SR1

I will briefly describe a differential geometric construction of Hitchin's projectively flat connection in the Verlinde bundle, over Teichm\"uller space, formed by the Hilbert spaces arising from geometric quantization of the moduli space of flat connections on a Riemann surface. We will work on a general symplectic manifold sharing certain properties with the moduli space. Toeplitz operators enter the picture when quantizing classical observables, but they are also closely connected with the notion of deformation quantization. Furthermore, through an intimate relationship between Toeplitz operators, the Hitchin connection manifests itself in the world of deformation quantization as a connection on formal functions. As we shall see, this formal Hitchin connection can be used to construct a deformation quantization, which is independent of the Kähler polarization used for quantization. In the presence of a symmetry group, this deformation quantization can (under certain cohomological conditions) be constructed invariantly. The talk presents joint work with J. E. Andersen.

I will present a new proof of Mumford's conjecture on the rational cohomology of moduli spaces of curves, which is substantially different from those given by Madsen--Weiss and Galatius--Madsen--Tillmann--Weiss: in particular, it makes no use of Harer--Ivanov stability for the homology of mapping class groups, which played a decisive role in the previously known proofs. This talk represents joint work with Soren Galatius.

This is an overview, mostly of work of others (Denef, Loeser, Merle, Heinloth-Bittner,..). In the first part of the talk we give a brief introduction to motivic integration emphasizing its application to vanishing cycles. In the second part we discuss a join construction and formulate the relevant Sebastiani-Thom theorem.

This is an overview, mostly of work of others (Denef, Loeser, Merle, Heinloth-Bittner,..). In the first part of the talk we give a brief introduction to motivic integration emphasizing its application to vanishing cycles. In the second part we discuss a join construction and formulate the relevant Sebastiani-Thom theorem.

This talk concerns the relationships between Donaldson-Thomas, Pandharipande-Thomas, and Szendroi invariants established via analysis of the geometry of wall crossing phenomena of suitably general moduli spaces. I aim to give a reasonably detailed account of the simplest example, the conifold, where in fact all of the major ideas can be easily seen.

The goal of this talk is to give sufficient conditions for the existence of points on certain varieties defned over finite fields.