We meet every Thursday at 3pm. The topic for Spring ’22 is “Representation theory, analysis and geometry around cluster varieties”.

Talks:
1) Apr 14: Gus Schrader – Introduction
Notes: PDF
References:
Gross-Hacking-Keel: https://arxiv.org/abs/1309.2573
Gross-Hacking-Keel-Kontsevich: https://arxiv.org/abs/1411.1394
Gammage-Le (mentioned by Eric): https://arxiv.org/abs/2103.12232
Hacking-Keating: https://arxiv.org/abs/2005.05010
Fock-Goncharov on higher Teichmuller theory: https://arxiv.org/abs/math/0311149
Goncharov-Shen survey article on local systems: https://arxiv.org/abs/1904.10491
Fock-Goncharov on quantization and dilogarithm: https://arxiv.org/abs/math/0702397

2) Apr 21: Juan Diego Rojas – Dilogarithm
Notes: PDF
References:
Zagier – The dilogarithm function
Gangl – Zagier’s polylogarithm conjecture revisited (slides)

3) Apr 28: Zhenyi Chen – Cluster Poisson structure on the moduli space of local systems on decorated surfaces
References:
Goncharov, Shen – Quantum geometry of moduli spaces of local systems and representation theory
Goncharov lecture series: https://www.youtube.com/watch?v=zt0Xo_QlwRo

4) May 5: Wenyuan Li – The cluster coordinates for PGL_2 framed local systems
Notes: PDF
Recording: Zoom (last 15 minutes – on mutation)
References:
Goncharov, Shen – Quantum geometry of moduli spaces of local systems and representation theory
Fock, Goncharov – Moduli spaces of local systems and higher Teichmuller theory
Goncharov – Ideal webs, moduli spaces of local systems, and 3d Calabi-Yau categories

5) May 12: Mingyuan Hu – Cluster varieties from Legendrian knots
References:
Shende, Treumann, Williams, Zaslow – Cluster varieties from Legendrian knots

5) May 19: Eric Zaslow – Quantum geometry and mirror symmetry after Goncharov

6) May  26: Hang Yuan – Gross-Hacking-Keel construction from a non-Archimedean perspective
Recording: Zoom
References:
Yuan – Family Floer mirror space for local SYZ singularities
Yuan – Family Floer superpotential’s critical values are eigenvalues of quantum product by c_1
Gross, Hacking, Keel – Birational geometry of cluster algebras

7) June 2: Ben Zhou – Quantization of cluster varieties
References:
Fock, Goncharov – Cluster ensembles, quantization and the dilogarithm

8) June 9: Dogancan Karabas – On the combinatorics of exact Lagrangian surfaces
Notes: PDF
References:
Shende, Treumann, Williams – On the combinatorics of exact Lagrangian surfaces

Other References:
Treumann, Williams, Zaslow – Kasteleyn operators from mirror symmetry
Kontsevich, Soibelman – Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
Kontsevich, Soibelman – Lectures on motivic Donaldson-Thomas
invariants and wall-crossing formulas

We meet every Thursday at 3pm. The topic for Winter ’22 is “Donaldson-Thomas invariants”.

Talks:
1) Dec 16 & 23: Eric Zaslow – DT invariants from 30,000 feet

2) Jan 6: Alex Karapetyan – Supersymmetry and BPS States
Recording: Zoom

3) Jan 20: Zhenyi Chen – Cohomological Donaldson-Thomas invariants
References:
Richard Thomas lecture series: https://www.youtube.com/watch?v=emLX3Za6mtY

4) Jan 27: Hang Yuan – Wall-crossing of Donaldson-Thomas invariants
References:
Kontsevich – Donaldson-Thomas invariants https://www.ihes.fr/~maxim/TEXTS/DTinv-AT2007.pdf
Bridgeland – Hall algebras and Donaldson-Thomas invariants (section 1) https://arxiv.org/abs/1611.03696

5) Feb 3: Benjamin Zhou – Scattering diagrams, curves, and sheaves
Notes: PDF
References: Bousseau – Scattering diagrams, sheaves, and curves https://arxiv.org/abs/2002.08741

6) Feb 10: Alex Karapetyan – (-1)-shifted symplectic Darboux theorem
References:
Pantev, Toen, Vaquie, Vezzosi – Shifted Symplectic Structures https://arxiv.org/abs/1111.3209
Brav, Bussi, Joyce – A ‘Darboux theorem’ for derived schemes with shifted symplectic structure https://arxiv.org/abs/1305.6302

7) Feb 17: Yuxuan Hu – Noncommutative Donaldson-Thomas invariants
References:
Szendroi – Noncommutative Donaldson-Thomas Invariants https://people.maths.ox.ac.uk/szendroi/nc_dt_GT.pdf

8) Feb 24: Mingyuan Hu – Euler number of Hilb^n(\C^3)

9) Mar 3: Wenyuan Li – Cohomological DT invariants and Hall algebras
Notes: PDF
References:
Szendroi – Cohomological Donaldson-Thomas invariants https://arxiv.org/abs/1503.07349

10) Mar 10: Zhenyi Chen – Simplicial descent for Chekanov-Eliashberg dg-algebras
References:
Asplund – Simplicial descent for Chekanov-Eliashberg dg-algebras https://arxiv.org/abs/2112.01915
Asplund, Ekholm – Chekanov-Eliashberg dg-algebras for singular Legendrians https://arxiv.org/abs/2102.04858

Other references:
Hori, Katz, Klemm, Pandharipande, Thomas, Vafa, Vakil, Zaslow – Mirror symmetry
Szendroi homepage: http://people.maths.ox.ac.uk/szendroi/
Szendroi slides: Nekrasov’s partition function and refined Donaldson–Thomas theory
Szendroi slides: Dimer models and local non-commutative algebraic geometry
Behrend – Donaldson-Thomas invariants via microlocal geometry https://arxiv.org/abs/math/0507523
Khan, Moore – Categorical Wall-Crossing in Landau-Ginzburg Models https://arxiv.org/abs/2010.11837

We meet every Thursday at 3pm. The topic for Fall ’21 is “Microlocal sheaves and Legendrians”.

Talks:
1) Oct 21: Dogancan Karabas – Introduction to microlocal sheaves
Notes: PDF
References:
Kashiwara, Schapira – Sheaves on manifolds
Nadler, Zaslow – Constructible sheaves and the Fukaya category
Nadler – Microlocal branes are constructible sheaves
Karabas – Microlocal sheaves on pinwheels (chapter 2)

2) Oct 28 & Nov 4: Hang Yuan – Legendrian knots and microlocal sheaves
References:
Shende, Treumann, Zaslow – Legendrian knots and constructible sheaves

3) Nov 11 & 18: Wenyuan Li – Lagrangian cobordism functor in microlocal sheaf theory
References:
Wenyuan Li – Lagrangian cobordism functor in microlocal sheaf theory
Ng, Rutherford, Shende, Sivek, Zaslow – Augmentations are sheaves

4) Dec 2 & 9: Mingyuan Hu – Sheaf quantization of Hamiltonian isotopies and applications to non displaceability problems
References:
Guillermou, Kashiwara, Shapira – Sheaf quantization of Hamiltonian isotopies and applications to non displaceability problems
Shende, Treumann, Zaslow – Legendrian knots and constructible sheaves

5) Jan 13: Mingyuan Yu – Microlocal Morse theory of wrapped Fukaya categories
References:
Ganatra, Pardon, Shende – Microlocal Morse theory of wrapped Fukaya categories

Other references:
Wenyuan Li – Estimating Reeb chords using microlocal sheaf theory
Karabas – Homotopy colimits of semifree dg categories (to glue microlocal sheaves)

Please comment for more references or possible talks.

After the current theme, we can get into the following themes.

1) Lagrangian mutations
Pascaleff, Tonkonog – The wall-crossing formula and Lagrangian mutations
Shende, Treuman, Williams, Zaslow – Cluster varieties from Legendrian knots
Shende, Treumann, Williams – On the combinatorics of exact Lagrangian surfaces
Casals, Vianna – Sharp ellipsoid embeddings and toric mutations

2) Superpotentials & mirrors
Carl, Pumperla, Siebert – A tropical view on Landau-Ginzburg models
Auroux – Mirror symmetry and T-duality in the complement of an anti-canonical divisor
Auroux – Special lagrangian fibrations, wall-crossing, and mirror symmetry
Cho, Oh – Floer cohomology and disc instantons of Lagrangian torus fibers in Fano toric manifolds

3) (Logarithmic) GW theory & Donaldson-Thomas invariants from coherent sheaves
Bousseau et al.
Abramovich, Chen et al.
van Garrel, Graber, Ruddat – Local Gromov-Witten invariants are log invariants
Gross, Pandharipande, Siebert – The tropical vertex

4) Point counts over finite fields
Treumann, Zaslow – Cubic Planar graphs and Legendrian surface theory
Casals, Murphy – Differential algebra of cubic planar graphs
Casals, Zaslow – Legendrian weaves: N-graph calculus, flag moduli and applications
Shen, Weng

5) Dynamical systems and stability conditions on Fukaya categories and coherent sheaves
Haiden, Katzarkov, Kontsevich – Flat surfaces and stability structures
Bridgeland, Smith – Quadratic differentials as stability conditions
Dimitrov, Haiden, Katzarkov, Kontsevich – Dynamical systems and categories
Kikuta, Takahashi – On the categorical entropy and the topological entropy

6) Tropical geometry and Gross-Siebert Program

Please suggest more references and possible topics.