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Augsburg / Regensburg Seminar: The chiral de Rham complex
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| Titel: | Augsburg / Regensburg Seminar: The chiral de Rham complex |
| Dozent(in): | Prof. Dr. Katrin Wendland, Dr. Emanuel Scheidegger |
| Termin: | vierzehntägig Freitags, 14:00-19:00 Uhr |
| Gebäude/Raum: | abwechselnd in Augsburg (L1, Raum 1008) und in Regensburg |
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Termin und Ort |
Titel |
Beschreibung |
Sprecher |
|---|---|---|---|
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24.4. Regensburg |
The chiral de Rham complex I |
- reminder on VOA, super and conformal structures, operator product expansion technique, etc. - construction of the CDR in the affine case (bosonic and fermionic part), verifications ([1] §§1 ,2)
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Uli Bunke Nadine Grosse |
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8.5. Augsburg |
The chiral de Rham complex II |
- localization ( [1], Thm 3.2 and details) - implementation of coordinate transformations ( [1], Thm 3.7 and details) - the conformal and topological structure [1], §4 |
Nadine Grosse Bernd Ammann Katrin Wendland |
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20.5. München ausnahmsweise mittwochs um 13:00 Uhr |
The chiral de Rham complex III |
- implementation of coordinate transformations ( [1], Thm 3.7 and details) - the conformal and topological structure [1], §4 - superconformal structures, topological twists [10], §11 |
Bernd Ammann Katrin Wendland Uli Bunke |
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19.6 Augsburg |
The gerbe of chiral differential operators |
- determination of the automorphism group - description of the gerbe of chiral diff. operators [3] - background on Spin, String structures etc. |
Uli Bunke Bernhard Hanke |
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3.7. Augsburg
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Geometric structures and supersymmetries |
- background on Spin, String structures etc. - the superfield formalism - N=1,2 4 supersymmetry algebra - from geometric structures to supersymmetries [6] |
Bernhard Hanke Marc Nieper-Wißkirchen |
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10.7 Regensburg
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Vertex algebroids and vertex algebras |
- the notion of an vertex algebroid - functorial transition between vertex algebroids and vertex algebras - application to the chiral de Rham complex - relation with generalized geometry (background reminder) [2], [3], [9] |
Marc Nieper-Wißkirchen Katrin Wendland Christian Blohmann |
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16.7. Regensburg, ausnahmsweise donnerstags um 13:15 Uhr |
Elliptic genera |
-Background on elliptic genera - description of vertex algebras related with elliptic genera [9], [10]§§14-16 - the chiral Dolbeault complex [9] and the Witten genus [11], [12].[13] |
Nadine Grosse Emanuel Scheidegger |
1 . math.AG/9803041 Chiral de Rham complex. Fyodor Malikov, Vadim Schechtman, Arkady Vaintrob. Commun.Math.Phys. 204 (1999) 439-473. math.AG.
2 .math.AG/9901065 Chiral de Rham complex. II. Fyodor Malikov, Vadim Schechtman. math.AG.
3. math.AG/9906117 Gerbes of chiral differential operators. Vassily Gorbounov, Fyodor Malikov, Vadim Schechtman. math.AG.
4. math.AG/0003170 Gerbes of chiral differential operators. II. Vassily Gorbounov, Fyodor Malikov, Vadim Schechtman. math.AG.
5. math.AG/0005201 Gerbes of chiral differential operators. III. Vassily Gorbounov, Fyodor Malikov, Vadim Schechtman. math.AG.
6. math.QA/0601532 Supersymmetry of the Chiral de Rham Complex. David Ben-Zvi, Reimundo Heluani, Matthew Szczesny. math.QA (math.AG).
7. math/0603633 Supersymmetric vertex algebras. Reimundo Heluani, Victor G. Kac. Commun.Math.Phys.271:103-178,2007. math.QA (physics.math-ph).
8. arXiv:0812.4855 Generalized Calabi-Yau manifolds and the chiral de Rham complex. Reimundo Heluani, Maxim Zabzine. math.QA (math.DG physics.hep-th).
9. arXiv:0811.1418 Vertex algebras and the Witten genus. Pokman Cheung. math.AT (math.QA).
10. VERTEX OPERATOR ALGEBRAS AND DIFFERENTIALGEOMETRY JIAN ZHOU
11. math.AG/000712 Elliptic Genera of singular varieties, orbifold elliptic genus and chiral deRham complex. Lev A Borisov, Anatoly Libgober. math.AG.
12. math.AG/9904126 Elliptic Genera and Applications to Mirror Symmetry. Lev A. Borisov, Anatoly Libgober. math.AG (physics.hep-th).
13. math.AG/9809094 Vertex Algebras and Mirror Symmetry. Lev A. Borisov. Commun.Math.Phys. 215 (2001) 517-557. math.AG.
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