My name is Dennis Borisov. I am an assistant professor of mathematics (tenure-track) at the University of Windsor, Canada

email:          Dennis dot Borisov at uwindsor dot ca
                   

Research Interests

Together with Kobi Kremnizer (Oxford, UK), we are constructing chiral algebras using Beilinson-Drinfeld Grassmannians in differential geometry. Our approach is based on the infinitesimal theory in smooth geometry, that we have recently discovered ("Beyond perturbation 1: de Rham spaces"). It allows us to systematically go beyond perturbation, and in particular to construct line bundles on affine Grassmannians having the factorization property ("Beyond perturbation 2: asymptotics and Beilinson-Drinfeld Grassmannians in differential geometry"). To transport these line bundles to the Ran space we have developed the theory of "Quasi-coherent sheaves in differential geometry".

Previously I was working with D.Joyce, constructing moduli of Spin(7) instantons using shifted sympectic forms on moduli spaces of sheaves on Calabi-Yau four-folds. I have revisited this topic recently in joint works with Ludmil Katzarkov, Artan Sheshmani and Shing-Tung Yau.

Mathematical works

Papers accepted for publication:
  1. "Beyond perturbation 1: de Rham spaces" - joint work with Kobi Kremnizer. Journal of Geometry and Physics 124 (2018).
  2. "Virtual fundamental classes for moduli spaces of sheaves of Calabi-Yau four-folds" - joint work with Dominic Joyce. Geometry and Topology 21 (2017).
  3. "Topological characterization of various types of rings of smooth functions" Comm. in Analysis and Geometry Vol. 23, No. 2 (2015).
  4. "What is the higher-dimensional infinitesimal groupoid of a manifold?'' Journal of the Australian Mathematical Society 90 (2011).
  5. "Generalized operads and their inner cohomomorphisms'' - joint work with Yuri I. Manin. Progress inMathematics, Vol. 265 (2007).
  6. "Homotopy Gerstenhaber structure on deformation complex of a morphism''  Journal of Pure and Applied Algebra 210 (2007).
  7. "Formal deformations of morphisms of associative algebras''  International Mathematics Research Notices No. 41 (2005).

Preprints

  1. "Global shifted potentials for moduli spaces of sheaves on CY4" - joint work with Artan Seshmani and Shing-Tung Yau
  2. "Shifted symplectic structures on derived Quot-stacks" - joint work with Ludmil Katzarkov and Artan Sheshmani
  3. "Beyond perturbation 2: asymptotics and Beilinson-Drinfeld Grassmannians in differential geometry" - joint work with Kobi Kremnizer
  4. "Quasi-coherent sheaves in differential geometry" - joint work with Kobi Kremnizer (2017).
  5. "Derived manifolds and d-manifolds" (2012)
  6. "Simplicial approach to derived differential manifolds" - joint work with Justin Noel (2011).
  7. "The club of simplicial sets" (2010).
  8. "Higher dimensional operads'' (2009).
  9. "Calabi-Yau versus Landau-Ginzburg'' - Master thesis at university of Bonn, Germany (2002).

Employment

Currenlty               Assistant professor (tenure track) at the Department of Mathematics and Statistics, University of Windsor, Canada.
2018-2019            Joint appointment at Harvard (CMSA), USA and University of Aarhus, Denmark.
2014-2018            Postdoc at the Mathematical Institute, University of Göttingen, Germany.
2012-2014            Postdoctoral Research Assistant, Mathematical Institute, University of Oxford, UK.
2010-2012            Postdoctoral Research Fellow, Max-Planck Institute for Mathematics, Bonn, Germany.  
2007-2010            Gibbs Assistant Professor, Department of Mathematics, Yale University, USA.

Awards and Fellowships

June 2007         Best Thesis Award (shared), Department of Mathematics, Northwestern University
2003-2006         Summer Research fellowship, Department of Mathematics, Northwestern University

Teaching Experience

2014-2018         Assistant at University of Göttingen, Germany
2007-2010         Assistant Professor, Department of Mathematics, Yale University
2006-2007         Lecturer in Mathematics at Northwestern University
2002-2006         Teaching assistant in Mathematics at Northwestern University

Courses taught:

Summer         2018         Analytic geometry and linear algebra II, University of Göttingen.
Winter     2017-2018       Analytic geometry and linear algebra I, University of Göttingen.
Summer         2017         Mathematics for physicists II, University of Göttingen.
Winter     2016-2017       Discrete Mathematics, University of Göttingen.
Summer         2015         Infinitesimal calculus II, University of Göttingen.
Winter     2014-2015       Discrete Mathematics, University of Göttingen.
Spring            2010         Quantum cohomology, Graduate School, Yale University.
Spring            2010         Modern Algebra II, Graduate School, Yale University.
Spring            2010         Number theory, Yale University.
Summer         2009         Multivariable Calculus, Summer School, Yale University. Syllabus.
Spring            2009         Operads and homotopical algebra, Graduate School, Yale University.
Fall                2008         Algebraic geometry, Graduate School, Yale University. Syllabus.
Fall                2008         Multivariable Calculus, Yale University.
Summer         2008         Multivariable Calculus, Summer School, Yale University. Syllabus.
Spring            2008         Algebraic geometry, Graduate School, Yale University.
Fall                2007         Multivariable Calculus, Yale University.
Fall                2007         Discrete Mathematics, Yale University. Syllabus.
Spring            2007         Abstract Algebra, School of Continuing Studies, Northwestern University. Syllabus.
Spring            2007         Introduction to Mathematics, Northwestern University.
Winter            2007         Game theory, School of Continuing Studies, Northwestern University. Syllabus.

Education

2002-2007         Northwestern University, USA; Degree earned: Ph.D. in Mathematics, June 2007 (advisor: Yu.I.Manin)
1998-2002         University of Bonn, Germany; Degree earned: Diplom Mathematiker (M.Sc.), April 2002