Seminars

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

Mathphys Analysis Seminar
Hosts: Laszlo Erdös, Robert Seiringer, Jan Maas, Julian Fischer
Algebraic Geometry & Number Theory Seminar
Hosts: Tamas Hausel and Tim Browning
Geometry & Topology Seminar
Hosts: Herbert Edelsbrunner, Uli Wagner
Mathematics%20and%20CS%20Seminar
 
October 2022
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Speaker: Anton Mellit
hosted 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
Oct 6 13:00 15:00
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Speaker: Szilard Szabo
hosted 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.
Oct 13 13:00 15:00
Speaker: Christian Hainzl
hosted 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.
Oct 13 16:15 17:15
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Speaker: Helmut Abels
hosted by Julian Fischer
Oct 20 16:15 17:15
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Speaker: Anne Moreau
hosted by Tamas Hausel
Oct 27 13:00 15:00
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