[geometry-ml:02973] MS seminar at Kavli IPMU -- Laura Schaposnik & Takeshi Ikeda

[Todor Milanov]

Dear all,

I would like to announce the following two Mathematics and String theory seminars at Kavli IPMU: 

1)
Speaker: Laura Schaposnik (University of Illinois at Chicago)
Date:	Tue, Jun 06, 2017, 13:15 - 14:45
Place:	Seminar Room A

Title:	Higgs bundles, branes and applications

Abstract: We shall begin the talk by first introducing Higgs bundles for complex Lie groups and the associated Hitchin fibration, and recalling how to realize Langlands duality through spectral data. We will then look at a natural construction of families of subspaces which give different types of branes, and explain how the topology of some of these branes can be described by considering the Hitchin fibration. Finally, we shall give some applications of the above approaches in relation to Langlands duality, and other correspondences between integrable systems. Some of the work presented during the talk is in collaboration with David Baraglia (Adelaide), Steve Bradlow (UIUC) and Sebastian Heller (Universität Tübingen).

2) 
Speaker: Takeshi Ikeda (Okayama University of Science)
Date:	Tue, Jun 06, 2017, 15:30 - 17:00
Place:	Seminar Room B

Title:	Peterson isomorphism in $K$-theory and Relativistic Toda lattice

Abstract: The $K$-homology ring of the affine Grassmannian of $SL_n(\mathbb{C})$ was studied by Lam, Schilling, and Shimozono. It is realized as a certain concrete Hopf subring of the ring of symmetric functions. On the other hand, for the quantum $K$-theory of the flag variety $Fl_n$, Kirillov and Maeno provided a conjectural presentation based on the results obtained by Givental and Lee. We construct an explicit birational morphism between the spectrums of these two rings. Our method relies on Ruijsenaars's relativistic Toda lattice with unipotent initial condition. From this result, we obtain a $K$-theory analogue of the so-called Peterson isomorphism for (co)homology. We provide a conjecture on the detailed relationship between the Schubert bases, and, in particular, we determine the image of Lenart--Maeno's quantum Grothendieck polynomial associated with a Grassmannian permutation.





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Todor Eliseev Milanov
Associate Professor 
Kavli IPMU,  Japan

todor.milanov ＠ ipmu.jp