My name is Dennis Borisov. I am a Postdoc at the Mathematical Institute, University of Göttingen, Germany. Dennis dot Borisov at gmail dot comemail: Research InterestsCurrently 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- "Quasi-coherent sheaves in differential geometry", (2017) preprint, joint work with Kobi Kremnizer
- "Beyond perturbation 1: de Rham spaces", (2017) preprint, joint work with Kobi Kremnizer
- "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
- "Derived manifolds and d-manifolds", (2012), preprint.
- "Simplicial approach to derived differential manifolds", (2011), preprint - joint work with Justin Noel.
- "Topological characterization of various types of rings of smooth functions", (2011), Comm. in Analysis and Geometry Vol. 23, No. 2 (2015).
- "The club of simplicial sets", (2010), preprint.
- "What is the higher-dimensional infinitesimal groupoid of a manifold?'' (2009), Journal of the Australian Mathematical Society 90 (2011), 155-170.
- "Higher dimensional operads'', (2009), preprint.
- "Generalized operads and their inner cohomomorphisms'' - Progress in
Mathematics, Vol. 265, 247-308, (2007) Birkhauser - joint paper
with Yu.I.Manin.
- "Homotopy Gerstenhaber structure on deformation complex of a morphism'' - Journal of Pure and Applied Algebra, 210 (2007), 751-770.
- "Formal deformations of morphisms of associative algebras'' - International Mathematics Research Notices (2005), No. 41.
- "Calabi-Yau versus Landau-Ginzburg'' - (2002) Master thesis at university of Bonn, Germany.
Employment2014-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 FellowshipsJune 2007 Best Thesis Award (shared), Department of Mathematics, Northwestern University 2003-2006 Summer Research fellowship, Department of Mathematics, Northwestern University Teaching Experience2007-2010 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.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 |