My name is Dennis Borisov. I am a Postdoc at the Mathematical Institute, University of Göttingen, Germany.

email:          Dennis dot Borisov at gmail dot com
                   

Research Interests

Currently I am working in differential geometry, applying the techniques of algebraic geometry. More precisely, together with Kobi Kremnizer we are developing the theory infinitesimals, coherent sheaves (= complexes of sheaves of Banach modules), quasi-coherent sheaves (= sheaves of bornological modules), D-modules (= quasi-coherent sheaves on de Rham spaces) etc. in the setting of differential geometry using the rings of smooth functions as local models. Our goal is construction of interesting chiral algebras (= algebras in D-modules on Ran spaces) in differential geometry adapting the techniques from algebraic geometry (Beilinson-Drinfeld, Gaitsgory-Rozenblyum).

Mathematical works
  1. "Quasi-coherent sheaves in differential geometry", (2017) preprint, joint work with Kobi Kremnizer
  2. "Beyond perturbation 1: de Rham spaces", (2017) preprint, joint work with Kobi Kremnizer
  3. "Virtual fundamental classes for moduli spaces of sheaves of Calabi-Yau four-folds", (2015) - joint work with Dominic Joyce - Accepted for publication in Geometry and Topology
  4. "Derived manifolds and d-manifolds", (2012), preprint.
  5. "Simplicial approach to derived differential manifolds", (2011), preprint - joint work with Justin Noel.
  6. "Topological characterization of various types of rings of smooth functions", (2011), Comm. in Analysis and Geometry Vol. 23, No. 2 (2015).
  7. "The club of simplicial sets", (2010), preprint.
  8. "What is the higher-dimensional infinitesimal groupoid of a manifold?'' (2009), Journal of the Australian Mathematical Society 90 (2011), 155-170.
  9. "Higher dimensional operads'', (2009), preprint.
  10. "Generalized operads and their inner cohomomorphisms'' - Progress in Mathematics, Vol. 265, 247-308, (2007) Birkhauser - joint paper with Yu.I.Manin.
  11. "Homotopy Gerstenhaber structure on deformation complex of a morphism'' - Journal of Pure and Applied Algebra, 210 (2007), 751-770.
  12. "Formal deformations of morphisms of associative algebras'' - International Mathematics Research Notices (2005), No. 41.
  13. "Calabi-Yau versus Landau-Ginzburg'' - (2002) Master thesis at university of Bonn, Germany.

Employment

2014-present        Postdoc at the Mathematical Institute, University of Göttingen, Germany (currently on leave to MPIM in Bonn).
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

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:

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