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Augsburg / Regensburg Seminar: The chiral de Rham complex

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

Inhalt:

Termin und Ort

Titel

Beschreibung

Sprecher

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)


Uli Bunke

Nadine Grosse

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

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

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

3.7. Augsburg

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

10.7 Regensburg










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

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



Literatur:

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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