Seminários

Linear wave propagation in complex environments can be described in the framework of normal modes theory. This representation of wavefields leads to systems of coupled equations for mode amplitudes.  Within the one-way approximation the amplitudes satisfy so-called pseudo-differential parabolic equations (PDPEs) involving square roots of certain differential operators. Existence, uniqueness and well-posedness results for such equations are established.
 

PDPEs for mode amplitudes can be efficiently solved using such techniques as the split-step Padé algorithm. Related numerical methods suitable for addressing real-world scenarios are considered (including source representation and artificial domain truncation). Applications of these methods to marine noise quantification and to mitigation of its environmental impact are discussed. The results of shipping noise and seismic survey signals simulation are presented.

In this talk, our main goal will be showing how a 200-year-old object—the Fourier transform—continues to shape modern mathematics. We will start our exploration with the timeless “uncertainty” at the heart of signal processing, then travel through its time-frequency avatar (the Short-Time Fourier Transform) and finally land on an unexpected connection to isoperimetry and calculus of variations. Along the way, we shall see how the same Fourier concepts that help us describe subatomic behavior of matter can also make us hear and see better, connecting both theoretical and practical landscapes and shaping modern analysis.

We study compact free boundary minimal submanifolds in spherical caps $\mathbb{B}^r$ and their geometric spectral properties. Following the foundational work of Fraser-Schoen, Lima-Menezes established the connection between free boundary minimal surfaces in spherical caps and spectral geometry. In this work, we present three main contributions: (1) We prove that any free boundary minimal Möbius band in $\mathbb{B}^r$ immersed by first Steklov eigenfunctions must be intrinsically rotationally symmetric; (2) We explicitly construct such a Möbius band in $\mathbb{B}^4$($r$) for $0<r<\frac{\pi}{2}$; and (3) We generalize Morse index estimates for free boundary minimal submanifolds in spherical caps, showing that non totally geodesic immersions have index at least $n$

Implicit neural representations (INRs) have emerged as a promising method for encoding low-dimensional signals (common in visual computing pipelines, such as implicit surfaces and radiance fields) into the parameters of neural networks. These parameters are implicitly optimized through a loss function that, in addition to enforcing data constraints, can incorporate differential properties of the signal to regularize training. In this talk, we will present an overview of the INR research being developed at the Visgraf Lab, covering applications, architectures, loss functions, and sampling strategies for the effective training of INRs.

The Eliashberg principle asserts that any obstruction to symplectic embeddings (beyond volume) must arise from J-holomorphic curves. In this talk, we demonstrate how Embedded Contact Homology (ECH)—a Floer-type homology theory—can be used to detect such curves in symplectic cobordisms. As an application, we compute the Gromov width of the cotangent disk bundle $D^*$$K$ of the Klein bottle $K$, endowed with its flat metric.

A space of matrices of constant rank is a vector subspace V, say of dimension n+1, ofthe set of matrices of size axb over a field k, such that any nonzero element of V has fixed rank r. It is a classical problem to look for different ways to construct such spaces of matrices. In this talk I will give an introduction up to the state of the art of the topic, and report on my latest joint project with D. Faenzi and D. Fratila, where we give a classification of all spaces of matrices of constant corank one associated to irreducible representation of a reductive group.