Colloquia 2012-2013

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Mathematics Colloquium

All colloquia are on Fridays at 4:00 pm in Van Vleck B239, unless otherwise indicated.

Spring 2011

date speaker title host(s)
jan 21 Emanuele Macri (University of Bonn) Stability conditions and Bogomolov-type inequalities in higher dimension Andrei Caldararu
jan 28 Marcus Roper (Berkeley) TBA Paul Milewski
jan 31, 2:30pm, room 901 Ana-Maria Castravet (Arizona) TBA Andrei
feb 4 Xinyi Yuan (Columbia University) TBA Tonghai
feb 25 Omri Sarig (Penn State) TBA Shamgar
mar 4 Jeff Weiss (Colorado) Nonequilibrium Statistical Mechanics and Climate Variability Jean-Luc
mar 11 Roger Howe (Yale) TBA Shamgar
mar 25 Pham Huu Tiep (Arizona) TBA Martin Isaacs
apr 1 Amy Ellis (Madison) TBA Steffen
apr 8 Alan Weinstein (Berkeley) TBA Yong-Geun
apr 15 Max Gunzburger (Florida State) TBA James Rossm.
apr 22 Jane Hawkins (U. North Carolina) TBA WIMAW (Diane Holcomb)
apr 29 Jaroslaw Wlodarczyk (Purdue) TBA Laurentiu

Abstracts

Emanuele Macri (University of Bonn)

Stability conditions and Bogomolov-type inequalities in higher dimension

Stability conditions on a derived category were originally introduced by Bridgeland to give a mathematical foundation for the notion of \Pi-stability in string theory, in particular in Douglas’ work. Recently, the theory has been further developed by Kontsevich and Soibelman, in relation to their theory of motivic Donaldson-Thomas invariants for Calabi-Yau categories. However, no example of stability condition on a projective Calabi-Yau threefold has yet been constructed.

In this talk, we will present an approach to the construction of stability conditions on the derived category of any smooth projective threefold. The main ingredient is a generalization to complexes of the classical Bogomolov-Gieseker inequality for stable sheaves. We will also discuss geometric applications of this result.

This is based on joint work with A. Bayer, A. Bertram, and Y. Toda.

Jeff Weiss (Colorado)

Nonequilibrium Statistical Mechanics and Climate Variability

The natural variability of climate phenomena has significant human impacts but is difficult to model and predict. Natural climate variability self-organizes into well-defined patterns that are poorly understood. Recent theoretical developments in nonequilibrium statistical mechanics cover a class of simple stochastic models that are often used to model climate phenomena: linear Gaussian models which have linear deterministic dynamics and additive Gaussian white noise. The theory for entropy production is developed for linear Gaussian models and applied to observed tropical sea surface temperatures (SST). The results show that tropical SST variability is approximately consistent with fluctuations about a nonequilibrium steady-state. The presence of fluctuations with negative entropy production indicates that tropical SST dynamics can, on a seasonal timescale, be considered as small and fast in a thermodynamic sense. This work demonstrates that nonequilibrium statistical mechanics can address climate-scale phenomena and suggests that other climate phenomena could be similarly addressed by nonequilibrium statistical mechanics.