Geometry of the SL(3,ℂ)-character variety of torus knots.

Let G be the fundamental group of the complement of the torus knot of type (m, n). It has a presentation G = . We find a geometric description of the character variety X(G) of characters of representations of G into SL(3,ℂ), GL(3,ℂ) and PGL(3,ℂ).

E-polynomial of the SL(3,C)-character variety of free groups.

We compute the E-polynomial of the character variety of representations of a rank r free group in SL(3,C). Expanding upon techniques of Logares, Muñoz and Newstead (Rev. Mat. Complut. 26:2 (2013), 635-703), we stratify the space of representations and compute the E-polynomial of each geometrically described stratum using fibrations. Consequently, we also determine the E-polynomial of its smooth, singular, and abelian loci and the corresponding Euler characteristic in each case. Along the way, we give a new proof of results of Cavazos and Lawton (Int. J. Math. 25:6 (2014), 1450058).

Simulation of the cold climate event 8200 years ago by meltwater outburst from Lake Agassiz

The cold climate anomaly about 8200 years ago is investigated with CLIMBER-2, a coupled atmosphere-ocean-biosphere model of intermediate complexity. This climate model simulates a cooling of about 3.6 K over the North Atlantic induced by a meltwater pulse from Lake Agassiz routed through the Hudson strait. The meltwater pulse is assumed to have a volume of 1.6 x 10^14 m^3 and a period of discharge of 2 years on the basis of glaciological modeling of the decay of the Laurentide Ice Sheet ( LIS). We present a possible mechanism which can explain the centennial duration of the 8.2 ka cold event. The mechanism is related to the existence of an additional equilibrium climate state with reduced North Atlantic Deep Water (NADW) formation and a southward shift of the NADW formation area. Hints at the additional climate state were obtained from the largely varying duration of the pulse-induced cold episode in response to overlaid random freshwater fluctuations in Monte Carlo simulations. The model equilibrium state was attained by releasing a weak multicentury freshwater flux through the St. Lawrence pathway completed by the meltwater pulse. The existence of such a climate mode appears essential for reproducing climate anomalies in close agreement with paleoclimatic reconstructions of the 8.2 ka event. The results furthermore suggest that the temporal evolution of the cold event was partly a matter of chance.

E-polynomials of the SL(2, C)-character varieties of surface groups

We compute the E-polynomials of the moduli spaces of representations of the fundamental group of a once-punctured surface of any genus into SL(2, C), for any possible holonomy around the puncture. We follow the geometric technique introduced in [12], based on stratifying the space of representations, and on the analysis of the behavior of the E-polynomial under fibrations.