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• Organizational Meeting

  Speaker: () -
  

  When: Tue, September 4, 2018 - 2:00pm
  Where: Kirwan Hall 3206
  
• Harmonic analysis in combinatorics: a case study

  Speaker: Dong Dong (UMD) -
  

  When: Tue, September 11, 2018 - 2:00pm
  Where: Kirwan Hall 3206
  

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  Abstract:
  The Roth theorem, which concerns the existence of three-term arithmetic progressions in certain sets, is a central topic in combinatorics. It also attracts researchers from different fields such as number theory, ergodic theory, analysis, and even computer science. In this talk, we will look at the Roth theorem from the harmonic analysis point of view. Surprisingly, harmonic analysis connects multilinear operators to very deep algebraic geometry. Although a few branches of mathematics are involved, this talk will be accessible to second-year graduate students and above.
  
  
• Constrictions of bent functions using a family of permutations and Reed-Muller type codes

  Speaker: Costas Karanikas (Aristotle University of Thessaloniki) - http://users.auth.gr/karanika/
  

  When: Tue, September 18, 2018 - 2:00pm
  Where: EGR 2116
  

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  Abstract: From a pair of permutations of the first n integers we get a family of permutations on 2^n objects. This family provides new bent functions ie Boolean sequences of length 2^(2n) whose Walsh transfom get values in {2^n,- 2^n}. The left half of a bent function determines a near-bent i.e., Boolean sequences of length 2^n (n odd) with Walsh spectrum in {0,2^n,-2^n} . We relate the support of near-bents with Reed - Muller type codes and using this we construct bents of higher degree using RM type codes and bents of lower type. We also discuss several ways for constructing bent functions and modify well-known constructions as for example Dillon H class and Maiorana- McFarland method .
  
• A sharp Schrodinger maximal estimate in R^2

  Speaker: Xiumin Du (UMD)
  

  When: Tue, September 25, 2018 - 2:00pm
  Where: Kirwan Hall 3206
  

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  Abstract: We consider Carleson’s pointwise convergence problem of Schrodinger solutions. It is shown that the solution to the free Schrodinger equation converges to its initial data almost everywhere, provided that the initial data is in the Sobolev space H^s(R^n) with s > n/2(n+1) (joint with Larry Guth and Xiaochun Li in the case n = 2, and joint with Ruixiang Zhang in the case n >= 3). This is sharp up to the endpoint, due to a counterexample by Bourgain. This pointwise convergence problem can be approached by estimates of Schrodinger maximal function, which have some similar flavors as the Fourier restriction/extension estimates. In this talk, we'll focus on the case $n=2$ and see how polynomial partitioning method and decoupling theorem play a role in such estimates.
  
• Mathematical approaches to understand and alter swallowing and gait functions in humans

  Speaker: Ervin Sejdic (PITT) -
  

  When: Tue, October 23, 2018 - 2:00pm
  Where: Kirwan Hall 1308
  

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  Abstract: A human body comprises of several physiological systems that carry out specific functions necessary for
  daily living. Traumatic injuries, diseases and aging negatively impact human functions, which can cause a
  decreased quality of life and many other socio-economical and medical issues. Accurate models of
  human functions are needed to propose interventions and treatments that can restore deteriorated
  human functions. Therefore, our research aims to develop novel mathematical approaches that can
  accurately assess changes in swallowing and gait functions by focusing on dynamical interactions
  between musculoskeletal and other physiological systems. In this talk, I will present some of our recent
  contributions dealing with both mathematical and clinical aspects of our work. Lastly, I will also present
  our future research goals and our strategy to achieve these goals.
  
  BIOGRAPHY
  Dr. Ervin Sejdić received B.E.Sc. and Ph.D. degrees in electrical engineering from the University of
  Western Ontario, London, Ontario, Canada in 2002 and 2008, respectively. From 2008 to 2010, he was a
  postdoctoral fellow at the University of Toronto with a cross-appointment at Bloorview Kids Rehab,
  Canada’s largest children’s rehabilitation teaching hospital. From 2010 until 2011, he was a research
  fellow at Harvard Medical School with a cross-appointment at Beth Israel Deaconess Medical Center.
  From his earliest exposure to research, he has been eager to contribute to the advancement of scientific
  knowledge through carefully executed experiments and ground-breaking published work. This has
  resulted in co-authoring over 130 journal publications. In February 2016, President Obama named Dr.
  Sejdić as a recipient of the Presidential Early Career Award for Scientists and Engineers, “…the highest
  honor bestowed by the United States Government on science and engineering professionals in the early
  stages of their independent research careers.” In 2017, Dr. Sejdić was awarded the National Science
  Foundation CAREER Award. In 2018, he was awarded the Chancellor’s Distinguished Research Award at
  the University of Pittsburgh. Dr. Sejdić’s passion for discovery and innovation drives his constant
  endeavors to connect advances in engineering to society’s most challenging problems. Hence, his
  research interests include biomedical signal processing, gait analysis, swallowing difficulties, advanced
  information systems in medicine, rehabilitation engineering, assistive technologies and anticipatory
  medical devices.
  
• Oscillations of Fourier series, Quantitative Sturm-Liouville Theory and Applications

  Speaker: Stefan Steinerberger (Yale) - https://users.math.yale.edu/users/steinerberger/
  

  When: Tue, November 6, 2018 - 2:00pm
  Where: Kirwan Hall 3206
  

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  Abstract: The function f(x) = a*sin(12*x) + b*sin(28x) has always between 24 and
  56 roots (unless a=b=0). This follows from a classical theorem of Sturm (1836) that
  has been forgotten and was recently rediscovered by Berard & Helffer. I will tell the
  (quite fascinating) story behind it, give a simple proof and discuss quantitative
  refinements, newly emerging connections to elliptic PDEs and the beginning of a
  Sturm-Liouville theorem in higher dimensions.
  
• Frames and some algebraic forays

  Speaker: Prof. John Benedetto (UMD) -
  

  When: Tue, November 13, 2018 - 2:00pm
  Where: Kirwan Hall 3206
  
• Training 10k-layer CNNs with mean field theory and dynamical isometry[joint w/ RIT on Deep Learning]

  Speaker: Lechao Xiao (Google Brain) - https://ai.google/research/people/105681
  

  When: Fri, November 16, 2018 - 12:00pm
  Where: EGR 0108
  

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  Abstract: In recent years, state-of-the-art methods in computer vision have utilized increasingly deep convolutional neural network architectures (CNNs), with some of the most successful models employing hundreds or even thousands of layers. A variety of pathologies such as vanishing/exploding gradients make training such deep networks challenging. While residual connections and batch normalization do enable training at these depths, it has remained unclear whether such specialized architecture designs are truly necessary to train deep CNNs. In this talk, we demonstrate that it is possible to train vanilla CNNs with ten thousand layers or more simply by using an appropriate initialization scheme. We derive this initialization scheme theoretically by developing a mean field theory for signal propagation and by characterizing the conditions for dynamical isometry, the equilibration of singular values of the input-output Jacobian matrix. These conditions require that the convolution operator be an orthogonal transformation in the sense that it is norm-preserving. We present an algorithm for generating such random initial orthogonal convolution kernels and demonstrate empirically that they enable efficient training of extremely deep architectures.
  
• Inference of interaction laws in systems of agents from trajectory data

  Speaker: Sui Tang (JHU) - http://www.math.jhu.edu/~stang/
  

  When: Tue, November 20, 2018 - 2:00pm
  Where: Kirwan Hall 3206
  

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  Abstract: Inferring the laws of interaction of agents in complex dynamical systems from observational data is a fundamental challenge in a wide variety of disciplines. We propose a non-parametric statistical learning approach to estimate the governing laws of distance-based interactions, with no reference or assumption about their analytical form, from data consisting trajectories of interacting agents. We demonstrate the effectiveness of our learning approach both by providing theoretical guarantees, and by testing the approach on a variety of prototypical systems in various disciplines. These systems include homogeneous and heterogeneous agents systems, ranging from particle systems in fundamental physics to agent-based systems modeling opinion dynamics under the social influence, prey-predator dynamics, flocking and swarming, and phototaxis in cell dynamics. This talk is based on the joint work with Fei Lu, Mauro Maggioni and Ming Zhong.
  
• Some topic in sparse optimization

  Speaker: Ahmad Mousavi (UMBC) -
  

  When: Tue, November 27, 2018 - 2:00pm
  Where: Kirwan Hall 3206
  

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  Abstract: In this presentation, we first discuss the unfavorable performance (specifically, the quantitative characterization of solution) of \ell_p-recovery with p>1 in reconstructing sparse vectors. Next, we talk about solution uniqueness conditions of several important problems that involve convex piecewise affine function(s). By leveraging their max-formulation and convex analysis tools, we develop dual variables based necessary and sufficient uniqueness conditions via simple and yet unifying approaches. Finally, we discuss uniform recovery under a coordinate-projection admissible constraint set via a generalization of the orthogonal matching pursuit algorithm and its convergence condition.