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The colloquium typically meets Mondays at 4:00 PM in Room 617 on the sixth floor of Wachman Hall.
The colloquium is preceded by tea starting at 3:30 in the Faculty Lounge, adjacent to Room 617. Click on title for abstract.
Nick Battista, The College of New Jersey
The ocean is home to an incredible diversity of animals of many shapes and sizes. Living life in a water-based environment presents unique challenges that vary based on the size and shape of each organism. Animals have evolved a variety of morphological structures, locomotor mechanisms, and swimming strategies that help reduce their energy expenditure by favoring more energetically efficient modes. Comprehensive studies that consider multiple morphological and kinematics traits and their influence on swimming performance are needed to investigate these differing strategies. Computational modeling gives us a tool to glean insight into how morphological or kinematics variation affects performance across different scales. For example, validated models can be used to thoroughly explore how varying multiple traits affects performance, where conducting an empirical study may be unrealistic due to finding enough organisms to test across the landscape of multiple traits. In addition, models can assess how natural variation affects performance and identify where trade-offs occur. In today's talk, I will describe my undergraduate lab's approach to studying the swimming behaviors for a variety of animals through a blend of math modeling, computational fluid dynamics, and machine learning. I will walk through our modeling process using Tomopteris, a polychaete, as an example, while also touching upon our own set of challenges, limitations, and future directions.
Fraydoun Rezakhanlou, University of California, Berkeley
Traditionally homogenization asks whether average behavior can be discerned from Hamilton-Jacobi equations that are subject to high-frequency fluctuations in spatial variables. A similar question can be asked for the associated Hamiltonian ODEs. When the Hamiltonian function is convex in momentum variable, these two questions turn out to be equivalent. This equivalence breaks down for general Hamiltonian functions. In this talk I will give a dynamical system formulation for homogenization and address some results concerning weak and strong homogenization phenomena.
Sara Maloni, University of Virgina
Abstract: The Teichmuller space of a surface S is the space of marked hyperbolic structure on S, up to equivalence. By considering the holonomy representation of such structures, this space can also be seen as a connected component of representations from the fundamental group of S into Isom(H^2). Generalizing this point of view, Higher Teichmuller Theory studies connected components of representations from the fundamental group of S into Lie groups of rank greater than 1.
We will discuss parts of the classical theory of deformations of geometric structures, Higher Teichmuller Theory and the notion of Anosov representation. We will then describe how Anosov representations correspond to deformation of certain geometric structures, and a joint work with Alessandrini, Tholozan and Wienhard about their topology.
Sourav Chatterjee, Stanford/IAS
I will talk about the Higgs mechanism for mass generation and some recent progress on this topic. No background is necessary. I will start by introducing lattice gauge theories coupled to Higgs fields. After a survey of existing results, I will discuss what is needed to prove rigorously that the Higgs mechanism can indeed generate mass in the continuum limit of these theories. Finally, I will present a result which shows that in a certain scaling limit in any dimension three or higher, SU(2) Yang-Mills-Higgs theory converges to a continuum limit object which has an explicit description as a scale-invariant random distribution. This allows an exact computation of the mass generated by the Higgs mechanism in the continuum limit of this theory.
2001 | 2002 | 2003 | 2004 | 2005 | 2006 | 2007 | 2008 | 2009 | 2010 | 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 | 2018 | 2019 | 2020 | 2021 | 2022 | 2023 | 2024