Microlocal Learning Seminar

This is the homepage for the USC Microlocal Learning Seminar in Spring 2025. The aim of this seminar is to study the basics of microlocal sheaf theory and its applications to contemporary research. This seminar will be held weekly at 3:30-4:30pm on Fridays at KAP 265. If you have any questions, please email Christopher Kuo at chrislpkuo(at)berkeley[dot]edu or Wenyuan Li at liwenyua(at)usc[dot]edu. Below is a tentative schedule of the seminar along with the references for each talk:

Schedule

• (01/31) Wenyuan Li, "Overview of microlocal sheaf theory and its applications".
• (02/07) Christopher Kuo, "Sheaves and the four-functor formalism".
  References: X. Jin, D. Treumann, Brane structure in microlocal sheaf theory, Section 2.2- 2.3; Volpe, The six operations in topology, Section 2.2, 3.1-3.3, 4, 5.1-5.3.
  Alternative reference: P. Scholze, Six-functor formalism, Section 2, 7.
• (02/14) Jishnu Bose, "The six-funtor formalism".
  References: X. Jin, D. Treumann, Brane structure in microlocal sheaf theory, Section 2.4- 2.5; Volpe, The six operations in topology, Section 6.1-6.2, 7.1-7.2.
  Alternative reference: P. Scholze, Six-functor formalism, Section 2, 7.
• (02/21) Boxi Hao, "Microsupport and non-characteristic deformation".
  Reference: X. Jin, D. Treumann, Brane structure in microlocal sheaf theory, Section 2.7.
  Alternative references: M. Robalo, P. Schapira, A lemma for microlocal sheaf theory in the ∞-categorical setting; S. Guillermou, C. Viterbo, The singular support of sheaves are γ-coisotropic, Section 3.
• (02/28) Christopher Kuo, "Estimation of microsupport".
  Reference: P. Schapira, A short review on microlocal sheaf theory, Section 2.2-2.3.
  Alternative reference: M. Kashiwara, P. Schapira, Sheaves on manifolds, Section 5.3-5.4.
• (03/07) Haosen Wu, "Sheaf quantization of Hamiltonian isotopies"
  Reference: S. Guillermou, M. Kashiwara, P. Schapira, Sheaf quantization of Hamiltonian isotopies and applications to non-displaceability problems, Section 2-3; C. Kuo, W. Li, Spherical adjunction and Serre functor from microlocalization, Section 3-4.
• (03/14) Siyang Liu, "Microsupports and constructible sheaves".
  Reference: S. Ganatra, J. Pardon, V. Shende, Microlocal Morse theory and wrapped Fukaya categories, Section 4.2-4.5.
  Alternative references: C. Kuo, Wrapped sheaves, Section 2.4-2.5; M. Kashiwara, P. Schapira, Sheaves on manifolds, Section 8.1-8.4.
• (03/21) Spring break.
• (03/28) Wenyuan Li, "Microsupports and constructible sheaves".
  Reference: P. Schapira, A short review on microlocal sheaf theory, Section 4.1-4.4, 5.1-5.3;
  C. Kuo, W. Li, Spherical adjunction and Serre functor from microlocalization, Section 2.2;
  R. Casals, W. Li, Positive microlocal holonomies are globally regular, Section 3.1-3.2.
• (04/04) Christopher Kuo, "Riemann-Hilbert correspondence".
  Reference: M. Kashiwara, P. Schapira, Sheaves on Manifolds, Section 11. M. Kashiwara, Riemann-Hilbert correspondence for holonomic systems.
  Further references: J-E. Björk, Analytic D-modules and applications; M. Kashiwara, D-modules and microlocal calculus;
  L. Côté, C. Kuo, D. Nadler, V. Shende, The microlocal Riemann-Hilbert correspondence for complex contact manifolds.
• (04/11) Siyang Liu, "The aborealization program".
  Reference: D. Nalder, Arboreal singularities, Section 2 & 4; D. Alvarez-Gavela, Y. Eliashberg, D. Nadler, Positive arborealization of polarized Weinstein manifolds.
  Further references: Y. Eliashberg, Weinstein manifolds revisited; D. Nadler, Non-characteristic expansion of Legendrian singularities;
  D. Alvarez-Gavela, Y. Eliashberg, D. Nadler, Geomorphology of Lagrangian ridges; D. Alvarez-Gavela, Y. Eliashberg, D. Nadler, Arboreal models and their stability.
• (04/18) Boxi Hao, "Coherent-constructible correspondence".
  B. Fang, M. Liu, D. Treumann, E. Zaslow, A categorification on Morelli's theorem. D. Truemann, Remarks on the non-equivariant coherent-constructible correspondence for toric varieties;
  P. Zhou, Twisted Polytope Sheaves and Coherent-Constructible Correspondence for Toric Varieties.
  Further references: T. Kuwagaki, Non-equivariant coherent-constructible correpondence for toric stacks; Q. Bai, Y. Hu, Toric mirror symmetry for homotopy theorists;
  V. Shende, Toric mirror symmetry revisited; B. Gammage, V. Shende, Mirror symmetry for very affine hypersurfaces.
• (04/25) Jishnu Bose, "C^0-symplectic geometry".
  Reference: T. Asano, Y. Ike, Persistence-like distance on Tamarkin's category and symplectic displacement energy; T. Asano, Y. Ike, Completeness of derived interleaving distances and sheaf quantization of non-smooth objects.
  Further references: S. Guillermou, Sheaves and symplectic geometry on cotangent bundles, Part 7; S. Guillermou, C. Viterbo, The singular support is γ-coisotropic.
• (05/02)