AAM Seminar

Typically the AAM Seminar runs Wednesdays at 2:30pm. Here is the latest schedule:

Fall 2024

• August 28, 2:30pm: Dr. Alex McDonald, KSU
  
  
  • Title: Prescribed projections and efficient coverings of sets by curves
  • Abstract: A remarkable result of Davies shows that an arbitrary measurable set in the plane can be covered by lines in such a way that the union of the lines minus the original set has measure zero. This theorem has an equivalent dual formulation which says that one can find a single set in the plane with given "prescribed" projections in almost every direction, up to measure zero errors. We extend these results to a non-linear setting and prove that a set in the plane can be covered efficiently by translates of a single curve satisfying a mild curvature assumption.
    
    
• September 4, 2:30pm: Dr. Emanuel Indrei, KSU
  
  
  • Title: On the equilibrium shape of a crystal
  • Abstract:  Minimizing the free energy under a mass constraint may generate a convex crystal in n−dimensions subject to assumptions on the potential. The problem attributed to Almgren is to understand if this is the case assuming g is convex or more generally if sub-level sets are convex. My talk will address this problem.
     
• September 25, 2:30pm: Dr. Henry Lamm, Fermilab
  
  
  • Title: Groups, Rings, and Hadrons
  • Abstract:  The advent of quantum computation provides an opportunity to solve new problems in theoretical physics. Taking advantage of this new hardware requires efficiently formulating quantum field theories as well as approximating and compiling arbitrary unitary gates from a small set of gates that can be prepared precisely on qubit or qudit devices.  In this talk, I will discuss how algebraic structures arise as a necessary component to running quantum computers, and some outstanding problems related to them.
    
    
• October 2, 1:15pm: Dr. Fumihiko Onoue, TU Munich
  
  
  • Title: Liquid drop model with nonlocal surface tension
  • Abstract:  George Gamow introduced the liquid drop model of the atomic nucleus in 1928 to explain the behaviour of atoms. The classical model is more or less well-studied today, for instance, by Knuepfer and Muratov. In this talk, we extend this model into the so-called nonlocal liquid drop model with ''nonlocal'' surface tension. We also see some geometric aspects of this nonlocal model.
    
    
• October 23, 2:30pm: Mark van den Bosch, Leiden University
  
  • Title: Multidimensional Stability of Planar Travelling Waves for Stochastically Perturbed Reaction-Diffusion Systems
  • Abstract:

     Travelling pulses and waves are a rich subset of feasible patterns in reaction-diffusion systems. Many have investigated their existence, stability, and other properties, but what happens if the deterministic dynamics is affected by random occurrences? How does the interplay between diffusion and noise influence the velocity, curvature, and stability of multidimensional patterns?

    We consider reaction-diffusion systems with multiplicative noise on a spatial domain of dimension two or higher. The noise process is white in time, coloured in space, and invariant under translations; based on applications. Inspired by previous works on the real line, we establish the multidimensional stability of planar waves on a cylindrical domain on time scales that are exponentially long with respect to the noise strength. In the deterministic setting, multidimensional stability of planar waves on the whole space has been obtained, and we show to what extend we can do this in the stochastic case.

    The metastability result above is achieved by means of a stochastic phase tracking mechanism that can be maintained over such long-time scales. The corresponding mild formulation of our problem features stochastic integrals with respect to anticipating integrands, which hence cannot be understood within the well-established setting of Itô-integrals. To circumvent this problem, we exploit and extend recently developed theory concerning forward integrals.
    
    

• November 13, 2:30pm: Rik Westdorp, Leiden University
  
  
  • Title: Stochastic Soliton Dynamics in the Korteweg-De Vries Equation with Multiplicative
    Noise
  • Abstract: In recent years, stochastic traveling waves have become a major area of interest in the field of stochastic PDEs. Various approaches have been introduced to study the effects of noise on traveling waves, mainly in the setting of Reaction-Diffusion equations. Of particular interest is the notion of a stochastic wave position and its dynamics. This talk focuses on solitary waves in the Korteweg-de Vries equation. Due to a scaling symmetry, this dispersive PDE supports a solitary wave family of various amplitudes and velocities. We introduce stochastic processes that track the amplitude and position of solitons under the influence of multiplicative noise over long time-scales. Our method is based on a rescaled frame and stability properties of the solitary waves. We formula expansions for the stochastic soliton amplitude and position, and compare their leading-order dynamics with numerical simulations. This is joint work with Prof. H. J. Hupkes. 
    
    
• November 20, 2:30pm: Dr. Thialita M. Nascimento, Iowa State
  
  
  • Title: Geometric estimates in Degenerate/Singular elliptic equations
  • Abstract: We obtain higher order regularity estimates for degenerate/singular elliptic equations in regions where the behavior of the solution is initially unknown. This is achieved via a geometric approach which is rooted in free boundary problems techniques.