Boris Tsygan's Homepage

Some Recent Preprints and Publications

• Oscilatory modules, Lett. Math. Phys. 88 (2009), no. 1-3, 343-369, arXiv:0905.0290
• Proof of Swiss Cheese Version of Deligne's Conjecture, with V. Dolgushev and D. Tamarkin, to appear in IMRN, arXiv:0904.2753,
• Noncommutative calculus and the Gauss-Manin connection, with V. Dolgushev and D. Tamarkin, Higher structures in geometry and physics, 139-158, Progr. Math., 287, Birkhäuser/Springer, New York, 2011 , arXiv:0902.2202
• Formality theorems for Hochschild complexes and their applications, with V. Dolgushev and D. Tamarkin, Lett. Math. Phys. 90 (2009), no. 1-3, 103-136arXiv:0901.0069
• Deformations of algebroid stacks, with P. Bressler, A. Gorokhovsky and R. Nest, Adv. Math. 226 (2011), no. 4, 3018–3087 arXiv:0810.0030
• Chern character for twisted complexes, with P. Bressler, A. Gorokhovsky and R. Nest, Geometry and dynamics of groups and spaces, 309–324, Progr. Math., 265, Birkhäuser, Basel, 2008, arXiv:0710.0643
• Riemann-Roch for real varieties, with P. Bressler, M. Kapranov, E. Vasserot, Riemann-Roch for real varieties. Algebra, arithmetic, and geometry: in honor of Yu. I. Manin. Vol. I, 125-164, Progr. Math., 269, Birkhäuser Boston, Inc., Boston, MA, 2009 arXiv:0612410
• Noncommutative differential calculus, homotopy BV algebras and formality conjectures, with D. Tamarkin math.KT/0002116, Metods of Functional Analysis and topology, 1, 2001
• Local formula for the index of a Fourier Integral Operator, with E. Leichtnam and R. Nest math.DG/0004022
• Riemann-Roch Theorems via deformation quantization I, with P. Bressler and R. Nest math.AG/9904121, to appear in Adv. Math.
• Riemann-Roch Theorems via deformation quantization II, with Paul Bressler and R. Nest, math.KT/0002115, , to appear in Adv. Math.
• Formality conjectures for chains, math.QA/9904132, AMS Translations, 194, 2,261-274
• Deformations of symplectic Lie algebroids, deformations of holomorphic symplectic structures, and index theorems, with R. Nest math.QA/9906020, to appear in Asian Mathematical Journal.
• Fukaya type categories for associative algebras, with R. Nest math.QA/9803140, Deformations and Quantizations, Ascona, 1996, Kluwer Publ. 1997
• On the cohomology ring of an algebra,with R. Nest math.QA/9803132, Advances in Geometry, Progress in Mathematics, 172, Birkhauser, 1997, 337-370

Teaching

• Winter, 2012:
• MATH 234-0, Multiple integration and vector calculus
• Spring, 2012:
• MATH 440-3, Geometry and topology
• Summer, 2012:
• Quantum mechanics, Northwestern undergraduate conference Quantization and Mathematics, June 18-30, 2012

Spring School on Algebraic Microlocal Analysis at Northwestern
Northwestern Department of Mathematics
Geometric Langlands Seminar, University of Chicago
Geometric Functional Analysis at Penn State
Russian books
Some links related to Israel