Boris Tsygan's Homepage

Northwestern Noncommutative Geometry Seminar

Schedule

• May 13, 2020. Time: 3:15 to 4:30. Speaker: Ben Antieau (UIC). Title: Hochschild homology in positive characteristic.
   
• May 20, 2020. Time: 3:15 to 4:30 pm. Speaker: Ben Antieau, II. Title: Hochschild homology in positive characteristic.
   
• May 27, 2020. Time: 3:00 to 4:30 pm. Speaker: Ezra Getzler (Northwestern). Title: The infinity-groupoid of an L-infinity algebra in the cubical formalism.
   

Abstract

In this series of talks, I will discuss work from three joint projects, with Vezzosi, with Bragg, and with Bhatt and Mathew, on Hochschild homology in characteristic p. Together these give a sense of when the Hochschild-Kostant-Rosenberg theorem is true in low dimension and what counterexamples in high dimensions. Along the way, we will also touch on the de Rham filtration on periodic cyclic homology as well as the filtration arising from the t-structure on cyclotomic structure, which is joint work with Nikolaus.

Videos

• May 13. Ben Antieau.
  https://northwestern.zoom.us/rec/share/xvApMqH63UxJTonLxh7yQKsvII76aaa80CMY-vQKmR2u811QkEh8HJLT4kBsQgph?startTime=1589401045000
   
  
• May 20. Ben Antieau.
  https://northwestern.zoom.us/rec/share/tMZeF-r3_FxOQIGTzVDiZoszHt6iX6a82yAf-vILzkupReKlAhITZRWnsoenib4r?startTime=1590005802000
   
  

Book in progress

• Cycic homology, with Ryszard Nest. Part1.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

Teaching

• Fall 2018: MATH 336 (Number theory); MATH 202 (Finite Mathematics).
• Spring 2019: MATH 308 (Graph Theory); MATH 202 (Finite Mathematics).

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