Awards day is the annual end of year event to recognize accomplishments of undergraduate students, graduate students, and faculty in the Mathematics Department. 

Come to the Math House on Friday afternoon for our annual Awards Day party.  Food, fun and celebration!

Title:  Hopf Lefschetz theorem for posets

Abstract:  The Hopf-Lefschetz theorem is a classical fixed point result from topology relating the Euler characteristic and the traces of certain matrices. In this talk we will prove a generalization of this theorem to order preserving maps on posets due to Baclawski and Björner. Additionally, we will prove a number of sufficient conditions on a poset P guaranteeing that all order preserving maps on P have a fixed point.

Title:  Uniform estimates in homogenization and applications

Abstract:  In a seminal paper of 1987, M. Avellaneda and F.H. Lin have introduced a powerfull method to show uniform Hölder and Lipschitz estimates for elliptic systems with oscillating coefficients. In this talk, I will investigate some consequences of these estimates for the large scale behavior of potentials and the asymptotics of boundary layers in homogenization. I will also address a generalization of the Lipschitz estimate to domains with oscillating boundary. The latter is a joint work with C. Kenig.

Title:  Groupoids with weak orders

Abstract:  We discuss certain groupoids equipped with partial orders satisfying properties which abstract those of weak orders of Coxeter groups (the resulting structures are not "partially ordered groupoids" in the usual sense). In particular, we describe braid presentations of the underlying groupoids and some of the very strong closure properties of these structures under natural categorical constructions. Applied even to familiar examples such as the symmetric groups, these constructions produce interesting new structures.

Spectacular developments in technology and resource exploitation have provided 2-3 billion people with unprecedented lifestyles and opportunities in the twentieth century. On the energy front, this has largely been achieved using inexpensive fossil fuels-- coal, oil and natural gas. The real costs of burning fossil fuels, many of which are hidden and long-term, have been environmental. Today, all species and nature, are being stressed at unprecedented levels and face conditions that have an increasing probability of resulting in catastrophes. Providing the same opportunities to nine or ten billion people will require 2-3 times current energy resources even with business-as-usual anticipated gains in efficiency. There is little doubt that, globally, we have the resources (100 more years of fossil fuels) and the technology to use fossil-fuels ever more cleanly so that the impacts on the environment are smaller and localized. Unfortunately, the emissions of green house gases and their contributions to climate change mandate we transform from the existing successful fossil-fuel system to zero-carbon emission systems. This talk will examine energy resources in different regions of the world and address the issue of whether these resources can provide energy security for the next fourty years. I will next examine how countries with enough resources (fossil, nuclear, hydroelectric) can reduce their carbon footprint in the power sector. I will then discuss the conditions needed to integrate large-scale solar and wind resources to create sustainable systems. Finally, I will identify areas which lack adequate reserves of fossil fuels and how they can address the simultaneous challenges of energy and climate security.

Refreshments are served in Chem-Phys 179 at 3:15 PM

Come celebrate GWS students and the end of the semester!