Boris Tsygan's Homepage

Teaching

• Algebraic K-theory
  • 0-Summary.pdf
  • 1-Symbols.pdf
  • 2-Dennis-Stein Symbols.pdf
  • 3-DS_Symbols 2.pdf
  • 4-Nerves.pdf
  • 5-Plus Construction.pdf
  • 6-Group Completion.pdf
  • 7-Q construction.pdf
  • 8-Plus, Q, And Group Comp.pdf
  • 9-Volodin K.pdf
  • 10-Waldhausen K.pdf
  • 11-Nonlin HC 2.pdf
  • 12-Nonlinear HC.pdf

Courses

• Lectures on D-modules, Fall 2022
• Mini-course in San Juan, Puerto Rico (June 2022) - Lectures in San Juan
• Shifted Poisson geometry and Calabi-Yau categories (Spring 2022) - Algebra 22_1, Algebra_22_2, Algebra_22_3
• Differential calculus in positive characteristic. Fall Semester 2020
• Spring 2019: MATH 308 (Graph Theory); MATH 202 (Finite Mathematics)
• Fall 2018: MATH 336 (Number theory); MATH 202 (Finite Mathematics)
• Lectures in Kyiv (May 2017, in Ukrainian) - Kyiv Lectures 2017_1, Kyiv Lectures 2017_2

Book in progress

• Cycic homology, with Ryszard Nest: Part1.pdf
• A review on noncommutative crystalline cohomology: Oberwolfachtext.pdf
• On noncommutative differential forms: NC_FORMS_AMS.pdf

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

Some mathematical institutions

Links

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
Russian books
Some links related to Israel