Nadler's GRT Seminar

2021–2022

“Think globally, act microlocally”

Topic: Sheaf theory and microlocal sheaf theory
Meeting time: Thursdays 12:30pm–2pm
Room: #939 Evans

Spring 2022 schedule

Microlocal perspective

Date Speaker Topic Notes
1/27 David Nadler Singular support I Notes
2/3 David Nadler Singular support II Notes
2/10 David Nadler Singular support III Notes
2/17 David Nadler Singular support IV Notes
2/24 David Nadler Microlocal sheaves Notes
3/3 David Nadler Examples of microlocal sheaves Notes
3/10 David Nadler More low-dimensional examples Notes
3/17 David Nadler Microlocal sheaves as an invariant Notes

Fall 2021 schedule

Date Speaker Topic Notes
8/31 David Nadler Organizational meeting / Sheaves on ℝ Notes
9/7 Dennis Chen Setup: Review of sheaf theory Notes
9/14 Dennis Chen Setup: dg categories, derived categories of sheaves, …
9/21 Dennis Chen & Peter Haine Setup continued Notes
9/28 Dennis Chen Setup continued
10/5 John Nolan Operations on sheaves: Grothendieck's six functors
10/12 John Nolan Operations on sheaves II
10/19 John Nolan Operations on sheaves III
10/26 David Nadler & John Nolan Operations on sheaves IV
11/2 John Nolan Operations on sheaves V
11/9 Mark Macerato Nearby and vanishing cycles I
11/16 Mark Macerato & David Nadler Nearby and vanishing cycles II
11/30 David Nadler Examples of nearby and vanishing cycles
12/7 Mark Macerato Nearby and vanishing cycles III

References

Microlocal sheaf theory

Key Reference
J X. Jin, Microlocal sheaf categories and the J-homomorphism, Preprint available at arXiv:2004.14270, Sep. 2020.
JT X. Jin and D. Treumann, Brane structures in microlocal sheaf theory, Preprint available at arXiv:1704.04291, April 2017.
KS M. Kashiwara and P. Schapira, Sheaves on manifolds, Grundlehren der Mathematischen Wissenschaften. Springer-Verlag, Berlin, 1994, vol. 292, pp. x+512, With a chapter in French by Christian Houzel, Corrected reprint of the 1990 original, ISBN: 3-540-51861-4.
NS D. Nadler and V. Shende, Sheaf quantization in Weinstein symplectic manifolds, Preprint available at arXiv:2007.10154, Feb. 2021.
S1 P. Schapira, A short review of microlocal sheaf theory, Preprint available at webusers.imj-prg.fr/~pierre.schapira/lectnotes/MuShv.pdf, Jan. 2016.
S2 P. Schapira, Microlocal analysis and beyond, Preprint available at arXiv:1701.08955, Jan. 2017.
Z J. Zhang, Quantitative Tamarkin category, Lecture notes available at arXiv:1807.09878, Jul. 2018.

Derived categories, dg categories, ∞-categories, etc.

Key Reference
C1 D. Clausen, Interlude on D(R), notes for a Course on algebraic de Rham cohomology. Available at sites.google.com/view/algebraicderham.
C2 D. Clausen, Interlude on sheaves with values in D(Z), notes for a Course on algebraic de Rham cohomology. Available at sites.google.com/view/algebraicderham.
K B. Keller, On differential graded categories, In: International Congress of Mathematicians. Vol. II. Eur. Math. Soc., Zürich, 2006, pp. 151–190. Available at arXiv:0601185.
MG A. Mazel-Gee, An invitation to higher algebra, Book project available at etale.site/teaching/w21/math-128-lecture-notes.pdf, 2021.
HTT J. Lurie, Higher topos theory, Annals of Mathematics Studies. Princeton, NJ: Princeton University Press, 2009, vol. 170, pp. xviii+925, ISBN: 978-0-691-14049-0; 0-691-14049-9.
HA J. Lurie, Higher algebra, Preprint available at math.ias.edu/~lurie/papers/HA.pdf, Sep. 2017.
SAG J. Lurie, Spectral algebraic geometry, Preprint available at math.ias.edu/~lurie/papers/SAG-rootfile.pdf, Feb. 2018.
T B. Toën, Lectures on dg-categories, In: Topics in algebraic and topological K-theory. Vol. 2008. Lecture Notes in Math. Springer, Berlin, 2011, pp. 243–302. DOI: 10.1007/978-3-642-15708-0. Available at perso.math.univ-toulouse.fr/btoen/files/2012/04/swisk.pdf
Y A. Yekutieli, Derived categories, Preprint available at arXiv:1610.09640, Apr. 2019.