אורן בן בסט Oren Ben-Bassat 松
HMI Spring Lecture Series 2021 (March/ April 2021): Derived Bornological and Analytic Geometry Notes of my first talk. YouTube video of my first talk. Notes of my second talk. YouTube video of my second talk. Notes of my third talk. YouTube video of my third talk. Errata
Together with Kremnizer I initiated Banach algebraic geometry, a new area of mathematics combining commutative algebra, algebraic geometry, and functional analysis in a new way. This is an active new field of research. Mingchen Xia has recently used our work in his article On Liu morphisms in non-archimedean geometry published in the Israel Journal of Mathematics. Our work was also used by Arun Soor in Quasicoherent sheaves for dagger analytic geometry .
Together with Joyce and his collaborators I found new properties of shifted symplectic derived stacks. These included the existence of a perverse sheaf on such a stack in certain cases, this sheaf measures the underlying topology. With Lino Amorim I studied multiple Lagrangian intersections which were recently used in the Oxford thesis of Jay Swar. These were also used in the article Shifted symplectic reduction of derived critical loci by Anel and Calaque published in Advances in Theoretical and Mathematical Physics.
My articles from journal websites or from the arxiv if not yet published:
(25) Moduli stacks of Higgs bundles on stable curves, joint with Sourav Das and Tony Pantev (2023).
(24) Blow-ups and normal bundles in connective and nonconnective derived geometries, joint with Jeroen Hekking (2023).
(23) Analytification, localization and homotopy epimorphisms, joint with Devarshi Mukherjee, Bulletin des Sciences Mathématiques 176, (2022).
(22) Fréchet Modules and Descent, joint with Kobi Kremnizer, Theory and Applications of Categories 39, (2023).
(21) Analytic geometry over F_1 and the Fargues-Fontaine curve, joint with Federico Bambozzi and Kobi Kremnizer, Advances in Mathematics 356, (2019).
(20) Bounded linear endomorphisms of rigid analytic functions, joint with Konstantin Ardakov, Proceedings of the London Mathematical Society, Vol. 117, Issue 5 (2018).
(19) Perversely categorified Lagrangian correspondences, joint with Lino Amorim. Advances in Theoretical and Mathematical Physics, Vol. 21, No. 2 (2017).
(18) Stein domains in Banach algebraic geometry, joint with Federico Bambozzi and Kobi Kremnizer. Journal of Functional Analysis, Volume 274, Issue 7 (2018).
(17) Non-Archimedean analytic geometry as relative algebraic geometry, joint with Kobi Kremnizer, Annales de la faculté des sciences de Toulouse Sér. 6, 26, 1 (2017).
(16) Dagger geometry as Banach algebraic geometry, joint with Federico Bambozzi, Journal of Number Theory, 162 (2016).
(15) A ‘Darboux theorem’ for shifted symplectic structures on derived Artin stacks, with applications, joint with Chris Brav, Vittoria Bussi, and Dominic Joyce, Geometry & Topology 19, 3 (2015).
(14) Multiple derived Lagrangian intersections, Contemporary Mathematics 643 (2015).
(13) Moduli Stacks of Bundles on Local Surfaces, joint with Elizabeth Gasparim, Springer UMI (2014).
(12) Milnor descent for cohesive dg-categories, joint with Jonathan Block, Journal of K-theory 12, 3 (2013).
(11) Berkovich Spaces and Tubular Descent, joint with Michael Temkin, Advances in Mathematics 234 (2012).
(10) Equivariant Gerbes on Complex Tori, Journal of Geometry and Physics 64 (2012).
(9) Gerbes and the holomorphic Brauer group of complex tori, Journal of Noncommutative Geometry 6, 3 (2012).
(8) Meromorphic Line Bundles and Holomorphic Gerbes, joint with Edoardo Ballico, Mathematical Research Letters 18 (2011).
(7) Cohomology Groups of Deformations of Line Bundles on Complex Tori, joint with Noam Solomon, Israel Journal of Mathematics 186 (2011).
(6) Twisting Derived Equivalences, Transactions of the American Mathematical Society 361 (2009).
(5) Non-commutative tori and Fourier-Mukai duality, joint with Jonathan Block and Tony Pantev, Compositio Mathematica 143 (2007).
(4) Mirror Symmetry and generalized complex manifolds Part II, Journal of Geometry and Physics 56, 7 (2006).
(3) Mirror Symmetry and generalized complex manifolds Part I, Journal of Geometry and Physics 56, 4 (2006).
(2) Submanifolds of generalized complex manifolds, joint with Mitya Boyarchenko, Journal of Symplectic Geometry, 2, 3 (2004).
(1) What is Not in the Domain of the Laplacian on Sierpinski Gasket Type Fractals, joint with R. S. Strichartz and A. Teplyaev, Journal of Functional Analysis 166 (1999).
I taught a course on Differential Graded Categories, at Oxford during Trinity Term 2013. Classes taught at the University of Haifa include Algebraic Groups, Modern Algebra B, Introduction to Number Theory, Functional Analysis, Analytic Geometry, Modern Algebra A, Lie Algebras, Linear Algebra A, Commutative Algebra, Topology and Knot Theory.
My research group maintains a blog called Derived Algebraic and Analytic Geometry.
2007-2008 NSF postdoc at Columbia University, New York
2008-2009 postdoc at The Hebrew University Of Jerusalem
2010-2014 tenure track lecturer at the University of Haifa
2012-2015 visiting faculty at the University of Oxford, supported by the European Commission as a Marie Curie fellow
2014-present senior lecturer with tenure at the University of Haifa
A slide presentation by Dominic Joyce summarizing his recent and current work and that of his group.
Some recent conferences where I gave a talk: Deformation Quantization of Shifted Poisson Structures, Derived Algebraic Geometry, with a focus on derived symplectic techniques, Mini-workshop on refined invariants, DG-enhancements and higher category methods, CATS 4, VBAC 2012, Hodge Theoretic Reflections on the String Landscape, Deformation Week, Mini-workshop: Non-archimedean analytic geometry and tropical geometry, Swansea, Higher Sturctures in Algebraic Analysis.
My mathematical genealogy (provided by mathematical uncle Jimmy Dillies).
My talk at the Perimeter Institute.
please do **not** spell my name any of the following ways: Oren Ben-Basset, Oren Ben Basset, Oren Ben Bassat, אורן בן-בסט