Research Interests
My research interests lie in the interactions between algebraic
geometry and number theory. More recently, I've become interested in
connections between algebraic geometry and model theory.
25: Homological VC Density: Bounds and Application. (pdf)
With S. Basu
(Submitted)
24: Nonnegativity of Signed Euler Characteristics of Moduli of
Curves and Abelian Varieties. (pdf)
With D. Arapura
(Submitted)
23: Local Monodromy of Constructible Sheaves (pdf)
With M. Nori
(Submitted)
22: Brylinski-Radon transforms in char. p > 0. (pdf)
With K.V. Shuddhodan
(Submitted)
21: Enriched Hodge structures on complex analytic links. (pdf)
With M. Nori and V. Srinivas
Progr. Math, 352
``Perspectives on Four Decades of Algebraic Geometry 1980-2020'' (A
volume in honor of Alberto Collino)), 2025, Pages 345-390.
20: Relative Fontaine-Laffaille Theory over power series over Witt
vectors. (pdf)
With Tong Liu and Yong Suk Moon.
IMRN, 2024, No. 5, 2024,
Pages 4384-4455.
19: A Kawamata-Viehweg type formulation of the logarithmic
Akizuki-Nakano Vanishing Theorem. (pdf)
With D. Arapura, K. Matsuki, and J.
Wlodarczyk.
Math. Zeitschrift,
Vol. 303, No. 4, 2023.
18: K-theory of microdifferential operators and de Rham epsilon
factors. (pdf)
(Submitted)
17 : VC Density of definable families over valued fields (pdf)
With Saugata Basu.
Journal of the European
Mathematical Society, Vol. 73, No. 7, 2021, pp. 2361-2403.
16: Connectivity of joins, cohomological quantifier elimination, and
an algebraic Toda's Theorem. (pdf)
With Saugata Basu.
Selecta Mathematica, New Series,
2020, pp. 26-71.
15: D^{\dagger}-affinity of formal models of flag varieties. (pdf)
With C. Huyghe, T. Schmidt, and M.
Strauch.
Mathematical Research Letters,
Vol. 26, No. 6, 2019, pp. 1677-1745.
14: Arithmetic differential operators on a semistable model of
P^{1}. (pdf)
With Tobias Schmidt and Matthias Strauch.
Math. Zeitschrift, Vol. 293, No. 1,
2019, pp. 319-338.
13: Specialization of cycles and the K-theory elevator. (pdf)
With C. Doran, J. Iyer, M. Kerr, J.
Lewis, S. Muller-Stach, P. Paleaz.
Communications in Number theory and
Physics, 13, No. 2, 2019, pp. 299-348.
12: Locally analytic representations of GL(2) via semistable models
of P^{1}. (pdf)
With Tobias Schmidt and Matthias
Strauch.
Journal of the Institute of Math.
of Jussieu, 18, No. 2, 2019, pp. 125-187.
11: On a localization formula for epsilon factors via microlocal
geometry. (pdf)
With Tomoyuki Abe.
Annals of K-Theory, Vol. 3,
No. 3, 2018, pp. 461-490.
10: Lefschetz theorems for torsion algebraic cycles in codimension
2. (pdf) (erratum)
With G.V. Ravindra.
Advances in Math., 315,
2017, pp. 554-575.
9: An infinitesimal Noether-Lefschetz theorem for Chow groups. (pdf)
With G.V. Ravindra.
Journal of Pure and Applied
Algebra, 221, No. 8, 2017, pp. 1926-1933.
8: Motivic structure on higher homotopy of hyperplane arrangements.
(pdf)
Mathematische Annalen, 366(1), 2016, pp.
279-300.
7: A relative version of the Beilinson-Hodge cojecture. (pdf)
With Rob de Jeu and James Lewis.
Recent advances in Hodge theory (period
domains, algebraic cycles, and arithmetic), Lecture Note
Series
London Mathematical Society, 247, Cambridge
University Press, 2016, pp. 241-263.
6. Locally analytic representations and sheaves on the Bruhat-Tits
building. (pdf)
With Tobias Schmidt and Matthias Strauch.
Algebra and Number Theory, 8, No. 6,
2014, pp. 1365-1445.
5: Weak Lefschetz for Chow groups: Infinitesimal Lifting. (pdf)
With G.V. Ravindra.
Homology Homotopy and Applications, 16,
No. 2, 2014, pp. 65-84.
4: Towards connectivity theorems for codimension 2 cycles:
Infinitesimal Deformations. (pdf)
With G.V. Ravindra.
Journal of Algebra, 399, 2014, pp.
407-422.
3: Integral models of P^{1} and analytic distribution algebras for
GL(2). (pdf)
With Tobias Schmidt and Matthias Strauch.
Munster Journal of Mathematics, 7, 2014,
pp. 241-271.
2: De Rham epsilon factors. (pdf)
Inventiones Mathematicae, Vol. 190, No.
2, 2012, pp. 299-355.
1: Power weak mixing does not imply multiple recurrence in infinite
measure and other counterexamples.
With Kate Gruher, Fred Hines, Cesar Silva, and
Robert Waelder.
New York Journal of Mathematics, Vol. 1,
2003, pp. 1-23.
In Preparation/Preprints
1: Cohomological Distality and Stability
With Saugata Basu
2: Algebraic Cycles on Prym Varieties from Geometric Class field
theory
With Yilong Zhang
3: Cycle Classes for Enriched Hodge structures on complex analytic
thickenings
With M. Nori and V. Srinivas
4: The Dubois Complex, revisited
5: The signed euler characteristic property and generic vanishing in
characteristic p.
6: Local Monodromy of Alexander Modules (pdf)
With M. Nori.