A stratum of differentials is the moduli space of curves together with a meromorphic form with prescribed multiplicities of zeroes and poles. The strata are phase spaces of an action of SL(2,R) and thus the central object of study in Teichmueller dynamics. On the other hand, they give natural high codimension subvarieties of the moduli of curves with marked points. The strata are non-compact, and we determine the number of their ends, and discuss a viewpoint towards further homology computations. This uses an algebraic compactification of the strata. Based on a joint work with Ben Dozier.

Given an family of polarized abelian varieties, let $\mathcal{L}$ be a relatively ample line bundle, consider the family effective divisors on the fibers or equivalently the space of theta-functions induced by $\mathcal{L}$. Mumford-Welters work endowed this family with a flat projective connection which is realized via the heat equations. Hitchin's paper on {\em Flat connections and geometric quantizations, 1990} generalizes the above construction. Namely, for a complex simply connected Lie group $G$ and a surface $\Sigma$, the Hitchin connection is a flat projective connection on a vector bundle over $\mathcal{M}_g$, whose fiber over a compact Riemann surface $C$ ($\Sigma$ and a complex structure) is the space of holomorphic sections of natural line bundle $\mathcal{L}$ on the moduli space of principal $G$ bundles on $C$. Hitchin's work can be realized as an initial step in the direction of Witten's proposal of quantization of Chern-Simons theory via the method of geometric quantization. In this talk, we will discuss the construction of a Hitchin-type connection for the moduli of parabolic bundles. We will start with a more general framework of constructing connections from heat operators with a given symbol map due to van Geeman-de Jong. We will also identify our connection with the Wess-Zumino-Witten/Tsuchiya-Ueno-Yamada connection in conformal field theory generalizing a result of Laszlo. If time permits, we will make further comments on the abelian case. This is a joint work with Indranil Biswas and Richard Wentworth.

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Poroelasticity equations arise from many applications in geophysics and biomechanics, so numerical simulations of poroelasticity equations are of great interest. In this talk I discuss advanced finite element methods for poroelasticity and related problems. In the first part, I introduce parameter-robust discretization of poroelasticity and explain that efficient preconditioners can be obtained by the operator preconditioning approach. In the second part, I present hybridizable discontinuous Galerkin (HDG) methods for the problems that Stokes/Navier-Stokes equations and porous/poroelastic equations are coupled with interfaces. The talk is based on joint works with K.-A. Mardal (University of Oslo), M. E. Rognes (Simula Research Laboratory), A. Cesmelioglu (Oakland University) S. Rhebergen (University of Waterloo), and other collaborators.

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Let $X$ be a K3 surface. Consider a finitely supported probability measure $\mu$ on $\operatorname{Aut}(X)$ such that $\Gamma_{\mu} = \langle \operatorname{Supp}(\mu)\rangle < Aut(X)$ is non-elementary. We do not assume that $\Gamma_{\mu}$ contains any parabolic elements. We study and classify hyperbolic ergodic $\mu$-stationary probability measures on $X$.

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Hamiltonian systems have long been a cornerstone of classical mechanics, providing a powerful framework to describe and analyze the motion of physical systems. But what happens when these mathematical structures take flight? In this talk, we will explore how the geometric principles of Hamiltonian mechanics play a crucial role in the modeling and control of modern aerial vehicles, including drones. From symplectic structures and variational principles to optimal control and real-world applications, we will uncover the elegant mathematical tools that bridge fundamental physics with cutting-edge drone technology. Whether you're interested in geometry, control theory, or just fascinated by the math behind autonomous systems, this talk will offer a compelling journey from theory to application in the skies.

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