Date  SPEAKER and TITLE  Host 

September 7  Luigi De Rosa, University of Basel, Switzerland (Virtual) TITLE: Intermittency and lower dimensional dissipation in fluid dynamics ABSTRACT: In the context of incompressible fluids, there is a quite strong empirical evidence of a lower dimensional accumulation of energy dissipation in the infinite Reynolds number limit. This phenomenon is nowadays known as "intermittency" and it is intrinsically linked to nonhomogeneous regularity exponents observed in the velocity field. In this talk I will describe a couple of possible ways to put the study of intermittent flows in a rigorous mathematical setting. This builds on various refinements of the theory of divergence measure fields, together with different notions of dimensions. The main difference in the choice of the notion of dimension is the possibility to study dissipations which happen to concentrate on dense sets. 
Torres 
September 14  Thomas Schmidt, University of Hamburg (Virtual)
TITLE: Perimeter functionals with measure data ABSTRACT : The talk is concerned with perimeter functionals $\mathscr{P}_{\mu_+,\mu_}$ given by \[ \mathscr{P}_{\mu_+,\mu_}[A]:=\mathrm{P}(A)+\mu_+(A^1)\mu_(A^+) \] on measurable sets $A\subset{\mathbb R}^n$ of finite volume $A<\infty$ and finite perimeter $\mathrm{P}(A)<\infty$, where the fixed nonnegative Radon measures $\mu_\pm$ on $\mathds{R}^n$ are (necessarily) evaluated on a measuretheoretic interior $A^1$ and a measuretheoretic closure $A^+$ of $A$. It will be shown that various existence results for minimizers of the functional $\mathscr{P}_{\mu_+,\mu_}$ can be obtained under a new and optimal condition on $\mu_\pm$, called the smallvolume isoperimetric condition. Moreover, it will be illustrated at hand of exemplary configurations that this condition admits a wide class of $(n{}1)$dimensional measures and that it is decisive for lower semicontinuity with cancellationcompensation effects between the perimeter and measure terms. The longterm goal of these considerations is to extend the variational approach to prescribedmeancurvature boundaries $\partial A$ in the spirit of Caccioppoli, De Giorgi, Miranda, Massari from $\mathrm{L}^1$ mean curvature to mean curvature given by a possibly lowerdimensional signed measure. 
Torres 
September 21  Jay Bang, University of Texas at San Antonio
TITLE: Rigidity of Steady Solutions to the NavierStokes Equations in High Dimensions and its Applications ABSTRACT : Solutions with scalinginvariant bounds such as selfsimilar solutions, play an important role in the understanding of the regularity and asymptotic structures of solutions to the NavierStokes equations. I proved with collaborators that any steady solution satisfying $u(x)\leq C/x$ for any constant $C$ in $\mathbb{R}^n\setminus \{0\}$ with $n\geq 4$, must be zero. Our main idea is to analyze the velocity field and the total head pressure via weighted energy estimates with suitable multipliers. The proof is pretty elementary and short. We do not assume any smallness or selfsimilarity. By using a blowup method, this theorem also help to remove a class of singularities of solutions and give the optimal asymptotic behaviors of solutions at infinity in the exterior domains. This is a joint work with Changfeng Gui, Hao Liu, Yun Wang, and Chunjing Xie. 
Wang 
September 28  Theodore Drivas, Stony Brook University (Virtual)
TITLE: The FeynmanLagerstrom criterion for boundary layers ABSTRACT: We study the boundary layer theory for slightly viscous stationary flows forced by an imposed slip velocity at the boundary. According to the theory of Prandtl (1904) and Batchelor (1956), any Euler solution arising in this limit and consisting of a single ``eddy" must have constant vorticity. Feynman and Lagerstrom (1956) gave a procedure to select the value of this vorticity by demanding a necessary condition for the existence of a periodic Prandtl boundary layer description. We will show that this condition is also sufficient for the existence of a periodic boundary layer described by the Prandtl equations. 
Novack 
October 5  Yannick Sire, Johns Hopkins University
TITLE: Harmonic maps between singular spaces ABSTRACT : After reviewing briefly the classical theory of harmonic maps between smooth manifolds, I will describe some recent results related to harmonic maps with free boundary, emphasizing on two different approaches based on recent developments by Da Lio and Riviere. This latter approach allows in particular to give another formulation which is wellsuited for such maps between singular spaces. After the works of Gromov, Korevaar and Schoen, harmonic maps between singular spaces have been instrumental to investigate superrigidity in geometry. I will report on recent results where we introduce a new energy between singular spaces and prove a version of Takahashi’s theorem (related to minimal immersions by eigenfunctions) on RCD spaces  Wang 
October 12 (NO SEMINAR) 
TITLE: NO SEMINAR ABSTRACT: NO SEMINAR 

October 16, 1:302:30pm (SPECIAL TIME)  Stefania Patrizi, University of Texas at Austin TITLE: Derivation of the 1D GromaBalogh equations from the PeierlsNabarro model ABSTRACT : We consider a semilinear integrodifferential equation in dimension one associated to the half Laplacian whose solution represents the atom dislocation in a crystal. The equation comprises the evolutive version of the classical PeierlsNabarro model. We show that for a large number of dislocations, the solution, properly rescaled, converges to the solution of a fully nonlinear integrodifferential equation which is a model for the macroscopic crystal plasticity with density of dislocations. This leads to the formal derivation of the 1D GromaBalogh equations, a popular model describing the evolution of the density of parallel straight dislocation lines. One of the main difficulties is that we allow dislocations to have opposite orientation and so we have to deal with collisions of them. This is a joint work with Tharathep Sangsawang. 
Torres 
October 26  Zhiyuan Geng, Purdue University (Virtual)
TITLE: On the triple junction problem without symmetry hypotheses ABSTRACT: For the scalar twophase (elliptic) AllenCahn equation, there is a rich literature dedicated to a celebrated conjecture of DeGiorgi, which establishes a connection between the diffuse interface and minimal surfaces. However, for the case of three or more equally preferred phases, a vector order parameter is required. In this scenario, the structure of the diffuse interface is analogous to a singular minimal cone. These solutions are studied mostly under an assumption of equivariance of the potential and the solution. In this talk, I will present the joint work with Nicholas Alikakos on the AllenCahn equation with a potential vanishing at exactly three points (energy wells). Our work involves constructing a locally minimizing entire solution that possesses a triple junction structure. We estimate the location and size of the diffuse interface by utilizing an energy upper/lower bound. Additionally, we investigate the asymptotic behavior at infinity by examining the blowdown limit. We do not impose any symmetry hypothesis on the solution or potential. 
Wang 
November 2  Jincheng Yang, University of Chicago TITLE: Higher regularity and trace estimates for NavierStokes equation ABSTRACT : We derive several nonlinear a priori trace estimates for the 3D incompressible NavierStokes equation. They recover and extend the current picture of higher derivative estimates in the mixed norm. The main ingredient is the blowup method and a novel averaging operator, which could apply to PDEs with scaling invariance and quantitative onescale εregularity. 
Novack 
November 9  Andre Schlichting, University of Munster, Germany (Virtual) TITLE: Meanfield PDEs on graphs and their continuum limit ABSTRACT : This talk reviews some recent results on nonlocal PDEs describing the evolution of a density on graph structures. These equations can arise from meanfield interacting jump dynamics, but also from applications in the data science field, or they can also be obtained by a numerical discretization of a continuum problem. We also show how those equations are linked to their continuous counterpart in suitable local limits. Joint works with Antonio Esposito, Georg Heinze, Anastasiia Hraivoronska and Oliver Tse. 
Gao 
November 16  Matt Novack, Purdue University TITLE: Weak kinetic shock solutions to the Landau equation ABSTRACT : Compressible fluids are known to form shock waves, which can be represented by discontinuous solutions of the compressible Euler equations. However, physical shocks are actually continuous and in certain regimes can be represented by a smooth shock profile. In this talk, I will discuss a construction of weak shock profiles which solve the kinetic Landau equation. This is based on joint work with Dallas Albritton (Wisconsin) and Jacob Bedrossian (UCLA). 
Wang 
November 23  No Seminar (Thanksgiving Holiday) TITLE: ABSTRACT : 

November 30  Andrea Pinamonti, Universita di Trento, Italy (Virtual)
TITLE: Variational solutions to the $\infty$Poisson equation with respect to Hörmander vector fields ABSTRACT : In this talk we study the asymptotic behavior of solutions to the subelliptic $p$Poisson equation as $p\to +\infty$ in Carnot Carath\'eodory spaces. In particular, introducing a suitable notion of differentiability, we extend the celebrated result of Bhattacharya, DiBenedetto and Manfredi \cite{BDM} and we prove that limits of such solutions solve in the sense of viscosity a hybrid first and second order PDE involving the $\infty$Laplacian and the Eikonal equation. The talk is based on a joint paper with L. Capogna, G. Giovannardi and S. Verzellesi. 
Wang 