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.


In Preparation

• Local Monodromy of Alexander Modules in characteristic p.


• Cycle Classes for Enriched Hodge structures on complex analytic thickenings
        With V. Srinivas


• The Dubois Complex, revisited


• The signed Euler characteristic property and generic vanishing in characteristic p.


• Higher dimensional Gassner Representations

Published/Submitted

• Local Monodromy of Alexander Modules (pdf)
        With M. Nori.
        (Submitted)


• Algebraicity of Hodge Cycles on some Generalized Prym varieties. (pdf)
        With Yilong Zhang
        (Submitted)


• Homological VC Density: Bounds and Application. (pdf)
        With S. Basu
        (Submitted)


• Brylinski-Radon transforms in char. p > 0. (pdf)
        With K.V. Shuddhodan
        (Submitted)


• Nonnegativity of Signed Euler Characteristics of Moduli of Curves and Abelian Varieties. (pdf)
        With D. Arapura
        Math. Annalen, 366, 2026


• Local Monodromy of Constructible Sheaves (pdf)
        With M. Nori
        (tp appear, Crelle)


• K-theory of microdifferential operators and de Rham epsilon factors. (pdf)
        to appear, Homology, Homotopy, and Applications


• 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.


• 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.


• 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.


• 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.


• Connectivity of joins, cohomological quantifier elimination, and an algebraic Toda's Theorem. (pdf)
        With Saugata Basu.
        Selecta Mathematica, New Series, 2020, pp. 26-71.


• 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.


• 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.


• 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.


• 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.


• 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.


• Lefschetz theorems for torsion algebraic cycles in codimension 2. (pdf) (erratum)
        With G.V. Ravindra.
        Advances in Math., 315, 2017, pp. 554-575.


• 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.


• Motivic structure on higher homotopy of hyperplane arrangements. (pdf)
      Mathematische Annalen, 366(1), 2016, pp. 279-300.


• 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.


• 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.


• Weak Lefschetz for Chow groups: Infinitesimal Lifting. (pdf)
      With G.V. Ravindra.
      Homology Homotopy and Applications, 16, No. 2, 2014, pp. 65-84.


• Towards connectivity theorems for codimension 2 cycles: Infinitesimal Deformations. (pdf)
      With G.V. Ravindra.
      Journal of Algebra, 399, 2014, pp. 407-422.


• 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.


• De Rham epsilon factors. (pdf)
      Inventiones Mathematicae, Vol. 190, No. 2, 2012, pp. 299-355.


• 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.