Talks

Future surveys will map the cosmic microwave background (CMB) with unprecedented precision. The high fidelity of the data will present new opportunities to extract deep insights about the history, contents, and evolution of our universe.  However, new tools and techniques will be required to maximize the potential of the forthcoming data.  I will describe the techniques necessary to address the emerging challenges and to harness the exciting opportunities provided by future CMB observations.

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Zoom link https://pitp.zoom.us/j/92999899446?pwd=YTNEUkMrV2RXOWE0Mk11b2tDQ2Q0Zz09

The moduli of Higgs bundles and the Hitchin fibration are central to many thriving research areas, such as mirror symmetry, non-abelian Hodge theory and the geometric Langlands program.  A group-theoretic or multiplicative version was introduced by Frenkel and Ngo in 2011 to give a geometric interpretation of orbital integrals and trace formulas from automorphic representation theory. Since then, there is an ongoing program to replicate the theory of Higgs bundles for the multiplicative case. One notable development is the study of multiplicative affine Springer fibers. Like the usual ones, they are local analogues of multiplicative Hitchin fibers. In this talk, I discuss my work in continuing this program and providing a multiplicative version of Z. Yun's global Springer theory. This involves the study of parabolic multiplicative Higgs bundles and affine Springer fibers.