My name is Dennis Borisov. I am an assistant professor of mathematics (tenure-track) at the University of Windsor, Canada Dennis dot Borisov at uwindsor dot caemail:Research InterestsTogether 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 worksPapers accepted for publication: - "Beyond perturbation 1: de Rham spaces" - joint work with Kobi Kremnizer.
*Journal of Geometry and Physics*124 (2018). - "Virtual fundamental classes for moduli spaces of sheaves of Calabi-Yau four-folds" - joint work with Dominic Joyce.
*Geometry and Topology*21 (2017). - "Topological characterization of various types of rings of smooth functions"
*Comm. in Analysis and Geometry*Vol. 23, No. 2 (2015). - "What is the higher-dimensional infinitesimal groupoid of a manifold?''
*Journal of the Australian Mathematical Society*90 (2011). - "Generalized operads and their inner cohomomorphisms'' - joint work with Yuri I. Manin. Progress inMathematics, Vol. 265 (2007).
- "Homotopy Gerstenhaber structure on deformation complex of a morphism''
*Journal of Pure and Applied Algebra*210 (2007). - "Formal deformations of morphisms of associative algebras''
*International Mathematics Research Notices*No. 41 (2005).
- "Global shifted potentials for moduli spaces of sheaves on CY4" - joint work with Artan Seshmani and Shing-Tung Yau
- "Shifted symplectic structures on derived Quot-stacks" - joint work with Ludmil Katzarkov and Artan Sheshmani
- "Beyond perturbation 2: asymptotics and Beilinson-Drinfeld Grassmannians in differential geometry" - joint work with Kobi Kremnizer
- "Quasi-coherent sheaves in differential geometry" - joint work with Kobi Kremnizer (2017).
- "Derived manifolds and d-manifolds" (2012)
- "Simplicial approach to derived differential manifolds" - joint work with Justin Noel (2011).
- "The club of simplicial sets" (2010).
- "Higher dimensional operads'' (2009).
- "Calabi-Yau versus Landau-Ginzburg'' - Master thesis at university of Bonn, Germany (2002).
EmploymentCurrenlty Assistant professor (tenure track) at the Department of Mathematics and Statistics, University of Windsor, Canada. 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 FellowshipsJune 2007 Best Thesis Award (shared), Department of Mathematics, Northwestern University 2003-2006 Summer Research fellowship, Department of Mathematics, Northwestern University Teaching Experience2014-2018 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.Education2002-2007 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 |