Speaker: Daniel Kaufman (UMD) -

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Speaker: Nicholas Paskal (MATH) -

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Speaker: Ryan Vinroot (William and Mary ) -

Abstract: It has been conjectured that if G is a finite simple group, then every complex irreducible representation of G may be realized over the real numbers if and only if every element of G is the product of two involutions of G. This follows for most families of finite simple groups from work of various people over the past several decades, but not for the cases that G is either $p(2n,F_q) with q even or the simple orthogonal group Omega^{\pm}(4m,F_q) with q even. We will discuss the proof that this statement indeed holds for these symplectic groups, and what modifications must be made to the proof for the same method to apply to the simple orthogonal groups.

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Speaker: Nicholas Paskal (University of Maryland) -

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

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Speaker: Discussion (Univ. of Maryland) - http://math.umd.edu/~lcw/IwasawaRIT.html

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Speaker: Brian Collier (UMD) - http://math.umd.edu/~bcollie2/

Abstract: In this talk we will give a complete count of the connected components of the character variety of representations of a closed surface group into SO(p,q). In particular, we will exhibit the existence of "exotic" connected component which are not labeled by a characteristic class of SO(p,q) bundles. Each of these exotic components is parameterized by the space of K^p-twisted SO(1,q-p+1) Higgs bundles with the vector space of holomorphic differentials of degree 2,4,...,2n-2. From this parameterization, the Betti numbers for q=p+1 and q=p+2 can be computed. In the end, we will give evidence that these new connected components consist entirely of geometrically interesting (Anosov) representations.

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Speaker: Dr. Paul Smith (University of Maryland) -

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Speaker: Brad Lackey (University of Maryland) - http://www.umiacs.umd.edu/~bclackey/

Abstract: I will provide a rapid introduction to the foundations of quantum theory, with an emphasis on the differences between classical and quantum probability.

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Speaker: Kung-Ching Lin (UMD) -

Abstract: Quantization theory is an integral part of signal processing, focusing on the discrete nature of data storage in electronic devices and the effect of that. It stems from the needs to navigate the errors occurred from the numerous physical constraints during both sampling and reconstruction. This talk will give a quick exhibition of the development on this theory and discuss about a specific quantization scheme: Distributed noise shaping. Such scheme is robust against the usual physical constraints and has near-optimal error decay rate, making it a favorable choice.

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Speaker: John Goodrick (Los Andes University) - https://matematicas.uniandes.edu.co/~goodrick/

Abstract: Recently there have been several advances in the study of ordered Abelian groups (OAGs) whose theories have finite dp-rank. Recall that every complete theory of OAGs has NIP (Gurevich), so it it is interesting to ask which ones are *strongly* dependent in the pure language {+, <} of ordered groups, and which ones have finite dp-rank. We will sketch a new proof of a characterization of such theories, which was discovered independently by several people in the past year.

Next, we will consider finite dp-rank theories of ordered Abelian groups in languages expanding {+,<}. Here there is much less known, though discrete definable can be analyzed (as in work by myself and Dolich): if there is an Archimedean model, then any discrete definable set must be a finite union of arithmetic sequences. Some preliminary attempts to analyze definable sets and functions will be discussed.

All the results presented in this talk are joint work with Alfred Dolich.

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Speaker: Franziska Weber (Department of Mathematics, University of Maryland, College Park) - https://terpconnect.umd.edu/~frweber/

Abstract: We present a convergent finite difference method for approximating wave maps into the sphere. The method is based on a reformulation of the second order wave map equation as a first order system by using the angular momentum as an auxiliary variable. This enables us to preserve the length constraint as well as the energy inherit in the system of equations at the discrete level. The method is shown to converge to a weak solution of the wave map equation as the discretization parameters go to zero. Moreover, it is fast in the sense that O(N log N) operations are required in each time step (where N is the number of grid cells) and a linear CFL-condition is sufficient for stability and convergence. The performance of the method is illustrated by numerical experiments.

The method can be extended to a convergent scheme for the damped wave map equation and the heat map flow. If time permits, I will also discuss possible extensions of the method to applications for liquid crystal dynamics.

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Speaker: Hamid Al-Saqban (UMD) -

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Speaker: Radu Balan (UMD) -

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Speaker: Dr. Nils Caillerie (Department of Mathematics and Statistics, Georgetown University) -

Abstract: In this talk, we will focus on a kinetic equation modeling the spatial dynamics of a set of particles subject to intra-specific competition. This equation is motivated by the study of the propagation of biological populations, such as the Escherichia coli bacterium or the cane toad Rhinella marina, for which the classical diffusion approximation underestimates the actual range expansion of the species. We will use the optics geometrics approach as well as Hamilton-Jacobi equations to study spreading results for this equation. As we will see, the multi-dimensional case engenders technical difficulties, and possible over-representation of fast individuals at the edge of the front.

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Speaker: Samir Khuller (University of Maryland Computer Science ) - https://www.cs.umd.edu/users/samir/

Abstract: NP-complete problems abound in every aspect of our daily lives. One approach is to simply deploy heuristics, but for many of these we do not have any idea as to when the heuristic is effective and when it is not. Approximation algorithms have played a major role in the last three decades in developing a foundation for a better understanding of optimization techniques - greedy algorithms, algorithms based on LinearProgramming (LP) relaxations have paved the way for the design of (in some cases) optimal heuristics. Are these the best ones to use in “typical” instances? Maybe, maybe not.

In this talk we will focus on two specific areas - one is in the use of greedy algorithms for a basic graph problem called connected dominating set, and the other is in the development of LP based algorithms for a basic scheduling problem in the context of data center scheduling.

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Speaker: Ricardo H. Nochetto (University of Maryland) - https://www.math.umd.edu/~rhn/

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Speaker: Miguel Sanjuan (King Juan Carlos U, Madrid)

Abstract: In nonlinear dynamics, basins of attraction link a given set of initial conditions to its corresponding final states. This notion appears in a broad range of applications where several outcomes are possible, which is a common situation in neuroscience, economy, astronomy, ecology and many other disciplines. Depending on the nature of the basins, prediction can be difficult even in systems that evolve under deterministic rules. From this respect, a proper classification of this unpredictability is clearly required. To address this issue, we introduce the basin entropy, a measure to quantify this uncertainty. Its application is illustrated with several paradigmatic examples that allow us to identify the ingredients that hinder the prediction of the final state. The basin entropy provides an efficient method to probe the behavior of a system when different parameters are varied.Additionally, we provide a sufficient condition for the existence of fractal basin boundaries: when the basin entropy of the boundaries is larger than log 2, the basin is fractal. These ideas have been applied to some physical systems such as experiments of chaotic scattering of cold atoms, models of shadows of binary black holes, and classical and relativistic chaotic scattering associated to the Hénon-Heiles Hamiltonian system in astrophysics.

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Speaker: Tristan Hubsch (Howard) - http://physics1.howard.edu/~thubsch/

Abstract: This will be a review of some basics of condensed matter theory.

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Speaker: Richard Wentworth (UMCP) -

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