Research Interests
My current research interests lie in the interactions between algebraic geometry and number theory. More recently, I've become interested in some aspects of model theory and logic.


21: Relative Fontaine-Laffaille Theory over power series over Witt vectors. (pdf)
      With Tong Liu and Yong Suk Moon.
      (Submitted)

20: A Kawamata-Viehweg type formulation of the logarithmic Akizuki-Nakano Vanishing Theorem. (pdf)
      With D. Arapura, K. Matsuki, and J. Wlodarczyk.
       (Submitted)

19: Gamma Motives 1: Etale realization, and monodromy. (pdf)
      With M. Nori.
      (Preprint)

18: K-theory of microdifferential operators and de Rham epsilon factors. (pdf)
      (Preprint.)

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

16 : VC Density of definable families over valued fields (pdf)
      With Saugata Basu.
      (to appear Journal of the European Mathematical Society)

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:

P1: Gamma Motives 2: De-Rham realization and Period Isomorphism for Tori.
      With M. Nori.

P2: Gamma Motives 3: Categorical Foundations.
      With M. Nori

P3: Singular supports of Brylinski-Radon transforms in char. p.
      With K.V. Shuddhodan

P4: Enriched Hodge structures on complex analytic links
     With M. Nori and V. Srinivas