no. 4, 3475-3500.
The Fano variety of lines and rationality problem for a cubic hypersurface, arXiv:1405.5154 (with Sergey Galkin), submitted.
The Fano variety of lines and rationality problem for a cubic hypersurface, arXiv:1405.5154 (with Sergey Galkin), submitted.
Derived categories and K-theory of singularities
Derived categories and K-theory of singularities
Derived categories of Fano threefolds and degenerations, arXiv:2305.17213 (with Alexander Kuznetsov).
Derived categories of Fano threefolds and degenerations, arXiv:2305.17213 (with Alexander Kuznetsov).
Homological Bondal-Orlov localization conjecture for rational singularities, arXiv:2212.06786 (with Mirko Mauri).
Homological Bondal-Orlov localization conjecture for rational singularities, arXiv:2212.06786 (with Mirko Mauri).
Homologically finite-dimensional objects in triangulated categories, arXiv:2211.09418 (with Alexander Kuznetsov).
Homologically finite-dimensional objects in triangulated categories, arXiv:2211.09418 (with Alexander Kuznetsov).
Categorical absorptions of singularities and degenerations, arXiv:2207.06477 (with Alexander Kuznetsov).
Categorical absorptions of singularities and degenerations, arXiv:2207.06477 (with Alexander Kuznetsov).
Obstructions to semiorthogonal decompositions for singular threefolds I: K-theory, arXiv:1910.09531 (with Martin Kalck, Nebojsa Pavic), MMJ.
Obstructions to semiorthogonal decompositions for singular threefolds I: K-theory, arXiv:1910.09531 (with Martin Kalck, Nebojsa Pavic), MMJ.
Derived categories of singular surfaces, arXiv:1809.10628 (with Joseph Karmazyn and Alexander Kuznetsov), JEMS.
Derived categories of singular surfaces, arXiv:1809.10628 (with Joseph Karmazyn and Alexander Kuznetsov), JEMS.
K-theory and the singularity category of quotient singularities, arXiv:1809.10919 (with Nebojsa Pavic), Annals of K-theory.
K-theory and the singularity category of quotient singularities, arXiv:1809.10919 (with Nebojsa Pavic), Annals of K-theory.
Geometry and derived categories
Geometry and derived categories
Group actions on categories and Elagin's Theorem Revisited, arXiv:1706.01714 , Eur. J. Math. 4 (2018), no. 1, 413-422.
Group actions on categories and Elagin's Theorem Revisited, arXiv:1706.01714 , Eur. J. Math. 4 (2018), no. 1, 413-422.
On the geometry of the LLSvS eightfold, arXiv:1601.08186, (with Andrey Soldatenkov), Kyoto J. Math. 57 (2017), no. 4, 789-806.
On the geometry of the LLSvS eightfold, arXiv:1601.08186, (with Andrey Soldatenkov), Kyoto J. Math. 57 (2017), no. 4, 789-806.
The Bogomolov-Prokhorov invariant of surfaces as equivariant cohomology, arXiv:1604.01991 , Bull. Korean Math. Soc. 54 (2017), no. 5, 1725–1741.
The Bogomolov-Prokhorov invariant of surfaces as equivariant cohomology, arXiv:1604.01991 , Bull. Korean Math. Soc. 54 (2017), no. 5, 1725–1741.
Derived Categories of Keum's Fake Projective Planes (with Sergey Galkin, Ludmil Katzarkov and Anton Mellit), Adv. in Mathematics, Vol. 278, 2015, Pages 238-253
Derived Categories of Keum's Fake Projective Planes (with Sergey Galkin, Ludmil Katzarkov and Anton Mellit), Adv. in Mathematics, Vol. 278, 2015, Pages 238-253
Exceptional collections of line bundles on the Beauville surface arXiv:1210.3339 (with Sergey Galkin), Adv. in Mathematics, Vol. 244, 2013, Pages 1033-1050
Exceptional collections of line bundles on the Beauville surface arXiv:1210.3339 (with Sergey Galkin), Adv. in Mathematics, Vol. 244, 2013, Pages 1033-1050
Motives
Motives
Linear Mahler Measures and Double L-values of Modular Forms arXiv:1206.1454 (with Masha Vlasenko), Journal of Number Theory Volume 142, September 2014, Pages 149-182.
Linear Mahler Measures and Double L-values of Modular Forms arXiv:1206.1454 (with Masha Vlasenko), Journal of Number Theory Volume 142, September 2014, Pages 149-182.
On the motive of the group of units of a division algebra, Journal of K-Theory, volume 13, issue 03, pp. 533-561.
On the motive of the group of units of a division algebra, Journal of K-Theory, volume 13, issue 03, pp. 533-561.
On the Riemann-Roch Theorem without Denominators, (with Oleg Podkopaev) St. Petersburg Math. J. Vol. 18 (2007), No. 6, Pages 1021–1027.
On the Riemann-Roch Theorem without Denominators, (with Oleg Podkopaev) St. Petersburg Math. J. Vol. 18 (2007), No. 6, Pages 1021–1027.
Mishchenko and Quillen Formulas for Oriented Cohomology Pretheories, St. Petersburg Math. J. Vol. 18 (2007), No. 4, Pages 671–678.
Mishchenko and Quillen Formulas for Oriented Cohomology Pretheories, St. Petersburg Math. J. Vol. 18 (2007), No. 4, Pages 671–678.