About

Vladimir Baranovsky is a faculty professor at UCI Mathematics, with a research area focused on Algebra and Number Theory. His contact email is vbaranov@math.uci.edu, and he is associated with the Department of Mathematics at the University of California, Irvine. Further details about his background, specific research contributions, or academic history are not provided on the page.

Research topics

• Computer Science
• Mathematics
• Pure mathematics
• Mathematical analysis
• Political Science
• Geometry

Selected publications

• Chern classes of quantizable coisotropic bundles

  Journal of Noncommutative Geometry · 2023-12-23

  articleOpen access1st authorCorresponding

  Let M be a smooth algebraic variety of dimension 2(p+q) with an algebraic symplectic form and a compatible deformation quantization of the structure sheaf. Consider a smooth coisotropic subvariety Y of codimension q and a vector bundle E on Y . We show that if the pushforward of E admits a deformation quantization (as a module), then its “trace density” characteristic class lifts to a cohomology group associated to the null foliation of Y . Moreover, it can only be nonzero in degrees 2q,\dotsc,2(p+q) . For Lagrangian Y , this reduces to a single degree 2q . Similar results hold in the holomorphic category.

  PublisherOA PDFDOI

• Zeta functions of projective hypersurfaces with ordinary double points

  European Journal of Mathematics · 2022-04-28

  article1st authorCorresponding
  PublisherDOI

• Representation Theory and Algebraic Geometry

  Trends in mathematics · 2022 · 2 citations

  1st authorCorresponding
  • Computer Science
  • Mathematics
  • Geometry
  PublisherDOI

• Obstructions of extension of vector bundles

  arXiv (Cornell University) · 2022

  1st authorCorresponding
  • Computer Science
  • Mathematics
  • Pure mathematics

  In the holomorphic or algebraic setting we consider a vector bundle E on a smooth subvariety X in a smooth variety Y over a field of characteristic zero. Assuming E extends to the l-th neighborhood of X in Y, we study cohomological obstructions to extending it further to the k-th neighborhood, for k > l.

  PublisherOA PDFDOI

• Chern classes of quantizable coisotropic bundles

  arXiv (Cornell University) · 2021-04-01

  preprintOpen access1st authorCorresponding

  Let $M$ be a smooth algebraic variety of dimension $2(p+q)$ with an algebraic symplectic form and a compatible deformation quantization $\mathcal{O}_h$ of the structure sheaf. Consider a smooth coisotropic subvariety $j: Y \to M$ of codimension $q$ and a vector bundle $E$ on $Y$. We show that if $j_* E$ admits a deformation quantization (as a module) then its characteristic class $\widehat{A}(M) exp(-c(\mathcal{O}_h)) ch(j_* E)$ lifts to a cohomology group associated to the null foliation of $Y$. Moreover, it can only be nonzero in degrees $2q, \ldots, 2(p+q)$. For Lagrangian $Y$ this reduces to a single degree $2q$. Similar results hold in the holomorphic category. This is a companion paper of a joint work with Victor Ginzburg on general quantizable sheaves.

  PublisherOA PDFDOI

• Curved L-infinity algebras and lifts of torsors

  arXiv (Cornell University) · 2021

  1st authorCorresponding
  • Computer Science
  • Pure mathematics
  • Mathematics

  Consider an extension of finite dimensional nilpotent Lie algebras $0 \to \mathfrak{h} \to \tilde{\mathfrak{g}} \to \mathfrak{g} \to 0$ (over a field $k$ of characteristic zero) corresponding to an extension of unipotent algebraic groups $1 \to H \to \tilde{G} \to G \to 1$. For a $G$-torsor $P$ on an algebraic variety $X$ over $k$, we study the problem of lifting $P$ to $\widetilde{G}$-torsor $\widetilde{P}$. Fixing a trivialization of $P$ on open subsets of an affine cover, we give the Cech complex of $\mathfrak{h}$-valued functions the structure of a curved $L_\infty$-algebra and define a curved version of the Deligne-Getzler groupoid. We show that this groupoid is isomorphic the groupoid of cocycle level $\tilde{G}$-lifts of $P$.

  PublisherOA PDFDOI

• Zeta functions of projective hypersurfaces with ordinary double points

  arXiv (Cornell University) · 2021-09-29

  preprintOpen access1st authorCorresponding

  We extend the approach Abbott, Kedlaya and Roe to computation of the zeta function of a projective hypersurface with $τ$ isolated ordinary double points over a finite field $\mathbb{F}_q$ given by the reduction of a homogeneous polynomial $f \in \mathbb{Z}[x_0, \ldots, x_n]$, under the assumption of equisingularity over $\mathbb{Z}_q$. The algorithm is based on the results of Dimca and Saito (over the field $\mathbb{C}$ of complex numbers) on the pole order spectral sequence in the case of ordinary double points. We give some examples of explicit computations for surfaces in $\mathbb{P}^3$.

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• A New International Order: Overcoming or Transforming the Existing One

  Social Sciences · 2019-06-30 · 2 citations

  article1st authorCorresponding
  PublisherDOI

• Russia and the World: 2020. Annual Forecast: Economy and Foreign Policy

  Primakov National Research Institute of World Economy and International Relations, Russian Academy of Sciences (IMEMO), 23, Profsoyuznaya Str., Moscow, 117997, Russian Federation eBooks · 2019-01-01 · 4 citations

  bookOpen access1st authorCorresponding

  НАЦИОНАЛЬНЫЙ ИССЛЕДОВАТЕЛЬСКИЙ ИНСТИТУТ МИРОВОЙ ЭКОНОМИКИ И МЕЖДУНАРОДНЫХ ОТНОШЕНИЙ имени

  PublisherOA PDFDOI

• Quantization of vector bundles on Lagrangian subvarieties

  arXiv (Cornell University) · 2017-01-06 · 1 citations

  preprintOpen access1st authorCorresponding

  We consider a smooth Lagrangian subvariety Y in a smooth algebraic variety X with an algebraic symplectic from. For a vector bundle E on Y and a choice Oh of deformation quantization of the structure sheaf of X, we establish when E admits a deformation quantization to a module over Oh. If the necessary conditions hold, we describe the set of equivalence classes of such quantizations.

  PublisherOA PDFDOI

Frequent coauthors

• Victor Ginzburg

  15 shared

• Jeremy Pecharich

  Pomona College

  7 shared

• Radmila Sazdanović

  3 shared

• Alexander Kuznetsov

  3 shared

• D. Kaledin

  3 shared

• Scott Stetson

  2 shared

• Tihomir Petrov

  California State University System

  2 shared

• Sam Evens

  2 shared

Labs

• Vladimir Baranovsky LabPI

Education

• Ph.D., Mathematics

  University of California, Irvine

  1990

• M.S., Mathematics

  University of California, Irvine

  1986

• B.S., Mathematics

  University of California, Irvine

  1984