Speaker: Konstantina Trivisa (University of Maryland) -

Abstract: http://www.terpconnect.umd.edu/~lvrmr/2017-2018-S/Classes/RIT.shtml

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Speaker: William Wylie (Syracuse University) - http://asfaculty.syr.edu/pages/math/wylie-william.html

Abstract: A weighted Riemannian manifold is simply a Riemannian manifold equipped with a (variable) density function. For example, a surface with a positive function that describes the density of the material that makes up the surface. In this talk we'll discuss a new geometric approach to weighted Riemannian manifolds that takes a natural torsion free connection as the fundamental object of study. This approach gives new comparison results that are valid under weaker Ricci curvature assumptions than have previously been considered in the literature, and also leads to novel rigidity phenomena. Time permitting, we'll also discuss how the connection leads to a theory of sectional curvature bounds for weighted Riemannian manifolds.

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Speaker: Marty Weissman (UCSC) - http://martyweissman.com/

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Speaker: Victor Yakovenko - University of Maryland Department of Physics

Abstract: Inequality is an important and seemingly inevitable aspect of the human society. Various manifestations of inequality can be derived from the concept of entropy in statistical physics. In a stylized model of monetary economy, with a constrained money supply implicitly reflecting constrained resources, the probability distribution of money among the agents converges to the exponential Boltzmann-Gibbs law due to entropy maximization. Our empirical data analysis [1] shows that income distributions in the USA, European Union, and other countries exhibit a well-defined two-class structure. The majority of the population (about 97%) belongs to the lower class characterized by the exponential ("thermal") distribution. The upper class (about 3% of the population) is characterized by the Pareto power-law ("superthermal") distribution, and its share of the total income expands and contracts dramatically during booms and busts in financial markets. Interestingly, the same equations can be also applied to heavy-ion collisions [2]. Globally, energy consumption (and CO2 emissions) per capita around the world shows decreasing inequality in the last 30 years and convergence toward the exponential probability distribution, as expected from the maximal entropy principle. In agreement with our prediction [3], a saturation of the global Gini coefficient for energy consumption at 0.5 is observed for the most recent years. All papers are available at http://physics.umd.edu/~yakovenk/econophysics/.

[1] Yong Tao et al., "Exponential structure of income inequality: evidence from 67 countries", Journal of Economic Interaction and Coordination (2017) http://doi.org/10.1007/s11403-017-0211-6 http://arxiv.org/abs/1612.01624

[2] Xuejiao Yin et al., "A new two-component model for hadron production in heavy-ion collisions", Advances in High Energy Physics (2017) 6708581, http://doi.org/10.1155/2017/6708581

[3] S. Lawrence, Q. Liu, and V. M. Yakovenko, "Global inequality in energy consumption from 1980 to 2010", Entropy 15, 5565 (2013), http://dx.doi.org/10.3390/e15125565

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Speaker: Diana Davis (Swarthmore College) - http://www.swarthmore.edu/NatSci/ddavis3/

Abstract: TBA

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Speaker: Ryan Hynd (U-Penn) - https://web.sas.upenn.edu/rhynd/

Abstract: We will consider the dynamics of a finite number of particles that interact pairwise and undergo perfectly inelastic collisions.

Such physical systems conserve mass and momentum and satisfy the Euler-Poisson equations. In one spatial dimension, we will show

how to derive an extra entropy estimate which allows us to characterize the limit as the number of particles tends to infinity.

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