Boris Tsygan's Homepage
Professor Of Mathematics
B4 Lunt Hall
2033 North Sheridan Avenue, Evanston IL 60208
Book in progress
Some Preprints and Publications
- Formality theorem for gerbes, Adv. Math. 273 (2015), 215–241, with P. Bressler, A. Gorokhovsky and R. Nest, arXiv:1308.3951
- Deligne groupoid revisited. Theory Appl. Categ. 30 (2015), 1001–1017, with P. Bressler, A. Gorokhovsky and R. Nest, arXiv:1211.6603
- On quasi-classical limits of DQ algebroids, with P. Bressler, A. Gorokhovsky and R. Nest, Compositio Matematica, v. 153, 1, p. 41-67 (2017), arXiv:1510.01361
- Algebraic and Analytic Microlocal Analysis, with M. Hitrik, D. Tamarkin,S. Zelditch (editors), Springer Proceedings in Mathematics and Statistics vol. 269 (2018), arXiv:1512.02747v2
- Microlocal category associated to a symplectic manifold, in: Algebraic and Analytic Microlocal Analysis, p. 225-341.
- 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, Int. Math. Res. Not. IMRN 2011, no. 20, 4666–4746, 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, 103-136 arXiv: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: J. differential geometry 59 (2001), 269-300 math.DG/0004022
- Riemann-Roch Theorems via deformation quantization I, with P. Bressler and R. Nest math.AG/9904121, Adv. Math. vol. 167, 1 (2002), Pages 1-25.
- Riemann-Roch Theorems via deformation quantization II, with Paul Bressler and R. Nest, math.KT/0002115, Adv. Math. vol. 167, 1 (2002), Pages 26-73.
- 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, Asian Journal of Mathematics, vol. 5, 599 (2001).
- 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
- Fall 2018: MATH 336 (Number theory); MATH 202 (Finite Mathematics).
- Spring 2019: MATH 308 (Graph Theory); MATH 202 (Finite Mathematics).
Conference "Modern Trends in Non-Commutative Geometry"
Mini-conference on topological Hochschild homology - Notes
Spring School on Algebraic Microlocal Analysis at Northwestern
Northwestern Department of Mathematics
Geometric Langlands Seminar, University of Chicago
Geometric Functional Analysis at Penn State
Some links related to Israel