### Seminars

The following seminars in mathematics are currently taught at IST Austria:

Mathphys Analysis SeminarHosts: Laszlo Erdös, Robert Seiringer, Jan Maas, Julian Fischer |

Algebraic Geometry & Number Theory SeminarHosts: Tamas Hausel and Tim Browning |

Geometry & Topology SeminarHosts: Herbert Edelsbrunner, Uli Wagner |

Mathematics%20and%20CS%20Seminar |

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Speaker: Anton Mellit Oct 6 13:00 15:00hosted by Tamas Hausel Abstract: By H_2 we denote the Lie algebra of polynomial hamiltonian vector fields on the plane. We consider the moduli space of stable twisted Higgs bundles on an algebraic curve of given coprime rank and degree. De Cataldo, Hausel and Migliorini proved in the case of rank 2 and conjectured in arbitrary rank that two natural filtrations on the cohomology of the moduli space coincide. One is the weight filtration W coming from the Betti realization, and the other one is the perverse filtration P induced by the Hitchin map. Motivated by computations of the Khovanov-Rozansky homology of links by Gorsky, Hogancamp and myself, we look for an action of H_2 on the cohomology of the moduli space. We find it in the algebra generated by two kinds of natural operations: on the one hand we have the operations of cup product by tautological classes, and on the other hand we have the Hecke operators acting via certain correspondences. We then show that both P and W coincide with the filtration canonically associated to the sl_2 subalgebra of H_2.Based on joint work with Hausel, Minets and Schiffmann | 7 | 8 | 9 |

10 | 11 | 12 |
Speaker: Szilard Szabo Oct 13 13:00 15:00hosted by Tamas Hausel Abstract: In the first part I will discuss about the Geometric variant of the P=W conjecture and its relationship to the original cohomological P=W conjecture. I will also introduce Donaldson--Thomas theory as a framework arising in various problems of Mathematical Physics, and point out its relevance to the aforementioned conjectures in some parabolic cases.In the second part, I will give more detail on some ingredients and parts of the proofs. Speaker: Christian Hainzl Oct 13 16:15 17:15hosted by Robert Seiringer Abstract: I will review recent joint works with M. Christiansen and P. T. Nam about the correlation energy of mean-field fermi gases, including a precise upper bound mimicking the Gell-Mann—Brueckner formula for the Coulomb gas. | 14 | 15 | 16 |

17 | 18 | 19 |
Speaker: Helmut Abels Oct 20 16:15 17:15hosted by Julian Fischer | 21 | 22 | 23 |

24 | 25 | 26 |
Speaker: Anne Moreau Oct 27 13:00 15:00hosted by Tamas Hausel | 28 | 29 | 30 |

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