Prof. Juan Manfredi, Department of Mathematics, University of Pittburgh
Tuesday, November 12, 2024, 16:00
- 17:00
Building 1, Level 3, Room 3119
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Abstract

Harmonic functions in Euclidean space are characterized by the

Thursday, November 07, 2024, 12:00
- 13:00
Building 9, Level 2, Room 2325
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Geospatial health data are essential to inform public health and policy. These data can be used to understand geographic and temporal patterns, identify risk factors, measure inequalities, and quickly detect outbreaks.
Prof. Alessandro Astolfi, Electronic Engineering, University of Rome Tor Vergata
Wednesday, November 06, 2024, 12:00
- 13:00
Auditorium between Building 2&3
The interplay between Pontryagin’s Minimum Principle and Bellman’s Principle of Optimality is exploited to revisit optimal control problems.
Prof. Antti Hannukainen, Aalto University
Tuesday, November 05, 2024, 16:00
- 17:00
Building 1, Level 3, Room 3119
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In this talk, I consider solving parametric generalized eigenvalue problem using model order reduction techniques.
Prof. Lawrence Craig Evans, Mathematics at the University of California, Berkeley
Tuesday, November 05, 2024, 14:00
- 15:00
Between Buildings 2 and 3, Auditorium 0215
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This will be an expository lecture, surveying many important methods for passing to limits for solutions of various nonlinear PDE. I will illustrate several of these techniques as applied to some simple examples, and discuss also many open problems.
Clarissa Astuto, Junior Assistant Professor, Department of Mathematics and Computational Science, University of Catania, Italy
Monday, November 04, 2024, 14:00
- 15:00
Building 1, Level 3, Room 3119
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In this talk we propose and validate a multiscale model for a Poisson-Nernst-Planck (PNP) system, focusing on the correlated motion of positive and negative ions under the influence of a (potentially vibrating) trap.
Sunday, November 03, 2024, 09:00
- 12:00
Building 2, Level 5, Room 5220
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This intensive series of short courses will bridge the theoretical foundations of nonlinear partial differential equations (PDEs) with real-world applications. Renowned speakers include Lawrence Craig Evans (UC Berkeley), Italo Capuzzo-Dolcetta (Rome), and Jose Carrillo (Oxford). Topics covered will include viscosity solutions, Hamilton-Jacobi equations, mean field games, kinetic theory, models of collective behavior, and regularity theory for elliptic and parabolic PDEs.
Thursday, October 31, 2024, 12:00
- 13:00
Building 9, Level 2, Room 2325
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Multiphysics and coupled problems, such as fluid-structure interactions and multiphase flows, are described by partial differential equations of different nature or with discontinuous coefficients. The computational domain is partitioned into several regions, which may evolve in time.
Prof. Giuseppe Di Fazio, University of Catania
Tuesday, October 29, 2024, 16:00
- 17:00
Building 1, Level 3, Room 3119
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We will review regularity results for linear and quasilinear uniformly elliptic equations. Focus is on the minimal assumptions we need to obtain a given degree of smoothness for generalized solutions of a given elliptic equation.
Simone Ciani, Researcher, University of Bologna
Thursday, October 24, 2024, 14:00
- 15:00
Building 1, Level 3, Room 3119
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Non-Newtonian fluids exhibit diverse and very interesting behaviors. In this talk, we will focus on power-like stress tensors, mainly addressing p-Laplacian-type scalar equations. What distinguishes singular and degenerate equations from the point of view of the properties enjoyed by their solutions? We will address this classic question and discuss the state of the art in the context of a more general non-Newtonian operator that interests only each coordinate direction with preferred diffusion and, for this reason, inherited the epithet anisotropic.
Dr. Anastasia Molchanova, TU Wien
Tuesday, October 22, 2024, 16:00
- 17:00
Building 1, Level 3, Room 3119
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Sobolev homeomorphisms play a fundamental role in geometric function theory, calculus of variations, and continuum mechanics.
Anastasia Molchanova, Postdoctoral Fellow, Institute of Analysis and Scientific Computing, TU Wien
Monday, October 21, 2024, 16:00
- 17:00
Building 9, Level 3, Room 3120
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In this talk, we discuss the weak limits of Sobolev homeomorphisms and their injectivity properties. We show that these mappings are almost everywhere injective when the Sobolev exponent p>n−1.
Thursday, October 17, 2024, 12:00
- 13:00
Building 9, Level 2, Room 2325
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We present a doubly enriched finite volume method for precisely computing highly dynamic fluid-particle interaction. This involves forces beeing exchanged between the particles and the fluid at the interface. In an earlier work we derived a monolithic scheme which includes the interaction forces and rigied-body motions into the Navier-Stokes equations by extending the test space. In highly dynamic particle-fluid interaction cases, pressure oscillations are a common issue.
Thursday, October 10, 2024, 12:00
- 13:00
Building 9, Level 2, Room 2325
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Non-convex Machine Learning problems typically do not adhere to the standard smoothness assumption. Based on empirical findings a more realistic generalized smoothness assumption was proposed, though it remains largely unexplored. Many existing algorithms designed for standard smooth problems need to be revised. In this paper we propose and analyze new Federated Learning methods with local steps, partial participation of clients, and Random Reshuffling without extra restrictive assumptions beyond generalized smoothness. Our theory is consistent with the known results for standard smooth problems, and our experimental results support the theoretical insights.
Thursday, October 03, 2024, 12:00
- 13:00
Building 9, Level 2, Room 2325
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This presentation explores mean field games (MFGs) through the lens of functional analysis, focusing on the role of monotonicity methods in understanding their properties and deriving solutions. We begin by introducing MFGs as models for large populations of interacting rational agents, illustrating their derivation for deterministic problems. We then examine key questions of the existence and uniqueness of MFG solutions.
Prof. Diego Marcon Farias, Universidade Federal do Rio Grande do Sul
Tuesday, October 01, 2024, 16:00
- 17:00
Building 1, Level 3, Room 3119
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In this talk, we explore the Lagrangian structure of relativistic Vlasov systems, including the relativistic Vlasov-Poisson equation and the quasi-electrostatic limit of the relativistic Vlasov-Maxwell equations.
Thursday, September 26, 2024, 12:00
- 13:00
Building 9, Level 2, Room 2325
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Traditional Topological Data Analysis (TDA) methods, such as Persistent Homology (PH), rely on distance measures (e.g., cross-correlation, partial correlation, coherence, and partial coherence) that are symmetric by definition. While useful for studying topological patterns in functional brain connectivity, the main limitation of these methods is their inability to capture the directional dynamics - which is crucial for understanding effective brain connectivity.
Tuesday, September 24, 2024, 16:00
- 17:00
Building 1, Level 3, Room 3119
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We consider the problem of how efficiently shallow neural networks with the ReLUk activation function and 𝑁 neurons can approximate functions from Sobolev spaces 𝑊𝑠(𝐿𝑝(Ω)) with error measured in the 𝐿𝑞(Ω)-norm.
Thursday, September 19, 2024, 12:00
- 13:00
Building 9, Level 2, Room 2325
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Free boundary problems emerge naturally in mathematical models representing physical, biological, or financial phenomena, such as ice melting, population dynamics, or stock market behavior. These problems involve solving partial differential equations for both an unknown function and an unknown domain. This talk will explore several free boundary problems and different methods to address them.
Thursday, September 12, 2024, 12:00
- 13:00
Building 9, Level 2, Room 2325
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Second-order partial differential equations (PDEs) are traditionally classified as being parabolic, elliptic, or hyperbolic in nature, and this classification largely determines the kind of analytical and numerical techniques that can be successfully applied to them.