Talk

In recent work with S. Naito, D. Sagaki, A. Schilling, and M. Shimozono, we show that in all untwisted affine types the specialization of a Macdonald polynomial at t=0 is the graded character of a tensor product of one-column Kirillov-Reshetikhin (KR) modules.

I will report on an ongoing project aiming at uncovering fundamental
features of N=(2,2) supersymmetric quantum mechanics on moduli spaces
of vortices on compact Riemann surfaces, in analogy with the spectrum
of quantum dyon-monopole bound states that emerged in connection with
Sen's S-duality conjectures in the 1990s. My focus in this talk will
be on the geometry underlying the coupling of waveforms to local
systems in effective theories for supersymmetric two-dimensional sigma-models
with toric gauge symmetry. I will consider models with

In the study of Hilbert, Jacobi and orthogonal modular forms
of low weight over number fields it is essential to understand the
representations of Hilbert modular groups or of certain two-fold
central extensions. In the case of the field of natural numbers it is
known that the key to the study of all representations of the modular
group $SL(2,Z)$ which are interesting in the mentioned context are
the Weil representations associated to finite quadratic modules. In
analogy to the case of the field of rational numbers we developed a

In this talk we will give an overview of the collapsing theory for 3-dimensional manifolds with a lower sectional curvature bound. This theory first developed by Shioya and Yamaguchi served as the completion of the last claim in Perelman's Proof of Geometrization Conjecture. The basic techniques used in the study will be presented with emphasis on Perelman's Fibration Theorem and Soul Theorem. Collapsing theory with bounded sectional curvature will also be quickly reviewed so that we can see the differences/parallel structures between these two theory.