Department of Mathematics

University of Kansas

1460 Jayhawk Blvd

Lawrence, Kansas 66045-7567

- Effective very ampleness, projective normality and higher syzygies of higher dimensional varieties of general type
- Deformation theory of finite morphisms with applications to
- describing the geometry of moduli spaces of varieties of general type by characterising the generic behaviour of canonical morphisms
- construction of low codimension subvarieties and non-split vector bundles on a projective space
- Geometry of moduli stacks of finite covers and computing their invariants

- On the projective normality and normal presentation of higher dimensional varieties with nef canonical bundle (with D. Raychaudhury) (J. Algebra 540 (2019), 121--155.)
- Remarks on projective normality for certain Calabi-Yau and hyperk\"ahler varieties (with D. Raychaudhury) (J. Pure Appl. Algebra 224 (2020), no. 10, 106383)
- Smoothing of multiple structures on embedded Enriques' manifolds (with D. Raychaudhury) (submitted)
- K3 carpets on minimal rational surfaces and their smoothing (submitted) (with P. Bangere, D. Raychaudhury)(submitted)
- Deformation of morphisms, varieties of low codimension and asymptotic limits (with P. Bangere, F.J. Gallego, D. Raychaudhury)(Preprint)
- Deformation of quadruple Galois canonical covers (with P. Bangere, F.J. Gallego, D. Raychaudhury) (Preprint)

- Research talk: Algebraic Geometry Seminar, University of Kansas, On the Projective Normality and Normal Presentation of Higher Dimensional Varieties with Nef Canonical Bundle
- Research talk: Algebraic Geometry Seminar, University of Kansas, Remarks on projective normality for certain Calabi-Yau and hyperkähler varieties
- Research talk (Preparatory): Algebraic Geometry Seminar, University of Kansas, Formal deformations and algebraization.
- Research talk: Algebraic Geometry Seminar, University of Kansas, Deformations of Quadruple Galois Canonical Covers.
- Poster Presentation: Western Algebraic Geometry Symposium, University of Utah, Smoothing of multiple structures on embedded Enriques manifolds.
- Research talk: MAGGC, University of Illinois at Chicago, Deformations of Quadruple Galois Canonical Covers.

- I am teaching Math 127 (Calculus III) this semester. (Fall 2020)