Christopher Dodd

About

Christopher Stephen Dodd is an Assistant Professor in the Department of Mathematics at the University of Illinois. His research is in algebraic geometry and geometric representation theory, with a recent focus on positive characteristic and p-adic techniques. He earned his PhD from MIT in 2011. His scholarly work includes contributions to the understanding of Lagrangian subvarieties, D-modules, and categorical actions in symplectic and algebraic varieties. Dodd has published multiple peer-reviewed articles in reputable mathematical journals, advancing the field through his investigations into monodromy divisors, skeleta, Koszul duality, and the structure of W-algebras.

Research topics

• Medicine
• Surgery
• Internal medicine
• Dentistry
• Orthodontics

Selected publications

• Associated graded of Hodge modules and categorical $${\mathfrak {sl}}_2$$ actions

  Selecta Mathematica · 2021-04-09 · 1 citations

  article
  PublisherDOI

• Lagrangian Skeleta and Koszul Duality on Bionic Symplectic Varieties

  arXiv (Cornell University) · 2024-07-18

  preprintOpen access

  We consider the category of modules over sheaves of Deformation-Quantization (DQ) algebras on bionic symplectic varieties. These spaces are equipped with both an elliptic $\mathbb{G}_m$-action and a Hamiltonian $\mathbb{G}_m$-action, with finitely many fixed points. On these spaces one can consider geometric category $\mathcal{O}$: the category of (holonomic) modules supported on the Lagrangian attracting set of the Hamiltonian action. We show that there exists a local generator in geometric cat…

  PublisherOA PDFDOI

• Witt Differential Operators

  arXiv (Cornell University) · 2023-08-07

  preprintOpen access1st authorCorresponding

  For a smooth scheme $X$ over a perfect field $k$ of positive characteristic, we define (for each $m\in\mathbb{Z}$) a sheaf of rings $\mathcal{\widehat{D}}_{W(X)}^{(m)}$ of differential operators (of level $m$) over the Witt vectors of $X$. If $\mathfrak{X}$ is a lift of $X$ to a smooth formal scheme over $W(k)$, then for $m\geq0$ modules over $\mathcal{\widehat{D}}_{W(X)}^{(m)}$ are closely related to modules over Berthelot's ring $\widehat{\mathcal{D}}_{\mathfrak{X}}^{(m)}$ of differential oper…

  PublisherOA PDFDOI

Frequent coauthors

• David W. Murray

  University of Oxford

  169 shared

• Hemant Pandit

  NIHR Leeds Musculoskeletal Biomedical Research Unit

  132 shared

• C. Jenkins

  Nuffield Orthopaedic Centre

  78 shared

• Stephen Mellon

  University of Oxford

  51 shared

• H.S. Gill

  University of Bath

  48 shared

• David Beard

  46 shared

• Thomas W. Hamilton

  35 shared

• Andrew Price

  Nuffield Orthopaedic Centre

  32 shared

Similar researchers at University of Illinois Urbana-Champaign

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• William Yun Chenh-40
• Yuliy Baryshnikovh-26