Lecture series
- Raf Bocklandt: Curves, surfaces and A-infty categories
- Julian Külshammer: How to make modules simple using A-infinity algebras
- Alice Rizzardo: An categories and triangulated structures
Exercises
Alice (all exercises)
Typo: In Raf's first exersises, the module S32 should have been labeled S23.
Schedule
|
Monday |
Tuesday |
Wednesday |
Thursday |
Friday |
| 08:00 |
Breakfast |
Breakfast |
Breakfast |
Breakfast |
Breakfast |
| 09:00 |
Bocklandt 1 |
Rizzardo 2 |
Bocklandt 4 |
Rizzardo 4 |
Bocklandt 6 |
| 09:45 |
Coffee |
Coffee |
Coffee |
Coffee |
Coffee |
| 10:15 |
Külshammer 1 |
exercises |
Külshammer 4 |
Bocklandt 5 |
Külshammer 6 |
11:15 |
Rizzardo 1 |
exercises |
exercises (11:00) |
Külshammer 5 |
Rizzardo 6 |
| 12:30 |
Lunch |
Lunch |
Lunch (11:30) |
Lunch |
Lunch |
| 13:30 |
exercises |
Bocklandt 3 |
|
Rizzardo 5 |
|
| 14:15 |
exercises |
Coffee |
|
Coffee |
|
| 14:45 |
Coffee (15:15) |
Külshammer 3 |
excursion (12:30) |
exercises |
|
| 15:45 |
Bocklandt 2 |
Rizzardo 3 |
|
exercises |
|
| 16:45 |
Külshammer 2 |
|
|
|
|
| 18:30 |
Dinner |
Dinner |
Dinner (19:00) |
Dinner |
Dinner |
There will also be dinner on Sunday evening and breakfast on Saturday morning, for the people who arrive on Sunday and leave on Saturday, respectively.
Tentative plan for the individual lectures
Bocklandt 1: Representation theory of A_n and polygons
Külshammer 1: Ext^n and representations of quivers
Rizzardo 1: Hochschild cohomology and deformations of algebras
Bocklandt 2: Definition of A-infinity algebras
Külshammer 2: The bar and cobar constructions
Rizzardo 2: A-infinity categories
Bocklandt 3: Kadeishvili's theorem
Külshammer 3: A_infinity structures on Ext-algebras
Rizzardo 3: Twisted complexes and triangulated categories
Bocklandt 4: General surfaces
Külshammer 4: Exact Borel subalgebras and bocses
Rizzardo 4: A_n-algebras, A_n-cats and truncated twisted complexes
Bocklandt 5: Description of D^b(P^1) using geometry and A-infinity structures
Külshammer 5: Ext-algebra of simple modules and quivers with relations
Rizzardo 5: Pretriangulated A_n-categories
Bocklandt 6: Generalisations
Külshammer 6: Koszul duality for A-infinity algebras and construction of exact Borel subalgebras
Rizzardo 6: An example of triangulated categories without enhancement
Literature
Here is a list of suggested preparatory reading.
Surveys:
- Keller: A-infinity algebras in representation theory, Representations of algebra. Vol. I, II, 74–86, Beijing Norm. Univ. Press, Beijing, 2002.
- Keller: A-infinity algebras, modules and functor categories, Trends in representation theory of algebras and related topics, 67–93, Contemp. Math., 406, Amer. Math. Soc., Providence, RI, 2006.
- Keller: Introduction to A-infinity algebras and modules, Homology Homotopy Appl. 3 (2001), no. 1, 1–35.
- Külshammer: In the bocs seat: Quasi-hereditary algebras and representation type, Representation theory—current trends and perspectives, 375–426, EMS Ser. Congr. Rep., Eur. Math. Soc., Zürich, 2017.
Articles:
- Bocklandt: Noncommutative mirror symmetry for punctured surfaces, Trans. Amer. Math. Soc. 368 (2016), no. 1, 429–469.
- Haiden, Katzarkov, Kontsevich: Flat surfaces and stability structures, Publ. Math. Inst. Hautes Études Sci. 126 (2017), 247–318.
- Lefevre-Hasegawa: Sur les A-infini catégories, preprint.
- Lu, Palmieri, Wu, Zhang: A-infinity structure on Ext-algebras, J. Pure Appl. Algebra 213 (2009), no. 11, 2017–2037.
- Lu, Palmieri, Wu, Zhang: A-infinity algebras for Ring Theorists, Conference Paper in Algebra Colloquium.
- Lu, Palmieri, Wu, Zhang: Koszul equivalences in A-infinity algebras, New York J. Math. 14 (2008) 325–378.
- Lu, Palmieri, Wu, Zhang: Regular algebras of dimension 4 and their A-infinity Ext-algebras, Duke Math. J. Volume 137, Number 3 (2007), 537-584.
- Koenig, Külshammer, Ovsienko: Quasi-hereditary algebras, exact Borel subalgebras, A-infinity categories and boxes, Adv. Math. 262 (2014), 546–592.
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