General and Broad Topics
- Qual syllabus: algebraic topology, Riemannian geometry, complex analysis #todo
- A bunch of undergrad topics: https://www.quantstart.com/articles/How-to-Learn-Advanced-Mathematics-Without-Heading-to-University-Part-3/
Algebraic Geometry
Learning Resources Algebraic Geometry
Floer and Symplectic
Learning Resources Symplectic Topology
Number Theory
Learning Resources Number Theory
Algebraic Topology
Learning Resources Algebraic Topology
Representation Theory
Categorification
Note from Arik: If you want to learn more about the Hilbert schemes and the GNR conjectures you might find this video interesting as a starting point: https://www.newton.ac.uk/seminar/20170628100011001. There seems to be some support in the department to have Negut speak in our algebra seminar in the fall (most likely via Zoom) and give an update on the status of these conjectures. As far as I am informed they are still open. But some progress has been made since 2017 (the year when this video was recorded).
One of the beautiful things about these link homology theories is that they have so many different (equivalent) constructions. For Khovanov homology (categorification of the Jones polynomial) I want to point out the following: Bar-Natan (TQFTs, cobordism pictures) https://arxiv.org/abs/math/0410495 Seidel–Smith (symplectic geometry) https://arxiv.org/abs/math/0405089 Stroppel (Lie theory, category O) http://ems.math.uni-bonn.de/people/stroppel/TemperleyLieb.pdf Cautis–Kamnitzer (derived categories of coherent sheaves, geometric Satake) https://arxiv.org/abs/math/0701194
You can pick the one closest to your field and learn some more by looking at these papers if you want. The triply graded link homology as discussed in the course can be found here https://arxiv.org/abs/math/0510265. An equivalent version using matrix factorizations can be found here https://arxiv.org/abs/math/0505056. Recall that the Jones polynomial is obtained as a certain specialization of the HOMFLY-PT polynomial. This process of “specialization” is categorified by a spectral sequence from the triply graded homology (HOMFLY-PT homology) to Khovanov homology https://arxiv.org/abs/math/0607544.
Lie Theory
Categorical Rep Theory
- MSRI Summer school on Soergel Bimodules
- CMSA conference on relations to algebraic geometry and mathematical physics
- Categorification Master Class
Representation Stability
Prism-y p-adic-y Hodge-Theory-y Stuff
- Seminar on crystalline and prismatic cohomology
- Seminar on p-adic modular forms
- Seminar on p-adic Hodge theory
- Noncommutative Hodge-to-de Rham degeneration
- https://www.youtube.com/watch?v=euSBxp7qsA4&list=PLCe-H2N8-ny6d-EHaxrqy_RMwQ569C3Zx&index=4
- Kiran Kedlaya’s course: https://kskedlaya.org/math206a-spr21/
Geometric Topology
Spring 2021, Math 276. Knot Theory (Agol)
Fall 2020, Math 277. Poisson Geometry (Reshetikhin)
Fall 2020, Math 277. Ricci Flow (Bamler)
Spring 2020, Math 277. Categorical Structures in Symplectic Geometry (Wehrheim)
Spring 2018, Math 277. Complex/Kaehler Geometry (Sun)
Fall 2017, Math 276. Knots and Links (Agol)
Spring 2017, Math 277. Ricci curvature (Bamler)
Spring 2016, Math 276. Factorization Algebras (Teichner)
Spring 2016, Math 277. Applied Holomorphic Curve Theory (Hutchings)
Fall 2015, Math 270. Gauge Theory (Wehrheim)
Spring 2015, Math 276. Gauge Field Theory (Teichner)
Spring 2015, Math 277. Ricci Flow (Lott)
Spring 2014, Math 276. Functorial Field Theories and Ring Spectra (Teichner)
Spring 2014, Math 276. Regularization of Moduli Spaces (Wehrheim)
Fall 2013, Math 278. Pseudoholomorphic Curves (Wehrheim)
Spring 2013, Math 277. The Quantum Riemann-Roch-Hirzebruch Theorem (Givental)
Fall 2012, Math 277. Contact Homology (Hutchings)
Spring 2012, Math 277. Kaehler Geometry (Lott)
Spring 2011, Math 270. The Blob Complex (Teichner)
Spring 2011, Math 276. The Index Theorem (Teichner)
Fall 2010, Math 276. Seiberg-Witten-Floer Theory (Hutchings)
Fall 2010, Math 277. Optimal Transport (Lott)
Spring 2010, Math 270. Perturbative Quantization (Teichner)
Spring 2010, Math 276. Three-Manifold Topology (Agol)
Fall 2009, Math 277. Mirror Symmetry (Auroux)
Fall 2009, Math 277. Exterior Differential Systems (Bryant)
Fall 2009, Math 277. Ricci Flow (Lott)
Spring 2009, Math 270. Topological Field Theory (Teichner)
Fall 2008, Math 276. Rational Homotopy Theory (Teleman)
Kirby Calculus
Functional Analysis
http://www.math.chalmers.se/Math/Grundutb/CTH/tma401/0304/handinsolutions.pdf